Integrated supply chain
network design models for
vaccines: a literature
review
Lemmens S, Decouttere C, Vandaele N, Bernuzzi M.
KBI_1414
Integrated supply chain network design models for
vaccines: A literature review
Stef Lemmensa,∗, Catherine Decoutterea , Nico Vandaelea , Mauro Bernuzzib
a Research
Center for Operations Management and Department of Decision Sciences and
Information Management, KU Leuven, Naamsestraat 69, 3000 Leuven, Belgium
b GlaxoSmithKline Vaccines, Avenue Fleming 20, 1300 Waver, Belgium
Abstract
This paper reviews the relevant literature for designing a vaccine supply chain.
We show that vaccines are not like commodities and introduce the typical characteristics of a vaccine supply chain. We study the decisions at strategic, tactical
and operational levels that are integrated in the research field on supply chain
network design. We provide an overview of how uncertainty is incorporated in
the reviewed literature by distinguishing strategic uncertainty and operational
variability. Our future vaccine supply chain network needs to be sustainable,
hereby taking the preferences of different stakeholders into account for obtaining a set of economical, technological and value key performance indicators that
need to be satisfied by the design. This review emphasizes the need of these
three types of performance criteria and shows the criteria that are described
in the literature. Finally, we identify the most frequently used modeling and
solution techniques and discuss the real-life applicability of the research up to
now.
Keywords: Vaccine Supply Chain, Supply Chain Network Design, Supply
Chain Integration, Literature Review, Multi-Criteria Decision Making,
Stakeholder Approach
∗ Corresponding
author
Email addresses: [email protected] (Stef Lemmens),
[email protected] (Catherine Decouttere), [email protected]
(Nico Vandaele), [email protected] (Mauro Bernuzzi)
1. Introduction
Companies all over the world are confronted with designing and redesigning their supply chain. A typical supply chain consists of the following levels:
suppliers, plants, distribution centers and customer markets. The location of
Distribution Centers (DC’s) is, for example, an expensive and an almost irreversible long-term, strategic decision that can be tackled with Supply Chain
Network Design (SCND). However, tactical and operational levels decisions are
often taken into account when addressing SCND issues: the material flow and
order quantity between consecutive supply chain stages depend on the network
design. The complexity of supply chain design increases with the number of
stages, products and integrated decision levels. The importance of integrating these decision levels can hardly be overestimated. Production capacities
and inventory decisions regarding the determination of the size and location of
the different stock levels can be, for example, taken into consideration when
addressing strategic network design issues.
The aim of this literature review is twofold. We provide an updated overview
on integrated SCND and we study the issues for the design of a supply chain
network for a peculiar pharmaceutical product: vaccines. Vaccines are not ordinary commodities and concern the human race. They reduce the worldwide
disease burden of many infectious diseases. The methods of distribution are
country dependent and affected by national vaccination policies. Smith et al.
[126] distinguish three types of vaccine procurement: (1) non-governmental organizations, (2) private markets and (3) tenders. Recently, the World Health
Organization (WHO) announced that the public health is threatened by a unexpected surge of polio [4]. These three types of vaccine procurement and unexpected surges in disease dynamics complicate the vaccine demand forecasting
to a large extent. The total production lead time of vaccines varies between
9 and 22 months [3] which makes it even more difficult to balance supply and
demand. These long lead times are due to the permanent quality control and
quality assurance. The perishability of vaccines requires cold chain management
2
to ensure a safe vaccination for the entire world population. Zaffran et al. [159]
emphasize the strategic importance of choosing the right cold chain equipment:
this choice influences the delivery routes and shipment frequency of the vaccines.
Furthermore, the high inventory value and the short shelf-life of the vaccines
complicate the inventory management.
SCND has been studied widely in the last few decades. Schmidt and Wilhelm
[116] provide an extensive definition of the operational, tactical and strategic
decision levels. They classify the reviewed literature according to these decision
levels and discuss modeling issues in the remainder of their work. The authors
agree that these three decision levels interact and that a unified approach is
necessary for designing a competitive global supply chain.
We searched the databases Web of Science, PubMed and SCIRIUS for relevant review articles on integrated SCND and discovered three classes of nonexclusive integrated SCND models: (1) location-allocation, (2) inventory-location
and (3) production-distribution models. We extended the current state-of-artliterature by checking the manuscripts that were cited by these review articles.
Literature reveals that a large variety of journals contribute to the research
area of integrated SCND. We also explored two closely related research fields:
humanitarian aid distribution and reverse logistics design.
1. Location-allocation models. Cooper [27] presents one of the very first
facility location-allocation problems. The objective is to decide the location of
the warehouses and the allocation of the customer demand to these warehouses.
These location-allocation models have also been extensively applied in health
care settings. Daskin and Dean [30] review three basic facility location models:
the set covering model, the maximal covering model and the p-median model. A
demand node is said to be covered if the distance between the facility and the demand node is less than or equal to some exogenously specified coverage distance.
The authors also classify existing location literature into three areas for locating
health care facilities: accessibility models, adaptability models and availability
models. Rahman and Smith [109] review the use of location-allocation models
in health service development planning in the developing nations. They mention
3
the problem of the huge number of children which get blinded or crippled each
year, most of them as a result of polio, in developing countries. For this disease,
effective vaccines are available and the location decision of health services is
crucial. The location-allocation models and methods reviewed in their paper
are formulated either as p-median problems or covering problems. More general reviews of facility location-allocation models are published by Scott [117],
Beaumont [17] and Narula [92].
2. Inventory-location models. Shen [123] offers a review of integrated
supply chain design models. He mainly targets three types of integrated decision making models: (1) location-routing models, (2) inventory-routing models
and (3) location-inventory models. The routing decision refers to the vehicle
routing problem, which is NP-hard. We are particularly interested in the characteristics of the inventory-location models for our future research. The author
also provides mathematical formulations of a selected number of papers.
3. Production-distribution models. A recent review of Fahimnia et al.
[42] presents an overview of integrated production-distribution models. They
classify these models based on their degree of complexity. This degree of complexity is described by the number of products, plants, warehouses, end users,
transport paths and time periods. In the remainder of their paper, Fahiminia
et al. [42] reclassify the papers into four groups according to the used solution
techniques: (1) mathematical techniques, (2) heuristic techniques, (3) simulation modeling and (4) genetic algorithms. Our classification approach will also
focus on the use of multiple perspectives.
Mula et al. [89] review mathematical programming models for supply chain
production and distribution planning. They classify the literature based on the
following elements: supply chain structure, decision level, modeling approach,
purpose, shared information, limitations, novelty and application. An overview
of academic work on integrated analysis of production and distribution systems
is written by Sarmiento and Nagi [115]. They review papers that explicitly
consider the transportation system in their analysis. The authors also mention whether the work concerns designing the distribution system or concerns
4
optimization problems for a provided distribution system. We are particularly
interested in the consideration of the distribution decision at the strategic level.
Meixell and Gargeya [84] review decision support models for the design of
global supply chains. They include the following four review dimensions: (1)
decisions addressed in the model, (2) performance metrics, (3) the degree to
which the model supports integrated decision processes and (4) globalization
considerations. One of the conclusions of Meixell and Gargeya [84] is that the
performance measures used in global supply chain models need to be broadened
in definition to address alternative objectives. We will tackle this issue later in
this article. Other review papers on integrated production-distribution models with an emphasis on globalization are written by Vidal and Goetschalckx
[145] and by Goetschalckx et al [49]. Both papers classify the reviewed literature according to the model characteristics. A similar approach is part of our
classification process.
The remainder of this paper is organized as follows. Section 2 proposes the
different classification criteria used in our literature review. Section 3 classifies
the reviewed literature based on the model characteristics of the supply chain
network. An overview of uncertainty incorporation in SCND is discussed in
Section 4. We offer an overview of the performance measures of a supply chain
in Section 5 and we reclassify the articles on the basis of the research methodologies used in Section 6. The real-life applicability of the reviewed papers
will be discussed in Section 7. Finally, Section 8 concludes and identifies the
implications for further research.
2. Organization of the review
Researchers frequently differentiate between location-allocation, inventorylocation and production-distribution models. Our first classification opts for a
differentiation of the models based on the system characteristics and decisions involved. However, the three distinguished classification groups are non-exclusive
(Section 3).
5
A major difficulty for designing a supply chain is the incorporation of uncertainty. We distinguish between vaccine demand and supply uncertainty. We
previously mentioned three vaccine demand types which complicate the forecasting. The supply of vaccines is characterized by highly uncertain manufacturing
lead times, throughput and inventory levels in the supply chain. These uncertainties are ignored in a deterministic supply chain design approach. We will
present how stochastic supply chain design approaches deal with these uncertainties (Section 4).
Current literature often proposes one or more performance criteria of the
supply chain and subsequently models these measures as objective functions of
a mathematical model while taking network characteristics at strategic, tactical
and operational levels into account. Despite of the fact that minimizing the cost
is the most popular objective function of a supply chain network, additional Key
Performance Indicators (KPI’s) are required for measuring the performance of
the vaccine supply chain. Decouttere and Vandaele [33] present a broader view
on health care system design. The authors emphasize that the implementation
of a newly designed system can suffer because not all the important stakeholders
were involved in the design phase. Three types of KPI’s are distinguished for
the design of a nuclear magnetic resonance scanning unit from a stakeholders
viewpoint: economies, values and technology. Our work reviews the different
SCND performance metrics according to this classification and discusses the
performance measures needed for designing a vaccine supply chain in detail
(Section 5).
Most of the SCND problems are formulated and studied as mathematical
programming problems. Taking more than one performance measure into account often leads to a multi-objective optimization problem. Decomposition
methods, the epsilon constraint method and evolutionary algorithms are commonly used solution approaches. We reclassify the existing literature according
to the modeling and optimization approach (Section 6).
We also provide information on the applicability of previous research. This
implies that the real-life applicability and scalability of the developed models
6
will be discussed for the vaccine industry. We report information about the
testing data and implemention of the research (Section 7).
Each section consists of the description of the field terminology, the categorization of the manuscripts and the illustration of the relevance for the vaccine
industry. Pooling all the previous sections will indicate the available and missing
building blocks for the future design of a vaccine supply chain (Section 8).
3. Network characteristics
This section classifies the existing literature related to SCND based on network characteristics. In our search process, we found a wide range of different
supply chain network assumptions and decisions. Our goal is not to provide
an exhaustive overview of all the manuscripts on SCND, but to present which
complexities are yet integrated in the design of a supply chain network and are
useful for our future research. We review models classified as location-allocation,
inventory-location or production-distribution models and identify missing building blocks for our future work. Table 1 shows an overview of the most common
decisions that are integrated in SCND based on the proposed decision variables.
We make a distinction between strategic, tactical and operational levels decisions. The strategic decisions, also called network configuration decisions, are
often modeled with binary decision variables. The location decision refers to
locating a plant and/or DC and the allocation decision refers to the sourcing
decision of a retailer, DC or plant by the next supply chain actor. The tactical
level decisions include the quantities of products to be distributed between the
successive supply chain stages and the selection of the appropriate transportation mode, the choice of the available capacities at the plants and/or DC’s,
the allocation and/or the number of products to stocked and produced and
the (production) technology selection. The operational level decisions include
production scheduling and order quantity decisions. Table 1 emphasizes the
strategic focus of SCND. Our future research will take the relevant decisions
across these three levels into account which are of strategic relevance for SCND
7
in the vaccine industry. The different decisions shown in Table 1 will be further
clarified in the remainder of this section.
3.1. Location-allocation models
Facility location problem. The classical Uncapacitated Facility Location
Problem (UFLP) minimizes the sum of the costs of locating facilities at a set of
candidate locations and the transportation costs from the facilities to the customers. The customer demand needs to be satisfied. A capacity to the customer
demand that can be satisfied by the potential facilities can be added. The Capacitated Facility Location Problem (CFLP) is a classical location problem and
forms the basis of many of the location models that have been used in supply
chain design.
Health care services. Location-allocation models have been used extensively for quantitative analysis in health services for increasing demand coverage.
Verter and Lapierre [144], Gu et al. [55] and Shariff et al. [122] present mathematical programming formulations to locate facilities for health care services
like immunization. These papers maximize the participation of the residents
of population centers based on their travel distances. However, no economical
criteria are considered by these papers.
Multiple criteria. Pappis and Karacapilidis [103] consider a locationallocation model with an economical and a service level criterion. Their proposed method to locate DC’s assumes a distance limit between distribution
centers and customers and relates this limit to the service level of the organization. Lee et al. [73] argue that the cost minimization models are not
appropriate for location-allocation problems. Cost remains an essential consideration, but social, psychological and public safety oriented noneconomic criteria
need also to be taken into account. The authors advocate a more comprehensive approach to analyze various multiple and often conflicting objectives in
the location-allocation problem. Eight goals are modeled, based on priorities,
with an integer goal programming formulation. They take the quality of life,
a qualitative factor, into account for a plant location decision by obtaining a
8
Table 1: Classification according to network decisions
Reference
First
Year
Strategic level
Tactical level
Operational level
Author
Plant/facility
Allocation
location
Product
Transportation
Plant/facility
Production
Inventory
Technology
flow
mode
capacity
level
level
selection
9
[27]
Cooper
1963
X
[26]
Church
1974
X
[73]
Lee
1981
X
[103]
Pappis
1994
X
[31]
Daskin
1997
X
[66]
Jayaraman
1998
X
[93]
Nozick
1998
X
X
[13]
Badri
1999
X
X
[40]
Erlebacher
2000
X
X
X
[113]
Sabri
2000
X
X
X
[94]
Nozick
2001
X
X
[95]
Nozick
2001
X
X
[141]
Tsiakis
2001
X
X
[144]
Verter
2002
X
X
[67]
Jayaraman
2003
X
X
[124]
Shen
2003
X
X
[56]
Guillen
2005
X
[125]
Shen
2005
X
X
[127]
Snyder
2005
X
X
[6]
Altimarpak
2006
X
X
[22]
Chen
2006
X
X
[136]
Tanonkou
2006
X
X
[41]
Eskigun
2007
X
X
[76]
Lieckens
2007
X
[108]
Qi
2007
X
[128]
Snyder
2007
X
X
[130]
Sourirajan
2007
X
X
[142]
Tzeng
2007
X
[146]
Vidyarthi
2007
X
X
X
[153]
You
2007
X
X
X
[162]
Zhou
2007
X
Scheduling
Order quantity
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
(continued on next page)
Table 1: Classification according to network decisions
Reference
First
Year
Strategic level
Tactical level
Operational level
Author
Plant/facility
Product
Transportation
Plant/facility
Production
Inventory
Technology
location
Allocation
flow
mode
capacity
level
level
selection
[12]
Azaron
2008
X
X
[36]
Du
2008
X
X
[37]
Elhedhli
2008
X
X
[63]
Hinojosa
2008
X
X
[87]
Miranda
2008
X
X
[98]
Ozsen
2008
X
X
[140]
Tsiakis
2008
X
X
[155]
You
2008
X
X
[154]
You
2008
X
[47]
Gebennini
2009
X
[57]
Guillén-
2009
X
X
Scheduling
Order quantity
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Gosálbez
10
[62]
Hammami
2009
X
[99]
Ozsen
2009
X
X
X
[129]
Sourirajan
2009
X
X
[147]
Vitoriano
2009
[34]
Demirel
2010
X
[45]
Franca
2010
X
[55]
Gu
2010
X
[78]
Lim
2010
X
X
[101]
Paksoy
2010
[104]
Park
2010
X
X
[107]
Pishvaee
2010
X
X
[106]
Pishvaee
2010
X
X
[138]
Tiwari
2010
X
[151]
Yao
2010
X
X
[156]
You
2010
X
X
[21]
Cardona-
2011
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Valdés
[79]
Lin
2011
[80]
Longinidis
2011
X
X
(continued on next page)
Table 1: Classification according to network decisions
Reference
First
Year
Strategic level
Tactical level
Operational level
Author
Plant/facility
Allocation
location
[97]
Ortuño
2011
[139]
Torres-
2011
Product
Transportation
Plant/facility
Production
Inventory
Technology
flow
mode
capacity
level
level
selection
Scheduling
Order quantity
X
X
X
Soto
11
[148]
Vitoriano
2011
[149]
Wang
2011
X
X
[152]
Yazdian
2011
X
[157]
You
2011
X
X
[18]
Berman
2012
X
X
[38]
Elhedhli
2012
X
X
[48]
Ghaderi
2012
X
X
[77]
Lieckens
2012
X
X
[85]
Melo
2012
X
X
[96]
Olivares-
2012
X
X
X
X
X
X
X
X
X
X
X
X
X
Benitez
[100]
Paksoy
2012
[114]
Sadjady
2012
X
X
[122]
Shariff
2012
X
X
[134]
Tancrez
2012
X
[82]
Madadi
2012
X
[5]
Ahmadi-
2013
X
X
X
X
X
X
Javid
[59]
Hamedani
2013
X
X
X
X
X
[60]
Hamedani
2013
X
X
X
X
X
[71]
Kumar
2013
X
X
X
[88]
Mousavi
2013
X
[91]
Naimi
2013
X
[110]
Rajabalipour
2013
X
X
X
X
X
Cheshmehgaz
[120]
Shankar
2013
X
[121]
Shankar
2013
X
X
X
(continued on next page)
Table 1: Classification according to network decisions
Reference
First
Year
Strategic level
Tactical level
Operational level
Author
Plant/facility
Allocation
location
Product
Transportation
Plant/facility
Production
Inventory
Technology
flow
mode
capacity
level
level
selection
[137]
Teimuory
2013
X
X
X
[143]
Vahdani
2013
X
X
X
[43]
Firoozi
2013
X
X
[70]
Kristianto
2014
[23]
Chen
2014
Scheduling
Order quantity
X
X
X
X
X
12
quality of life index for every potential location from published studies. Badri
[13] combines the analytical hierarchy process and goal programming approach
to model a similar problem with conflicting criteria. For detailed information
about the analytical hierarchy process and goal programming, see Zahedi [160]
and Lee [72] respectively. Current et al. [28] published a review which classifies manuscripts regarding multi-objective analysis of facility location decisions
in four categories based on the modeled criteria: cost minimization, demand
oriented, profit maximization and environmental concern. They concluded that
environmental issues (air quality, quality of life and the surrounding population)
are rarely addressed in location-allocation decisions. Shankar et al. [120] present
a multi-objective location-allocation decision model for a multi-echelon supply
chain network. The total supply chain costs are minimized and the fill rate, defined as the total quantity shipped to the customer divided by the total customer
demand, is maximized. The same authors [121] present a non-dominated sorting algorithm for a similar mathematical program formulation of this problem.
The manuscript of Yazdiana et al. [152] proposes a multi-objective possibilistic approach for locating DC’s and allocating customer demands. Their first
objective function also minimizes the total supply chain costs and the second
objective function minimizes the total risk in the network. This risk consists of
three components: the risks associated with locating DC’s, the risk of shipping
products from plants to DC’s, and the risk of distributing products from DC’s
to customers. Risk of each potential DC location is associated with natural disasters and the risk related to the arcs imply inherent risk in the transportation
of products. These risks are considered as fuzzy numbers. In general, fuzzy
decision making methods are able to use an opinion in a form of linguistic terms
to provide estimations for uncertain parameters. The authors use a compromise
programming method to solve the proposed model.
3.2. Inventory-location models
Inventory costs. Most of the location-allocation models ignore the inventory impacts of facility location decisions. The classical facility location
13
problems mainly deal with the trade-off between facility costs and transportation costs. Erlebacher and Meller [40] recognize that inventory costs should
be considered together with other facility operation and transportation costs
in determining the optimal number of distribution centers and their locations.
The authors define a inventory-location problem as a location-allocation problem where inventory costs are also considered. The problem is formulated as a
mathematical programming model with a nonlinear objective function.
Inventory integration. Nozick and Turnquist [93] illustrate a method to
integrate inventory costs into the estimated fixed-charge coefficient of the facility location model. The authors assume that a replacement order is executed
immediately at the DC when an item is demanded at a retail outlet. The performance measures for a single DC are modeled as a M/G/s queue with a Poisson
arrival rate and a general service time distribution which is the delivery time of
a product from the single plant to the DC once an order is placed. The probability of waiting, a stock-out, is approximately derived to compute the minimum
inventory necessary at a DC for the specified stock-out rate. The total safety
stock requirement is subsequently approximated as a function of the number of
DC’s by a linear function. It is also assumed that the total expected demand
is allocated equally across the DC’s. The authors show how the inventory costs
are integrated in the fixed-charge coefficient of, for example, the fixed charge
facility location model of Daskin [29]. The same authors [94] extend this model
by adapting the objective function such that the model deals with providing a
high level of customer responsiveness in the system. This is done by minimizing the uncovered demand. The model formulation facilitates the integration
of coverage maximization and cost minimization. Nozick and Turnquist [95]
extend their method to a multi-product environment where also the decision
which products should be stocked at the DC’s and at the plant, needs to be
made. A tighter integration of the inventory and location decisions is presented
by the joint location-inventory model of Shen et al. [124]. The problem is described as follows: given a collection of retailers, each with uncertain product
demand, determine how many DC’s to locate, where to locate them, which re14
tailers to assign to each DC, how often to reorder at the distribution center,
and what level of safety stock to maintain to minimize total location, shipment,
and inventory costs, while ensuring a specified level of service. This problem is
also known as the Location-allocation Model with Risk Pooling (LMRP) and is
reformulated as a set-covering problem.
Risk pooling. Risk pooling benefits are inventory cost reductions that
can be achieved by centralizing stock at DC’s. These risk pooling benefits
result from previous work by Eppen [39], which considers risk pooling effects
for a multi-location newsboy model. Snyder et al. [128] present a stochastic
version of the LMRP. The transportation costs, retailer mean demands and
corresponding demand variances are scenario dependent. Each scenario has a
specified probability of occurrence. Distribution center opening decisions are
scenario independent and the allocation of the retailers to the DC’s is scenario
dependent. Kumar and Tiwari [71], Vidyarthi et al. [146] Park et al. [104] and
Ozsen et al. [98] elaborate risk pooling for more complex supply chain networks.
Perishability. Li et al. [75] classify deteriorating items in two categories:
the natural attributes of the first category of products loses usable and economic
value after a specific period of time (e.g. food, medicines, pharmaceutical products and flowers) and the economic value of the second category of items is
lost due to the changes in consumer preference and product upgrading (e.g.
computer chips, mobile phones, fashion and seasonal goods). The limited shelflife vaccines are classified into the first category. The remainder of the paper
proposes key factors which should be considered in the deteriorating inventory
studies and subsequently classifies the relevant literature into studies based on
an enterprise and those based on a supply chain. Firoozi et al. [43] emphasize
that the lifetime of products is not considered in network design models. These
authors extend the LMRP by integrating products with a fixed lifetime or predetermined expiry date. A constraint is added which takes the delivery lead
time from the supplier to the DC and the lifetime of the product into account
for determining the economic order quantity at a DC. The authors also show
the trade-off between enhancing storage conditions and inventory costs.
15
Trade-offs. The objective function of the minimizing cost and maximizing
service coverage model of Nozick and Turnquist [94] is emphasized by the work
of Shen and Daskin [125]. They extend the cost-based location-inventory model
of Shen et al. [124] by including a customer service element and developing
a weighting method to evaluate cost/service trade-offs. The authors measure
customer service by the fraction of all demands that are located within an exogenously specified distance of the assigned DC. Shen and Daskin [125] conclude
that the cost difference between the cost minimization solution and the service
maximization solution can be quite large. The trade-off between lead times and
inventory risk-pooling benefits is captured by the location-inventory model of
Sourirajan et al. [130, 129]. The replenishment lead time at the DC’s depends
on the flow through the DC and determines the safety stock held at the DC’s
and the expected pipeline inventory between plants and DC’s.
Coordination. Berman et al. [18] consider a coordinated inventory-location
model in which the DC’s are replenished by a single supplier. A periodic review
inventory policy is employed at the DC’s with two possible types of coordination: (1) partial coordination which allows each DC to have its own review
interval from a menu of options and (2) full coordination which states that
all DC’s have the same review interval. The results of the computational experiments show that the location and inventory cost increase is not significant
when comparing full coordination to partial coordination. This implies that full
coordination, which enhances the practical use of the inventory policy, is economically justifiable. Chick et al. [24] show how coordination of two key players
can be achieved in the influenza vaccine supply chain. The authors develop a
variation of the cost-sharing contract to coordinate the buyer (a single governmental public health service) and the supplier (a single vaccine manufacturer)
in order to attain a global social optimum. The lack of coordination leaves
the manufacturer with production yield risks and results in vaccine shortfalls
if the players act rationally. Manani et al. [83] extend this work by proposing
a cost-sharing contract to decrease the overall financial burden of an infection
globally when considering multiple governments and the possibility of disease
16
transmission across national boundaries, rather than focusing on a single buyer.
Capacitated vehicles. Tancrez et al. [134] present a location-inventory
model which takes vehicle shipment sizes into account. The authors emphasize
that previous SCND manuscripts never considered capacitated transportation.
However, we also opt for the integration of transportation queues. Frequently
shipping the items allows inventories to be kept limited, while accumulating
larger inventories in distribution centers leads to lower transportation costs.
This illustrates the trade-off between transport and storage costs. The authors
assume that the partners in the supply chain are perfectly coordinated. This
implies that shipments of items are only sent to a partner when the latter’s
inventory is empty.
Multiple sourcing. Tancrez et al. [134] also consider multiple sourcing in
each supply chain layer. Ozsen et al. [99] present a multi-sourcing version of the
capacitated LMRP and argue that multi-sourcing should be considered, as it
can bring benefits (lower transportation costs) and does not necessarily increase
the complexity of the network significantly. Their model allows that retailers are
served by more than one warehouse. A multi-product joint location-inventory
model of Yao et al. [151] incorporates multiple sourcing of the warehouses.
This complicates the determination of the safety stock levels at the opened
warehouses. Though multi-sourcing is motivated by previous papers, Daskin et
al. [32] states that many firms strongly prefer single sourcing solutions as they
make the management of the supply chain considerably simpler.
Multiple criteria. Multiple criteria can also be taken into account while
modeling inventory-location problems. Hamedani et al. [59] propose a multiobjective location-inventory model. They minimize the total costs and risk,
which is the variance of purchase, transportation, inventory holding, shortage
and ordering costs.
Guaranteed service approach. Grossman [54] states that the emerging
interest in enterprise-wide optimization in (chemical) process industries is due
to the increasing pressure for reducing costs and inventories in order to remain
competitive in the global market. The proposed model by You and Grossman
17
[155] integrates a stochastic inventory model with a SCND problem for chemical
companies. Their work is based on the joint inventory-location model of Shen
et al. [124]. The same authors [156] propose the guaranteed service approach
to model the multi-echelon inventory system in a supply chain network. For a
multi-echelon inventory system, the lead time of a downstream node depends
on the upstream node’s inventory level and demand uncertainty. The main
idea of the guaranteed service approach is that each node in the multi-echelon
inventory system quotes a guaranteed service time, by which this node will
satisfy the demand of its downstream node. For detailed information about the
guaranteed service approach, see Graves and Willems [51, 52]. The net lead time
of a node is the required time span to cover demand variation using the available
safety stocks at the node. This deterministic net lead time is defined as the
difference between the replenishment lead time of this node and its guaranteed
service time to its successor. The net lead times of the customer demand zones
and the DC’s and the guaranteed service times of the DC’s are modeled as
continuous variables in the presented mixed integer nonlinear program. The
authors also use this guaranteed serviced approach for tactical process planning
under uncertainty [158].
Responsiveness. You and Grossman [157] formulate a similar model that
also takes responsiveness into account. Their proposed measure for supply chain
responsiveness is the maximum guaranteed service time of the last echelon. This
maximum guaranteed service time is minimized simultaneously with a cost objective function. Two other quantitative characterizations for responsiveness
for process supply chains are presented by You and Grossman [153, 154]. The
first paper defines lead time [153] as the time of a supply chain network to
respond to customer demand changes in the worst case. Therefore, by assuming zero inventories, they use lead time as a measure of responsiveness. One
objective function of their problem formulation minimizes the maximum total
lead time of the entire supply chain network, while simultaneously maximizing the Net Present Value (NPV). The lead time of the supply chain is equal
to the length of the longest time path of chemical flows from a supplier to a
18
customer. The length of each time path is equal to the summation of all the
deterministic transportation and production times. The NPV takes income of
sales along with investment, operating, transportation and purchase costs into
account over a long-range time horizon.The second manuscript [154] minimizes
the maximum expected lead time of the supply chain network and maximizes
the NPV simultaneously. The expected lead time is defined as the delivery
lead time plus the production lead time multiplied by the stock-out probability.
The delivery lead time and the production lead time are in turn also equal to
the summation of all the deterministic production and transportation delays
incurred in the corresponding path. The stock-out probability is treated as a
continuous decision variable. Both papers consider, besides network structure
constraints, operational planning and cyclic scheduling constraints.
3.3. Production-distribution models
Production and distribution. Nozick and Turnquist [93] state that the
facility location problem is a subproblem of production-distribution system design. Indeed, the work of Gebennini et al. [47] shows an integrated productiondistribution model for the dynamic location-allocation problem. Besides locating the DC’s and allocating the demand to these DC’s, the model includes
production and distribution decisions such as the quantities that need to be manufactured during each time period and the product quantities that are delivered
in time. These decisions can be made because of the integration of production
lead times, delivery lead times between the successive supply chain stages and
required delivery times of the demand nodes in the model. However, the distinction with production-distribution models for aggregate planning should be
clarified: these models decide on the product flows and manufacturing quantities for the different echelons in an established supply chain network. We will
be particularly interested in the consideration of production and distribution
decisions for a new supply chain design.
Production rates, economies of scale and outsourcing. Tsiakis et
al. [141] model a supply chain network under demand uncertainty focusing
19
on production and transportation issues. They consider the production rate
for each product at any plant as a decision variable which is bounded between
a minimum production rate and a maximum production capacity. They also
include the possibility that some resources (e.g. equipment, utilities, manpower)
need to be shared by several production lines. The authors include economies
of scale by considering the total transportation costs between two stages in the
supply chain as a piecewise linear function of the flow of material. The proposed
model of Tsiakis and Papageorgiou [140] enables decision making on the number
of outsourced products delivered to the DC’s, the production rates at the plants,
the utilization of the plants (the number of production days per year) and the
number of days allocated for the manufacturing of each product at the plants.
They also take financial aspects, such as exchange rates and import duties, into
account. The model’s production allocation decisions can be set as production
targets for the advanced planning scheduling systems to optimize production
sequences.
Technology selection. Hammami et al. [61] discuss different delocalization strategies and five supply chain design aspects in a delocalization context:
(1) the difference in labor costs and technology between the country of origin
(developed) and the home country (developing), (2) the international facility
location (e.g. transfer prices and transportation issues), (3) the integration between all the different units in the supply chain, (4) the influence on the initial
supply chain (e.g. capacity relocation and facility closing costs) and (5) the
product life cycle which can influence the profitability. The same authors [62]
propose a mathematical formulation for a supply chain design problem in a
delocalization context. They focus on the integration of a number of delocalization aspects such as technology selection, supplier selection, capacity acquisition
and transfer prices for a given planning period. The model determines which
activities, defined as processes that convert a set of input products in to a set
of output products by the means of a certain technology and using a set of resources, should be delocalized. It can be that an automated technology cannot
be directly implemented in a developing country. A constraint ensures that a
20
set of technologies cannot be used in delocalized units before they have been
used in the country of origin. Elhedhli and Gzara [37] consider a problem where
the location of the plants and the DC’s and the corresponding technology need
to be determined. The installed capacity, the average unit cost of handling and
shipping a commodity to the next stage in the supply chain and the capacity absorption rate of the commodities depend on the technology choice of the
established plant or DC.
Financial statement analysis. Longinidis and Georgiadis [80] integrate
financial statement analysis in a design model under demand uncertainty. A
number of financial time dependent parameters such as the depreciation rate,
the short-term and long-term interest rate and the weighted average cost of
capital are defined in the proposed mathematical programming model. The
objective is to maximize the economic value added, which is the net operating
profit after taxes minus the invested capital cost, for a given planning period.
A lower or upper bound is set for a number of liquidity, asset management,
solvency and profitability ratios.
Multiple transportation modes. SteadieSeifi et al. [132] define multimodal, intermodal, co-modal and synchromodal transportation and provide
an overview of multimodal freight transportation planning at strategic, tactical
and operational levels. Eskigun et al. [41], Olivares-Benitez et al. [96] and Sadjady and Davoudpour [114] integrate a transportation mode selection decision
in a design problem. The deterministic transportation lead times depend on
the transportation mode and the distance between the nodes in the network.
Eskigun et al. [41] consider two transportation modes: if a demand area is close
enough to a plant, commodities are delivered from the plant to the demand
area directly by truck. Otherwise, they are first sent to a DC by rail and then
delivered to the demand area by truck. The two transportation modes are in
fact two types of sourcing: direct and indirect sourcing. Olivares-Benitez et
al. [96] and Sadjady and Davoudpour [114] consider a two-echelon supply chain
network. The number of allowable transportation modes can be chosen in both
echelons. Eskigun et al. [41] and Sadjady and Davoudpour [114] incorporate
21
deterministic transportation lead times in a cost objective function by multiplying them by a monetary value of lead time. The authors confirm that this
cost of lead time is hard to obtain. Multiple transportation options are also
integrated by Jayaraman [66] and Tiwari et al. [138].
4. Uncertainty
The previous section discussed which building blocks can be integrated in a
SCND model. This section emphasizes the importance of incorporating demand
and supply uncertainty in a SCND for a vaccine industry and reviews how previously published manuscripts take these uncertainties into account. Klibi et al.
[69] present a critical review of the proposed SCND models under uncertainty.
They discuss different disruptions that can threaten a supply chain network
and relevant evaluation criteria. In this paper, we will use the terms disruption
and strategic uncertainty interchangeably. The authors also review different
definitions of supply chain robustness, responsiveness and resilience and discuss
the importance of these concepts. We classify uncertainty into two major categories: strategic uncertainty and operational variability. Strategic uncertainties
are events that have a major impact on the supply chain such as earthquakes or
epidemic outbreaks. Operational variability influences operational factors that
are inherently uncertain. The impact of disruptions on a supply chain network
is considered to be much larger than the impact of operational variability. This
is why a lot of recent papers study how to mitigate disruptions in a supply
chain network. Table 2 shows in which extent uncertainty is incorporated in
the current literature. None of the papers considers all the different types of
uncertainties and only a few manuscripts incorporate both strategic uncertainty
and operational variability. The crosses at the supply side of operational variability refer to a variety of operational variabilities, e.g. variability in delivery
lead time, waiting time at workstations, (re)processing time and transportation
time. The demand side, at an operational level, is especially modeled by a
Normal Distribution (ND), Poisson distribution or a Fuzzy approach. In our
22
future research, we will deal with both strategic uncertainty and operational
variability. The different uncertainties shown in Table 2 will be further clarified
in the remainder of this section.
4.1. Strategic uncertainty
4.1.1. Supply
Reliability. Murray and Grubesic [90] define reliability as the probability
that a given element in a critical infrastructure system is functional at any given
time. This means having reliable suppliers, facilities and distribution modes in
the supply chain that is vulnerable to all kinds of disruptions like strikes or
power outages.
Unreliable facilities. Madadi et al. [82] confirm that some (health care)
supply chain disruptions may be catastrophic in spite of their low probability of
occurrence. They explicitly mention the disruption of flu vaccine manufacturing
which resulted in disastrous consequences. The government stopped production
when regulators inspected a manufacturing plant and found evidence of bacterial contamination problems which subsequently heavily reduced the supply of
vaccines during the flu season. A SCND model is presented with a cost objective
function minimizing five terms: (1) the fixed cost of selecting a facility, (2) the
transportation cost of shipping untainted products, (3) the cost of supplying
tainted products to the consumers, (4) the cost of discarding tainted products
and (5) the cost of inspection which is performed at a facility site. A binary
decision variable determines whether or not inspection is done at a particular facility. The authors implement a scenario based approach: the fraction of tainted
products before and after inspection are scenario dependent parameters.
Daskin et al. [31] propose the α-reliable p-median minimax regret model.
This model identifies the reliability set, a set of locations, that minimizes the
maximum regret with respect to an endogenously determined subset of scenarios. The total probability associated with the reliability set is at least the
reliability level, α. Chen et al. [22] build further on this work and present the
α-reliable mean-excess regret model. The computational results of both models
23
Table 2: Classification according to uncertainty incorporation
Reference
First Author
Year
Strategic uncertainty
Unreliable
Unreliable
facilities
portation
trans-
Operational variability
Unreliable
Demand
suppliers
scenarios
Supply
Demand
X
Poisson
24
[27]
Cooper
1963
[26]
Church
1974
[73]
Lee
1981
[103]
Pappis
1994
[31]
Daskin
1997
[66]
Jayaraman
1998
[93]
Nozick
1998
[13]
Badri
1999
[40]
Erlebacher
2000
[113]
Sabri
2000
X
ND
[94]
Nozick
2001
X
Poisson
[95]
Nozick
2001
X
Poisson
[141]
Tsiakis
2001
[144]
Verter
2002
[67]
Jayaraman
2003
[124]
Shen
2003
X
ND
[56]
Guillen
2005
[125]
Shen
2005
[127]
Snyder
2005
[6]
Altimarpak
2006
[22]
Chen
2006
[136]
Tanonkou
2006
[41]
Eskigun
2007
[76]
Lieckens
2007
[108]
Qi
2007
[128]
Snyder
2007
[130]
Sourirajan
2007
[142]
Tzeng
2007
[146]
Vidyarthi
2007
[153]
You
2007
[162]
Zhou
2007
[12]
Azaron
2008
X
X
X
X
ND
X
X
X
X
ND
X
X
ND
X
ND
Poisson
ND
Fuzzy
X
X
(continued on next page)
Table 2: Classification according to uncertainty incorporation
Reference
First Author
Year
Strategic uncertainty
Unreliable
Unreliable
facilities
portation
trans-
Operational variability
Unreliable
Demand
suppliers
scenarios
Supply
Demand
25
[36]
Du
2008
[37]
Elhedhli
2008
[63]
Hinojosa
2008
[87]
Miranda
2008
ND
[98]
Ozsen
2008
Poisson
[140]
Tsiakis
2008
[155]
You
2008
ND
[154]
You
2008
ND, triangular
[47]
Gebennini
2009
ND
[57]
Guillén-Gosálbez
2009
[62]
Hammami
2009
[99]
Ozsen
2009
[129]
Sourirajan
2009
[147]
Vitoriano
2009
[34]
Demirel
2010
[45]
Franca
2010
[55]
Gu
2010
[78]
Lim
2010
[101]
Paksoy
2010
[104]
Park
2010
ND
[107]
Pishvaee
2010
Fuzzy
[106]
Pishvaee
2010
[138]
Tiwari
2010
ND
[151]
Yao
2010
ND
[156]
You
2010
[21]
Cardona-Valdés
2011
[79]
Lin
2011
[80]
Longinidis
2011
[97]
Ortuño
2011
[139]
Torres-Soto
2011
[148]
Vitoriano
2011
[149]
Wang
2011
Poisson
Poisson
X
X
X
ND
X
X
X
X
(continued on next page)
Table 2: Classification according to uncertainty incorporation
Reference
First Author
Year
Strategic uncertainty
Unreliable
Unreliable
facilities
portation
trans-
Operational variability
Unreliable
Demand
suppliers
scenarios
Supply
Demand
26
[152]
Yazdian
2011
Fuzzy
[157]
You
2011
ND
[18]
Berman
2012
ND
[38]
Elhedhli
2012
[48]
Ghaderi
2012
[77]
Lieckens
2012
[85]
Melo
2012
[96]
Olivares-Benitez
2012
[100]
Paksoy
2012
[114]
Sadjady
2012
[122]
Shariff
2012
[134]
Tancrez
2012
[82]
Madadi
2012
[5]
Ahmadi-Javid
2013
[59]
Hamedani
2013
X
X
X
[60]
Hamedani
2013
X
X
X
[71]
Kumar
2013
ND
[88]
Mousavi
2013
Fuzzy
[91]
Naimi
2013
[110]
Rajabalipour Cheshmehgaz
2013
[120]
Shankar
2013
[121]
Shankar
2013
[137]
Teimuory
2013
X
[143]
Vahdani
2013
X
[43]
Firoozi
2013
[70]
Kristianto
2014
[23]
Chen
2014
X
X
X
Fuzzy
X
X
ND
X
Fuzzy
ND
X
are compared. Snyder and Daskin [127] incorporate reliability in the classical
p-median problem and the UFLP. The authors assume that facilities can fail
with a given probability and that customers are subsequently served by the
nearest non-disrupted facility. Lim et al. [78] consider the presence of random
facility disruptions in reliable SCND. Two types of DC’s are distinguished in
their model: unreliable and reliable DC’s. When a random disruption occurs in
an unreliable DC, it totally fails and the customers assigned to it are reassigned
to a reliable DC. The authors also consider the option of facility hardening,
an investment for hedging against the risk of disruption. Qi and Shen [108]
incorporate supply reliability by modeling the amount of goods delivered from
a facility to a retailer using the product of the order quantity from the retailer
and a random variable associated with the facility, which is called the reliability
coefficient. The reliability of facilities, which can fail with a certain probability,
is incorporated by Vahdani et al. [143] in a reverse logistics network design
context.
Unreliable transportation. Azad et al. [11] present a stochastic SCND
cost minimization model which includes disruptions at the locations of DC’s
and at the transportation modes between DC’s and customers. The authors
assume that a facility does not fully fail, but loses a fraction of its capacity
to the assigned customers. There exists a number of unsafe transportation
modes and a single safe transportation mode between a DC and its assigned
customers. The unsafe transportation modes can be disrupted with a given
probability and safe links are more expensive and outsourced. Additionally,
they consider the conditional value-at-risk approach to control the risk in the
model. The paper of Ahmadi-Javid [5] considers a location-routing problem in
a supply chain network with production and distribution disruption risks. The
DC’s to be opened and the vehicle routes of these opened DC’s to the allocated
customers need to be determined. Each vehicle may be randomly disrupted and
an extra cost is incurred because an unscheduled vehicle must finish the tour.
The authors use the expectation, conditional value-at-risk and worst-case risk
measures.
27
Unreliable suppliers. Azaron et al. [12] include unreliable suppliers into
their multi-objective SCND model. These suppliers may lose their ability to supply and the reliabilities of the suppliers are known in advance, but the actual
situation of the suppliers becomes clear after building the facilities. Tanonkou
et al. [136] propose a methodology based on Monte Carlo simulation and Lagrangean relaxation for solving a distribution network which considers failures
of suppliers. A two-period model is developed: the first period determines the
location of the DC’s and the suppliers that should replenish the DC’s while the
second period allows suppliers to fail and reorganizes the distribution network
with the opened DC’s and remaining suppliers.
Resilience. Christopher and Peck [25] define resilience as the ability of a
system to return to its original state or move to a new, more desirable state after
being disturbed. A resilient supply chain is characterized by the capability to react quickly to new events. Incorporating reliability and resilience in the design of
a supply chain network is an advantage in a dynamic and volatile environment.
Rice and Caniato [111] explain two methods that have the greatest potential to
create resilience in a supply chain network: creating flexibility and redundancy.
The authors explain that creating capabilities are needed to achieve flexibility.
Capabilities are created by investing in infrastructure and resources before they
are actually needed, e.g. developing a multi-skilled workforce, designing production systems that can adopt real-time changes and implementing sourcing
strategies that enable a swift switching of suppliers. Redundancy responds to
disruptions by investments in capital and capacity prior to the point of need,
e.g. maintaining production lines or facilities in excess of capacity requirements.
Tang and Tomlin [135] confirm that including flexibility enhances supply chain
resilience. They review different supply chain risks and study how much flexibility is needed to mitigate these risks. Gosling et al. [50] explore how supply
chain flexibility can be achieved in the construction industry, where high levels
of uncertainty arise from project specific demands. The authors emphasize supplier selection as an important determinant for achieving supply chain flexibility
and classify the suppliers in three categories, each with different flexibility im28
plications. Kristianto et al. [70] present a two-stage programming approach to
design a resilient supply chain network for reducing the impact of disruptions.
This is done by allocating excess capacity and/or inventory at certain pinch
points in the supply chain.
Pharmaceutical supply chain. Shah [118] discusses a number of key issues for the optimization of a pharmaceutical supply chain. One of these issues is
the capacity planning. The long lead times to make capacity effective mean that
decisions often need to be taken under conditions of high uncertainty. Waiting
for the uncertainty to be resolved leads to an unacceptable delay in the time to
market. A number of researchers study capacity planning in the pharmaceutical
industry under uncertainty. Gatica et al. [46] and Levis and Papageorgiou [74]
research how pharmaceutical industries deal with the use of limited resources
to obtain the highest possible profit from a potential product portfolio. The
authors present a mixed-integer programming approach to study the problem
of capacity planning under the uncertainty of the outcomes of clinical trials.
The outcomes of each potential product are modeled as different scenarios. The
presented models decide on the final product portfolio, the investment strategy
and the production planning. Levis and Papageorgiou [74] and Papageorgiou et
al. [102] include the time for scale-up and qualification runs of new products.
This reflects the time needed to learn how to manufacture the product in a
repeatable fashion and for the qualification of the first batches by the relevant
regulatory authorities. These papers also distinguish three types of business
centers in the supply chain network: production sites, the Intellectual Property
(IP) owner and sales regions. The IP-center is responsible for the funding and
the development of new products. The revenues, costs and relevant taxes of the
three types of business centers are taken into account.
4.1.2. Demand
Scenario generation. Natural disasters can cause serious, unexpected
vaccine demand disruptions. We already mentioned a number of papers [31,
82, 128] that capture uncertainty by modeling specific discrete scenarios. These
29
manuscripts consider demand parameters (the mean and variance of a normal
distributed demand) as scenario dependent parameters. Each scenario has a
specified probability of occurrence.
Disease and epidemiological dynamics. The demand of vaccines depends on how the corresponding disease propagates. Some manuscripts try to
model the dynamics of different diseases. Word et al. [150], for example, use
continuous differential equations to build a childhood infectious disease model.
The performance of this model depends on the parameter values which are estimated by disease data. Other manuscripts model the impact of vaccination
programs on epidemiological dynamics. Atkins et al. [10] model the impact of
a mass vaccination program on the reduction of the rotavirus infection disease
burden in England and Wales. The birth rate and vaccine efficacy are values
drawn from distributions. Uncertainty is also accounted for by analyzing four
scenarios from two independent changes in the model relating to the duration of
vaccine immunity and vaccine efficacy. Recently, the WHO announced a surge
in polio [4]. Polio is a viral disease which mainly affects young children and is
transmitted through contaminated food and water. It can only prevented by
immunization. The Global Polio Eradication Initiative [2], launched in 1988,
is a partnership between the WHO, Rotary International, the US Centers for
Disease Control and Prevention and the United Nations Children’s Fund. Its
goal is to eradicate polio worldwide.
Tenders. As mentioned before, Smith et al. [126] explain tenders as one
of the three types of vaccine procurement. Vaccine manufacturing companies
compete with each other on price, volume and reliability of supply for winning
a tender. The candidate suppliers learn two months before the delivery date
whether the tender is won or lost. The total production lead time of vaccines
varies between 9 and 22 months [3] which implies that vaccine manufacturers
are forced to begin production before knowing whether the tender is won or
lost. If the tender is lost, then the demand forecast drops to zero.
30
4.2. Operational variability
4.2.1. Supply
We previously mentioned the long manufacturing lead times and corresponding variability due to permanent quality control and quality assurance. We are
now interested in how published SCND models deal with supply variability in
terms of lead times, throughput and inventory levels.
Integration of a strategic and operational level submodel. Sabri
and Beamon [113] show a multi-objective approach to simultaneously integrate
the strategic and operational planning in supply chain design. Besides delivery
and demand uncertainty, production uncertainty is also included. The authors
show a strategic level submodel and an operational level submodel that need to
be solved iteratively until the location and allocation binary decision variables
converge. The operational level submodel integrates service levels, inventory
ordering policies, production batch sizes, unit variable costs, production lead
times and replenishment lead times. An expression for computing the variance
of the total production lead time, which is the sum of setup time, waiting time at
the workstations, processing time and material delay times, is derived. However,
the setup times and processing times are considered as deterministic.
Queueing relationships. Lieckens and Vandaele [76] incorporate the product’s cycle time and inventory holding costs in a reverse logistics network design
by modeling the reprocessing steps as a queueing system. A reprocessing facility
is modeled as a G/G/1 queueing model with general interarrival and processing
time distributions, a single server and infinite buffers. This queueing approach
is motivated by the high degree of uncertainty caused by the lack of control
over the quantity, quality and timing of returned products in a reverse logistics
network. This work is extended by the same authors [77] and takes stochastic transportation lead times of one transportation mode, quality dependent
routings and multiple levels into account.
31
4.2.2. Demand
Probabilistic approach. Demand variability is often captured by treating
one or more parameters as random variables with a known probability distribution. We already encountered a number of manuscripts that model the customer
demand as a mean and variance parameter drawn from a normal distribution.
These parameters can be customer-, product-, time- or even scenario dependent.
The time dependent parameters are typically integrated in so-called dynamic
models. Hinjosa et al. [63], Gebenni et al. [47] and Torres-Soto and Üster [139]
consider a multi-period SCND problem with a dynamic demand.
Fuzzy approach. Some manuscripts emphasize that it is difficult to assign
a probability distribution to the demand in a real environment. Zhou and Liu.
[162] and Mousavi and Niaki [88] consider the capacitated location-allocation
problem with fuzzy demand. These papers develop three types of fuzzy programming to model the problem.
5. Performance measures
We already mentioned the importance of imposing multiple performance
criteria on a supply chain network. Different stakeholders of a supply chain
can propose conflicting performance criteria for the same supply chain design.
This section discusses the performance measures that we encountered during
our search process on manuscripts for modeling a supply chain network and
also identifies performance criteria for a vaccine supply chain in the existing
literature. As mentioned before, these performance criteria will be classified
into three types distinguished by Decouttere and Vandaele [33]: economical,
technological and value criteria. The main driver for our classification of the
performance metrics focuses on the goal of imposing the KPI’s and not the way
that they are actually measured. Table 3 summarizes the performance criteria
imposed on a supply chain network. Most of the crosses in the economical and
the technological column of this table refer to cost and responsiveness criteria
respectively. Table 3 also reveals that value criteria are not often taken into
32
Figure 1: Trends in performance measures
account in the current body of SCND literature. Figure 1 shows the increasing
attention to technological and value performance measures in time. In our
future research, we will measure the performance of our SCND with criteria
arising from the three types of KPI’s. These three types of KPI’s are discussed
in the remainder of this section.
5.1. Economical criteria
Economies. Beamon [15] emphasizes that it is difficult to choose appropriate supply chain performance measures due to the complexity of these systems.
In the remainder of the manuscript, the author develops a framework for the selection of supply chain performance measures. However, an economic objective
(cost, profit, NPV) is present in almost every manuscript that we encountered
in the field of SCND modeling and the distribution of humanitarian aid.
Financial risk. Franca et al. [45] evaluate the financial risk associated with
the supply chain. They define it as the probability of a certain objective of cost
33
Table 3: Classification according to performance measures
Reference
First Author
Year
Economical
[27]
Cooper
1963
X
Technological
Value
[26]
Church
1974
[73]
Lee
1981
X
X
[103]
Pappis
1994
X
X
[31]
Daskin
1997
[66]
Jayaraman
1998
X
[93]
Nozick
1998
X
[13]
Badri
1999
X
[40]
Erlebacher
2000
X
[113]
Sabri
2000
X
X
[94]
Nozick
2001
X
X
[95]
Nozick
2001
X
[141]
Tsiakis
2001
X
[144]
Verter
2002
[67]
Jayaraman
2003
X
[124]
Shen
2003
X
[56]
Guillen
2005
X
X
[125]
Shen
2005
X
X
[127]
Snyder
2005
X
[6]
Altimarpak
2006
X
[22]
Chen
2006
[136]
Tanonkou
2006
X
[41]
Eskigun
2007
X
[76]
Lieckens
2007
X
[108]
Qi
2007
X
[128]
Snyder
2007
X
[130]
Sourirajan
2007
X
[142]
Tzeng
2007
X
[146]
Vidyarthi
2007
X
[153]
You
2007
X
[162]
Zhou
2007
X
[12]
Azaron
2008
X
[36]
Du
2008
X
[37]
Elhedhli
2008
X
[63]
Hinojosa
2008
X
[87]
Miranda
2008
X
[98]
Ozsen
2008
X
[140]
Tsiakis
2008
X
[155]
You
2008
X
[154]
You
2008
X
[47]
Gebennini
2009
X
[57]
Guillén-Gosálbez
2009
X
[62]
Hammami
2009
X
[99]
Ozsen
2009
X
[129]
Sourirajan
2009
X
[147]
Vitoriano
2009
X
X
X
[34]
Demirel
2010
X
X
X
[45]
Franca
2010
X
X
[55]
Gu
2010
[78]
Lim
2010
X
[101]
Paksoy
2010
X
[104]
Park
2010
X
[107]
Pishvaee
2010
X
X
[106]
Pishvaee
2010
X
X
[138]
Tiwari
2010
X
X
[151]
Yao
2010
X
[156]
You
2010
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
(continued on next page)
34
Table 3: Classification according to performance measures
Reference
First Author
Year
Economical
Technological
[21]
Cardona-Valdés
2011
X
X
Value
[79]
Lin
2011
X
X
X
[80]
Longinidis
2011
X
[97]
Ortuño
2011
X
X
X
[139]
Torres-Soto
2011
X
[148]
Vitoriano
2011
X
X
X
[149]
Wang
2011
X
[152]
Yazdian
2011
X
[157]
You
2011
X
[18]
Berman
2012
X
[38]
Elhedhli
2012
X
[48]
Ghaderi
2012
X
[77]
Lieckens
2012
X
[85]
Melo
2012
X
[96]
Olivares-Benitez
2012
X
[100]
Paksoy
2012
X
[114]
Sadjady
2012
X
[122]
Shariff
2012
[134]
Tancrez
2012
X
[82]
Madadi
2012
X
[5]
Ahmadi-Javid
2013
X
[59]
Hamedani
2013
X
[60]
Hamedani
2013
X
[71]
Kumar
2013
X
[88]
Mousavi
2013
X
[91]
Naimi
2013
X
X
[110]
Rajabalipour Cheshmehgaz
2013
X
X
[120]
Shankar
2013
X
X
[121]
Shankar
2013
X
X
[137]
Teimuory
2013
X
X
[143]
Vahdani
2013
X
[43]
Firoozi
2013
X
[70]
Kristianto
2014
X
[23]
Chen
2014
X
X
X
X
X
X
or profit not meeting a target level. Guillén et al. [56] Azaron et al. [12] and
Hamedani et al. [60] adopt the same definition of financial risk. A number of parameters, for example the demand, and variables, for example the flow between
the supply chain stages, are scenario dependent. These papers minimize the financial risk criterion, which is the weighted sum of the probability of occurrence
of each scenario times the achievement of the target level corresponding to that
scenario. Hamedani et al. [60] integrate financial risk and the variance of the
total costs in a multi-objective SCND model considering inventory decisions.
35
5.2. Technological criteria
Responsiveness. Cost and a combination of cost and customer responsiveness have been utilized predominantly as supply chain performance measures. In
the previous section we encountered fill rate and lead time as performance measures for responsiveness. The SCND model formulation of Cardona-Valdés et al.
[21] captures two objective functions: a minimizing cost objective and an objective that minimizes the maximum lead time from the plants to the customers
through the DC’s. The responsiveness objective of Rajabalipour Cheshmehgaz
et al. [110] minimizes the maximum order response time from DC’s to customers
and from suppliers to customers by direct shipment. Shah [118, 119] states that
a future research challenge is the development of rapid responsive vaccines and
other treatments that arise from emergencies (e.g. bioterrorism or fast developing epidemics). The author emphasizes that particularly the vaccine supply
chain is slow and unresponsive. The responsiveness criterion is, for example by
Pishvaee et al. [106], by Pishvaee and Torabi [107] and Du and Evans [36] also
utilized in a reverse logistics network design context.
Flexibility. The work of Sabri and Beamon [113], which is also briefly
discussed in the previous section, proposes flexibility, besides costs and customer
service level, as a third performance measure. The authors define flexibility as
the ability to respond to the customer requirements and distinguish two types
of flexibility: volume and delivery flexibility. Volume flexibility is measured by
capacity slack. For a plant, this slack is measured as the difference between
the plant capacity and its utilization and for a DC this slack is calculated as
the difference between the available throughput and the demand requirements.
The delivery flexibility is measured as the lead time slack which is the length
of time between the time when an order for an item is placed and when it is
actually available for satisfying the customer’s demand. The authors comment
that delivery flexibility is not often used in the industry or literature because
the majority of the inventory and supply chain models assume fixed lead times.
Equity of capacity utilization. The work of Altiparmak et al. [6] proposes a genetic algorithm approach for dealing with three criteria for the op36
timization of a supply chain network: costs, responsiveness and equity of the
capacity utilization of plants and DC’s. The responsiveness criterion is measured
by the percentage of the demand that is fulfilled within a stipulated access time.
The equity criterion ensures that the demand volumes are fairly distributed
among the opened DC’s and plants and is measured by the mean square error
of the capacity utilization ratios of the plants and DC’s. A smaller value of the
mean square error means a smaller deviation of the capacity utilization ratios
of the plants and DC’s from the equal capacity utilization ratio levels.
Quality. Zhang et al. [161] explain that supply chain coordination, technology application, risk management, and reliability assurance are a few important
measures for continuous supply chain quality improvement. A cost can be associated with the varying quality of different suppliers. Naimi Sadigh et al. [91]
and Franca et al. [45] incorporate a supplier selection decision in SCND as a
quality criterion. The work of Naimi Sadigh et al. [91] maximizes this quality
metric by multiplying the quality of each part of each supplier by the quantity
ordered of the considered part. Franca et al. [45] increase the quality level
by minimizing the number of raw material defects. Each material from each
supplier has a quality level and a weight estimating the impact of the material
defect on the manufacturing process.
Vaccine transport and storage. Assi et al. [7, 8, 9] also report transport
capacity utilization and storage capacity utilization as supply chain performance
measures for a custom designed discrete event simulation model which simulates
all processes, storage locations, administering locations, and storage equipment
in a vaccine supply chain. Vaccines need to be stored and transported in a cold
chain environment. Vaccines exposed to temperatures outside the recommended
ranges can have reduced potency and protection. All varicella-containing vaccines should be stored in a continuously frozen state at the manufacturer’s recommended freezer temperature (between -50°C and -15°C) until administration.
All inactivated vaccines require refrigerator storage temperatures (between 2°C
and 8°C). The following live attenuated vaccines must also be kept at refrigerator temperature: influenza, rotavirus, typhoid and yellow fever. The measles,
37
mumps, rubella vaccine can be stored either in the freezer or the refrigerator
[1]. Chen et al. [23] present a planning model for the vaccine distribution in
developing countries. The effective refrigerator, freezer capacities and transport
capacities between locations are parameters for generating the constraints of the
proposed model. It is also assumed that a small fraction of vaccines is lost in
storage and during transportation due to, for example, breakage and pilferage.
Another loss is because of the so-called open vial waste. This refers to discarding
the remainder of multi-dose vials that are not fully used during a vaccination
session. In addition, the authors propose an extension that allows a cold storage
or transport capacity expansion decision when the coverage is insufficient.
Human capital. Griffith [53] emphasizes the importance of human capital
in supply chains of global firms. The author explains a four-step assessment
procedure such that firms can assess and appropriately match supply chain
personnel to specific jobs, thereby increasing the global competitiveness of the
firm. MacCarthy and Atthirawong [81] investigate and identify factors affecting international location decisions. Rozek [112] presents risk and regulatory
factors that affect a country’s attractiveness for the location decisions of industrial activities (research, clinical trials, manufacturing and regional offices) by
research-based pharmaceutical companies. These papers mention the importance of the availability of a sufficient supply of skilled workers for increasing a
country’s attractiveness. Demirel et al. [34] takes quantitative and qualitative
criteria into account for the selection of a warehouse location. The authors distinguish five main criteria: costs, labor characteristics, infrastructure, markets
and macro environment. The linguistic preferences of the respondents for the
degree of importance of each criterion, the performance levels of the locations
and tolerance zones of each criterion are surveyed. The linguistic terms in the
study are quantified by the use of trapezoidal fuzzy numbers. The authors illustrate how the Choquet integral can be used to make a multi-criteria evaluation
of different warehouse location alternatives. The success of a Choquet integral
depends on an appropriate representation of fuzzy measures, which captures
the importance of individual criteria or their combination. More research on
38
the use of the Choquet integral with fuzzy numbers in multiple criteria decision
support systems is done by Meyer and Roubens [86].
5.3. Value criteria
Vaccine availability. Assi et al. [7, 8, 9] and Haidari et al. [58] mention the
importance of vaccine transportation and storage in supply chain management.
These papers explain how the deterministically modeled transportation capacity
can be a bottleneck in the vaccine supply chain, reducing vaccine availability.
They define vaccine availability as an important supply chain performance measure. The vaccine availability at a health center is computed as the number of
patients receiving a vaccine divided by the number of people arriving for a vaccine. A similar performance criterion is maximized by the previously mentioned
work of Chen et al. [23]. The objective of the proposed linear programming
model maximizes the number of fully immunized children (children that received the multiple doses for complete immunization) across all the vaccination
locations. The authors assume that vaccine manufacturers can supply enough
vaccines to satisfy the demand.
Environmental.
During the last decade, a large amount of literature
emerged on the concept of green supply chain management. Manufacturing
processes are often viewed as the culprit of the degradation of the environment.
In the supply chain design phase, environmental investment decisions can be undertaken to build a sustainable supply chain. Beamon [14] presents performance
measures appropriate for an extended supply chain. This is a supply chain that
considers the total immediate and eventual environmental effects of all products
and processes. A single objective green SCND model is shown by Elhedhli and
Merrick [38]. The minimizing objective function contains a pollution cost to the
environment. This part of the objective function is determined by an emission
cost function and the flow between plants and DC’s and between DC’s and customers. Wang et al. [149] propose a multi-objective SCND optimization model
that captures the trade-off between the total cost and the environment influence.
The total cost objective function contains an investment cost on environmental
39
protection equipment. The environment objective function minimizes the total
CO2 emission in the supply chain which is the summation of (1) the emission
in all facilities depending on the product type, the facility and the environment
protection level and (2) the emissions between two nodes in the network depending on the transportation mode and the product type. Guillén-Gosálbez and
Grossmann [57] measure environmental performance through the Eco-indicator
99, which incorporates the recent advances made in life cycle assessment. Life
cycle assessment covers the entire life cycle of a product, process or activity.
The article explicitly considers the uncertainty of the emissions released and
feedstock requirements associated with the network operations. The authors
describe the calculation of the Eco-indicator 99 metric in detail. The greenness
criterion is also utilized, for example by Paksoy et al. [100, 101], in a reverse
logistics network design context. Their work minimizes the total CO2 emissions produced by trucks in the forward chain. Another criterion encourages
customers to use recyclable products. This is done by minimizing the difference
between the purchasing cost and the total opportunity profits that are gained
via using recyclable products.
Equity of demand and demand prioritization. In general, humanitarian logistics provide assistance in the form of food, water, medicine, shelter, and
supplies to areas affected by large-scale emergencies. In some of these emergencies, vaccines need to be distributed. We are interested in which performance
measures are taken into account for modeling a humanitarian relief chain. Beamon and Balcik [16] compare performance measurement in the humanitarian
relief chain with performance measures in the commercial supply chain, develop
performance metrics for the humanitarian relief chain, and present a framework
that can be used as a basis for a performance measurement system for the relief
chain. Also in the field of humanitarian logistics, conflicting criteria (e.g. costs
versus saving lives) need to be optimized. Vitoriano et al. [147, 148] and Ortuño
[97] et al. use goal programming to model six criteria for the distribution of
humanitarian relief: cost, time, equity, priority, reliability and security. Following upon the above based discussion, we classify cost as an economic criterion
40
and time, reliability and security as technological criteria. The costs depend
on the number of vehicles that have to be used to transport the aid and the
distance that needs to be traveled. The time to reach a demand node is critical
in humanitarian logistics and is kept below a target value. Equity is a fairness
criterion that tries to satisfy the same proportion of each demand node by preventing humanitarian aid to be only delivered to the more accessible areas and
difficult-to-reach areas to be neglected. Prioritization can be done by taken into
account special requirements of demand nodes (e.g. higher demand volume).
Some parts of the infrastructure can be perceived as unreliable due to potential
aftershock earthquakes or after-disaster weather conditions. The reliability of
an arc in the distribution network is defined as the probability for successfully
crossing that arc and the reliability of a route is subsequently defined as the
multiplication of the probabilities of completing each arc of the route, assuming
independence between arcs. The humanitarian operation should be developed in
a secure way. Vehicles can be ransacked when traveling. An assumption is that
the ransack probability of an arc decreases with the number of vehicles traveling
as a convoy. We briefly mention which performance criteria are modeled by two
other papers in the humanitarian logistics field. The multi-objective model of
Tzeng et al. [142] features three objective functions: minimizing costs, minimizing travel time and maximizing the minimum demand satisfaction of a demand
node. The work of Lin et al. [79] minimizes (1) the penalty costs for unsatisfied
demand, (2) the travel time and (3) the difference in satisfaction rates of the
demand nodes. Buccier and Gaetz [20] discuss the ethical principles of equity
and demand prioritization for the distribution of limited influenza vaccines.
6. Research methodology
6.1. Modeling approach
Literature reveals that the modeling methodology of the majority of SCND
papers can be classified into mathematical programming categories such as
(Mixed) Integer Programming (M)IP, (Mixed Integer) Nonlinear Programming
41
(MI)NLP and Multi-Objective Programming (MOP). Other categories are Fuzzy
Programming (FP), Possibilistic Programming (PP), Goal Programming (GP),
queueing and simulation. The main categories distinguished in the solution approach are Decomposition Techniques (DT), Evolutionary Algorithms (EA) and
the Epsilon Constraint Method (ECM). Table 4 shows the classification of the
papers according to the modeling and solution methodologies described above.
We classify multi-objective nonlinear programming models in both (MI)NLP
and MOP categories. A substantial body of single-objective SCND problems
are modeled using (M)IP or (MI)NLP and subsequently solved using DT or EA.
SCND problems that consider two or more performance criteria are often modeled as a MOP and subsequently solved with the ECM or EA. The remainder
of this section clarifies the different modeling and solution approaches.
Mixed integer programming. The UFLP and CFLP are NP-hard problems. An overwhelming majority of the reviewed SCND manuscripts are extensions of the UFLP and CFLP that aim at minimizing the total fixed and
variable costs. Researchers try to overcome this NP-hardness by decomposition techniques (e.g. Lagrangian relaxation) and improvement heuristics (e.g.
genetic algorithms).
Nonlinear programming. The classical joint location-inventory problems
of Erlebacher and Meller [40] and Shen et al. [124], the LMRP, are modeled
as a mixed integer program with a nonlinear objective function. This nonlinear objective function is obtained by integrating the inventory centralization
benefits at the retailers. We mentioned before that Yao et al. [151] include
multiple sourcing of the warehouses in a multi-product joint location-inventory
problem. This further complicates the nonlinear objective function because of
the appropriate safety stock levels determination of the products at the opened
warehouses. The capacitated LMRP of Ozsen et al. [98] has nonlinear terms in
the objective function and in a constraint related to the capacitated EOQ problem. The previously discussed joint location-inventory problem of Tancrez et
al. [134] is formulated as a nonlinear continuous program. They emphasize the
avoidance of integer variables for being able to analyze large real-life problems
42
Table 4: Classification according to research methodology
Reference
First author
Year
Modeling approach
(M)IP
(MI)NLP
FP and PP
MOP
Optimization approach
GP
Other
DT
EA
ECM
X
Other
43
[27]
Cooper
1963
[26]
Church
1974
X
[73]
Lee
1981
[103]
Pappis
1994
X
X
[31]
Daskin
1997
X
X
[66]
Jayaraman
1998
X
[93]
Nozick
1998
X
[13]
Badri
1999
[40]
Erlebacher
2000
[113]
Sabri
2000
[94]
Nozick
2001
X
X
X
[95]
Nozick
2001
X
X
X
[141]
Tsiakis
2001
X
[144]
Verter
2002
X
[67]
Jayaraman
2003
X
[124]
Shen
2003
[56]
Guillen
2005
[125]
Shen
2005
[127]
Snyder
2005
[6]
Altimarpak
2006
[22]
Chen
2006
[136]
Tanonkou
2006
X
X
[41]
Eskigun
2007
X
X
[76]
Lieckens
2007
X
[108]
Qi
2007
X
X
[128]
Snyder
2007
X
X
[130]
Sourirajan
2007
X
[142]
Tzeng
2007
[146]
Vidyarthi
2007
X
[153]
You
2007
X
[162]
Zhou
2007
[12]
Azaron
2008
X
[36]
Du
2008
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
(continued on next page)
Table 4: Classification according to research methodology
Reference
First author
Year
Modeling approach
(M)IP
(MI)NLP
FP and PP
MOP
Optimization approach
GP
Other
DT
44
[37]
Elhedhli
2008
X
[63]
Hinojosa
2008
X
[87]
Miranda
2008
X
X
[98]
Ozsen
2008
X
X
[140]
Tsiakis
2008
[155]
You
2008
X
[154]
You
2008
X
[47]
Gebennini
2009
X
[57]
Guillén-Gosálbez
2009
X
[62]
Hammami
2009
[99]
Ozsen
2009
X
[129]
Sourirajan
2009
X
[147]
Vitoriano
2009
[34]
Demirel
2010
[45]
Franca
2010
[55]
Gu
2010
X
[78]
Lim
2010
X
[101]
Paksoy
2010
[104]
Park
2010
[107]
Pishvaee
2010
[106]
Pishvaee
2010
[138]
Tiwari
2010
[151]
Yao
2010
X
[156]
You
2010
X
[21]
Cardona-Valdés
2011
X
X
[79]
Lin
2011
X
X
[80]
Longinidis
2011
[97]
Ortuño
2011
[139]
Torres-Soto
2011
[148]
Vitoriano
2011
[149]
Wang
2011
[152]
Yazdian
2011
[157]
You
2011
EA
ECM
Other
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
(continued on next page)
Table 4: Classification according to research methodology
Reference
First author
Year
Modeling approach
(M)IP
(MI)NLP
FP and PP
MOP
Optimization approach
GP
Other
X
DT
EA
45
[18]
Berman
2012
[38]
Elhedhli
2012
X
[48]
Ghaderi
2012
X
[77]
Lieckens
2012
[85]
Melo
2012
[96]
Olivares-Benitez
2012
[100]
Paksoy
2012
[114]
Sadjady
2012
X
[122]
Shariff
2012
X
[134]
Tancrez
2012
[82]
Madadi
2012
X
[5]
Ahmadi-Javid
2013
X
[59]
Hamedani
2013
X
X
[60]
Hamedani
2013
X
X
[71]
Kumar
2013
X
X
[88]
Mousavi
2013
[91]
Naimi
2013
X
X
[110]
Rajabalipour Cheshmehgaz
2013
X
X
[120]
Shankar
2013
X
X
[121]
Shankar
2013
X
X
[137]
Teimuory
2013
X
[143]
Vahdani
2013
[43]
Firoozi
2013
[70]
Kristianto
2014
[23]
Chen
2014
ECM
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Other
X
X
X
X
in a computational efficient way.
Fuzzy and possibilistic programming. We define fuzzy programming as
mathematical programming with fuzzy parameters and/or fuzzy relations and
possibilistic programming as fuzzy programming when fuzzy sets of uncertain
(fuzzy) parameters are regarded as possibility distributions. We refer the reader
to the work of Inuiguichi et al. [65] and Inuiguchi and Ramı̀k [64] for more
information about fuzzy and possibilistic programming respectively. We already
mentioned the work of Zhou and Liu. [162] and Mousavi and Niaki [88] that
consider the capacitated location-allocation problem with a fuzzy demand. Both
papers above present three fuzzy approaches to formulate the problem. In the
work of Yazdiana et al. [152], the customer demand and capacity of each DC
are assumed to have some possibilistic distribution which are expressed using
trapezoidal fuzzy numbers. We further refer to Vahdani et al. [143] and Pishvaee
and Torabi [107] which use possibilistic programming in a reverse logistics design
context.
Queueing. We encountered queueing as a methodology to analyze various
performance measures of different types of supply chain networks. From the
analytical supply chain network modeling approaches of Kerbache and Smith
[68], Dong and Chen [35] and Srivathsan and Kamath [131], we conclude that
exact results are difficult to find if not impossible. The above mentioned work of
Lieckens and Vandaele [76, 77] introduces queueing nonlinearities in the design
of a reverse logistics network. They present a mathematical formulation with a
nonlinear objective function. The authors also illustrate that the use of queueing
theory can be found in the design of service systems.
Simulation.
Simulation is often used to capture the interrelationships
among parameters that are difficult to model analytically in a mathematical
program. At a strategic level, simulation is mainly used to evaluate alternative
supply chain configurations. Persson and Olhager [105] present a simulation
study for a real case, concerned with the manufacturing of mobile communication systems, and evaluate different supply chain designs with respect to quality,
46
lead times, lead time variability, inventory and costs as performance measures.
In order to evaluate three different supply chain structures, three different simulation models were built. Bottani and Montanari [19] assess the effects of different supply chain configurations on the total supply chain costs and bullwhip
effect for a fast mover consumer goods supply chain. Their analysis covers 30
possible supply chain configurations, resulting from the combination of several
design parameters, such as number of echelons, inventory policy adopted, demand information sharing mechanisms, demand behaviour and responsiveness
of supply chain players.
Multi-objective programming. Literature reveals that multi-objective
programming is the most used modeling technique to deal with multiple performance criteria. Each criterion is modeled as an objective function. Most
multi-objective programs on SCND handle two or three objective functions.
This approach is also often combined with a nonlinear objective function or
constraint that we discussed earlier. The use of fuzzy set theory and possibility
theory can also be included in multi-objective optimization.
Goal programming. Goal programming is a branch of multi-criteria decision analysis and is also used to model multiple, usually conflicting performance
measures. Each of these metrics has a goal or target value to be achieved and
unwanted deviations are subsequently minimized in an achievement function.
Although lexicographic and weighed goal programming are the most popular
goal programming modeling techniques, a lot of other variants exist. Tamiz et
al. [133] provide an overview of advances of goal programming in multi-criteria
decision analysis. As we mentioned earlier, Lee et al. [73] use integer goal
programming to model a location-allocation problem with eight performance
criteria. The weighted and lexicographic goal programming approach are also
used by Vitoriano et al. [147, 148] and Ortuño et al. [97] to model economical,
technological and value criteria for a humanitarian aid distribution problem.
The authors prefer goal programming because of its flexibility, capacity to deal
with many criteria and success in many real-life applications.
47
6.2. Optimization approach
Decomposition techniques. A substantial body of the literature uses
Lagrangian relaxation as a decomposition technique to solve single criterion
SCND problems. Fisher [44] explains that many hard problems can be viewed
as easy problems complicated by a relatively small set of side constraints. A Lagrangian problem can be generated by dualizing this set of side constraints. This
Lagrangian problem is easy to solve and produces, for minimization problems,
a lower bound on the optimal value of the original problem. The author also
documents a number of successful applications, e.g. location problems, of this
technique. Miranda and Garrido [87] present an inventory-location problem and
replace the typical location capacity constraints by an order size constraint as
well as a stochastic constraint for inventory capacity. The resulting mathematical model is complex due to the integration of nonlinear terms in the constraints
and objective function and subsequently motivated the researchers to develop a
solution method based on Lagrangian relaxation.
Single-objective metaheuristics. The computational complexity of the
studied models motivated researchers to design efficient heuristic algorithms to
solve these problems. Literature reveals that the application of evolutionary
algorithms received a lot of attention. In an evolutionary algorithm, a population of candidate solutions evolves iteratively towards better solutions. Each
candidate solution has a set of properties which can evolve by different operations. A fitness function, usually the value of the objective function, is used
to evaluate the performance of a candidate solution. The previously mentioned
work of Sourirajan et al. [129] uses genetic algorithms, which is a subclass of
evolutionary algorithms, to solve a single product network design model and
compare their computational results to the performance of a Lagrangian heuristic that they developed in previous work [130]. The authors comment that the
effectiveness of the Lagrangian approaches suggested in the literature for this
and similar problems depends on exploiting special structures present in the
objective function. The reverse logistics network design papers of Lieckens and
Vandaele [76, 77] motivate the use of differential evolution as a solution tech48
nique which also belongs to the class of evolutionary algorithms. We mention a
tabu search algorithm of Melo et al. [85] and a simulated annealing algorithm
by Jayaraman and Ross [67] as a small set of other examples of metaheuristic
approaches for solving single criterion SCND problems.
Multi-objective metaheuristics. Evolutionary algorithms are also used
for generating pareto-efficient solutions in a multi-objective problem. The work
of Pishvaee et al. [106] develops a memetic algorithm for a multi-objective
integrated forward/reverse logistics network design. Memetic algorithms are
population-based search heuristics for optimization problems similar to genetic
algorithms with often additional local searches proved to be of practical success. They compare the performance of the memetic algorithm with the multiobjective genetic algorithm of Altiparmak et al. [6] and conclude that the
memetic algorithm outperforms the genetic one in terms of average ratio of
pareto-optimal solutions obtained. Shankar et al. [120, 121] and Hamedani et
al. [59] develop a multi-objective hybrid particle swarm optimization algorithm
for solving a multi-objective SCND problem.
Epsilon constraint method. The epsilon constraint method is a technique to obtain a set of pareto-efficient solutions of a multi-objective program.
Teimuory et al. [137] propose a multi-objective reliable capacitated SCND
model and apply the epsilon constraint method. The authors explain the method
by distinguishing the following three steps:
1. One of the objective functions is selected as the main function and the
other objectives are formulated as constraints and thus bounded by some
allowable levels.
2. The problem is solved each time by contemplating one of the objective
functions and getting the values of each objective.
3. The allowable levels of the objective functions modeled as constraints are
adapted.
49
7. Applicability of research
Validation. Finally, Table 5 classifies the studied literature on the basis of
their applicability context. We distinguish the use of real-life data and desktop
data for validating the proposed model and solving procedure. A number of
papers, e.g. Gebenni et al. [47], Yao et al. [151], Berman et al. [18] and
Tancrez et al. [134], provide extensive numerical experiments to evaluate the
solving capability and a real-life case study. About 2/5 of the papers validate
their approach with real-life data and about 2/3 with desktop data.
Implementation. As our future research aims to be implemented in the
vaccine industry, we are interested in the number of SCND publications that
have been implemented. We define research as implemented when results of
an actual implementation in real-life are shown. Studying the relevant literature leads to the conclusion that publications lack any real-life implementation.
We briefly mention a number of papers using a real-life application to evaluate the solution of the proposed methodology. Hammami et al. [62] compare
the delocalization decisions of the model solution to the past decisions of a
company which manufactures and distributes automotive electrical harnesses.
The capacitated maximal covering location problem proposed by Shariff et al.
[122] locates a public health care facility in one of the districts of Malaysia.
The potential new locations and potential upgradeable facilities are identified
to increase the coverage taking the effect of population growth in the next ten
years into account. Gu et al. [55] show that the accessibility of breast cancer
screening services in the province of Alberta (Canada) can be increased using
the proposed model. The planning model for the vaccine distribution in developing countries of Chen et al. [23] has been adapted for supply chains in
three different countries (Niger, Thailand, and Vietnam). The solution of the
model reports the cold room capacities that should be added in the regions of
Niger. Furthermore, the model is also used to evaluate four types of changes
or updates in policy: (1) removing a distributional level from the supply chain
network, (2) changing the vial size, (3) the introduction of new vaccines and (4)
50
Table 5: Classification according to applicability of research
Reference
First Author
Year
Numerical exper-
Numerical exper-
iments by means
iments by means
of real-life data
of desktop data
[27]
Cooper
1963
X
[26]
Church
1974
X
[73]
Lee
1981
[103]
Pappis
1994
[31]
Daskin
1997
[66]
Jayaraman
1998
X
[93]
Nozick
1998
X
[13]
Badri
1999
X
[40]
Erlebacher
2000
X
[113]
Sabri
2000
[94]
Nozick
2001
X
[95]
Nozick
2001
X
[141]
Tsiakis
2001
[144]
Verter
2002
X
[67]
Jayaraman
2003
X
[124]
Shen
2003
X
[56]
Guillen
2005
X
[125]
Shen
2005
X
[127]
Snyder
2005
[6]
Altimarpak
2006
[22]
Chen
2006
[136]
Tanonkou
2006
[41]
Eskigun
2007
[76]
Lieckens
2007
X
[108]
Qi
2007
X
[128]
Snyder
2007
X
[130]
Sourirajan
2007
[142]
Tzeng
2007
[146]
Vidyarthi
2007
[153]
You
2007
[162]
Zhou
2007
X
[12]
Azaron
2008
X
[36]
Du
2008
X
[37]
Elhedhli
2008
X
[63]
Hinojosa
2008
X
[87]
Miranda
2008
X
[98]
Ozsen
2008
[140]
Tsiakis
2008
[155]
You
2008
[154]
You
2008
X
X
[47]
Gebennini
2009
X
X
[57]
Guillén-Gosálbez
2009
[62]
Hammami
2009
[99]
Ozsen
2009
[129]
Sourirajan
2009
[147]
Vitoriano
2009
X
[34]
Demirel
2010
X
[45]
Franca
2010
X
[55]
Gu
2010
X
[78]
Lim
2010
[101]
Paksoy
2010
[104]
Park
2010
[107]
Pishvaee
2010
X
[106]
Pishvaee
2010
X
[138]
Tiwari
2010
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
(continued on next page)
51
Table 5: Classification according to applicability of research
Reference
First Author
Year
Numerical exper-
Numerical exper-
iments by means
iments by means
of real-life data
of desktop data
X
X
[151]
Yao
2010
[156]
You
2010
[21]
Cardona-Valdés
2011
[79]
Lin
2011
X
[80]
Longinidis
2011
X
[97]
Ortuño
2011
X
[139]
Torres-Soto
2011
[148]
Vitoriano
2011
[149]
Wang
2011
X
[152]
Yazdian
2011
X
[157]
You
2011
[18]
Berman
2012
[38]
Elhedhli
2012
[48]
Ghaderi
2012
[77]
Lieckens
2012
[85]
Melo
2012
X
[96]
Olivares-Benitez
2012
X
[100]
Paksoy
2012
X
[114]
Sadjady
2012
[122]
Shariff
2012
X
X
[134]
Tancrez
2012
X
X
[82]
Madadi
2012
X
[5]
Ahmadi-Javid
2013
X
[59]
Hamedani
2013
X
[60]
Hamedani
2013
X
[71]
Kumar
2013
X
[88]
Mousavi
2013
X
[91]
Naimi
2013
X
[110]
Rajabalipour Cheshmehgaz
2013
X
[120]
Shankar
2013
[121]
Shankar
2013
[137]
Teimuory
2013
[143]
Vahdani
2013
[43]
Firoozi
2013
[70]
Kristianto
2014
X
[23]
Chen
2014
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
capacity expansion.
8. Conclusions and implications for further research
The aim of this literature review is twofold: we provide a literature review
on integrated SCND while introducing the reader to the typical characteristics
of a vaccine supply chain. The number of lives saved worldwide by vaccines is
admirable. We identify three types of vaccine procurement and show that the
vaccine demand also depends on disease propagation. Recently, an expected
52
surge of polio was announced by the WHO. This clarifies that the difficulty of
vaccine demand forecasting can not be overestimated. The supply of vaccines is
characterized by highly uncertain manufacturing lead times due to continuous
quality control and quality assurance. The perishability of vaccines requires
cold chain storage and cold chain distribution which is especially difficult for
developing countries. Guaranteeing a worldwide safe vaccination requires the
involvement of a large number of stakeholders: vaccine manufacturers, transportation companies, the government, regional and world health organizations,
health care facilities, the people who administer the vaccines and the final customer are all involved.
Our paper reviews a number of modeled network characteristics and shows
the decisions at strategic, tactical and operational levels that are integrated
in the design of a supply chain network. The importance of integrating the
relevant tactical and operational levels can not be overlooked despite of the fact
that SCND is seen as decision making at strategic level. Choosing the right
cold chain transportation equipment, for example, is a decision of strategic
importance.
We study how strategic uncertainty and operational variability is incorporated in the SCND literature and motivate the need for including both in our
future SCND. Supply chain disruptions, e.g. earth quakes, contamination problems, the outcome of clinical trials, epidemiological outbreaks, lead to disastrous
consequences for the vaccine supply and/or demand. A substantial body of the
literature reveals that such disruptions are taken into account by using a scenario
based approach. We observe that only a few papers take operational variability
on the supply side into account. The incorporation of lead times, throughput, WIP is often neglected or lead times (delivery times, processing times,
transportation times) are only considered as deterministic parameters. A normal distribution, Poisson distribution or fuzzy approach is often used to model
the demand variability. Our future research will take both strategic uncertainty
and operational variability into account by using a modeling methodology which
combines mathematical programming and queueing theory.
53
The fact that vaccines are lifesaving products and a large number of stakeholders are involved in the vaccine supply chain requires appropriate economical, technological and value KPI’s to be defined and balanced in an appropriate
way. Clearly, minimizing the costs of a SCND is the most frequently occurring
(economical) performance measure. We identify responsiveness as the most
frequently occurring performance criterion and are interested in technological
performance criteria to analyze a vaccine production system. Vaccines need to
be distributed in a fair way. Exploring the research field of humanitarian logistics reveals a few value performance criteria for fairly distributing humanitarian
aid when limited supply is available. We also observe that researchers presented
so-called green SCND models in the past five years. These papers impose an
ecological value criterion for the design of a supply chain network.
Imposing multiple performance criteria requires multi-criteria decision making methods. A substantial body of the relevant literature reveals multi-objective
optimization as the most popular modeling technique to deal with multiple criteria and identifies the epsilon constraint method and evolutionary algorithms
as the most frequently used solution techniques. We also observe that both single criterion and multi-criteria models are often nonlinear. The overwhelming
literature on SCND are extensions of the classical facility location problems,
which are already NP-hard problems. The computational complexity motivates researchers to develop decomposition techniques (Lagrangian relaxation)
and improvement heuristics (evolutionary algorithms) to decrease computation
times.
Our future research aims to be implemented in the vaccine industry and
results of this implementation will be provided. We observe that none of the
studied manuscripts explicitly mentions the results of a real-life implementation.
We briefly illustrated four papers that evaluate the solution of their proposed
methodology, using a real-life application.
54
Acknowledgement
The authors gratefully acknowledge financial support from the GlaxoSmithKline Research Chair on Operations Management.
References
[1] Centers for disease control and prevention. vaccine storage and handling.
http://www.cdc.gov/vaccines/pubs/pinkbook/vac-storage.html.
Accessed: 2014-05-21.
[2] Global polio eradication initiative. http://www.polioeradication.org/. Accessed: 2014-05-21.
[3] Vaccines
europe.
how
are
vaccines
produced?
http://www.vaccineseurope.eu/about-vaccines/key-facts-onvaccines/how-are-vaccines-produced/. Accessed: 2014-05-21.
[4] Who statement on the meeting of the international health regulations
emergency committee concerning the international spread of wild poliovirus. http://www.who.int/mediacentre/news/ statements/2014/polio20140505/en/. Accessed: 2014-05-21.
[5] Amir Ahmadi-Javid and Amir Hossein Seddighi. A location-routing problem with disruption risk. Transportation Research Part E: Logistics and
Transportation Review, 53(0):63–82, 2013.
[6] F. Altiparmak, M. Gen, L. Lin, and T. Paksoy. A genetic algorithm approach for multi-objective optimization of supply chain networks. Computers & Industrial Engineering, 51(1):196–215, 2006.
[7] T. Assi, S. Brown, A. Djibo, B. Norman, J. Rajgopal, J. Welling, S. Chen,
R. Bailey, S. Kone, H. Kenea, D. Connor, A. Wateska, A. Jana, S. Wisniewski, W. Van Panhuis, D. Burke, and B. Lee. Impact of changing the
measles vaccine vial size on niger’s vaccine supply chain: a computational
model. BMC Public Health, 11(1):425, 2011.
55
[8] T. Assi, S. Brown, S. Kone, B. Norman, A., D. Connor, A. Wateska,
J. Rajgopal, R. Slayton, and B. Lee. Removing the regional level from
the niger vaccine supply chain. Vaccine, 31(26):2828–2834, 2013.
[9] T. Assi, K. Rookkapan, J. Rajgopal, V. Sornsrivichai, S. Brown,
J. Welling, B. Norman, D. Connor, S. Chen, R. Slayton, Y. Laosiritaworn, A. Wateska, S. Wisniewski, and B. Lee. How influenza vaccination
policy may affect vaccine logistics. Vaccine, 30(30):4517–4523, 2012.
[10] K. Atkins, E. Shim, V. Pitzer, and A. Galvani. Impact of rotavirus
vaccination on epidemiological dynamics in england and wales. Vaccine,
30(3):552–564, 2012.
[11] N. Azad, H. Davoudpour, G. Saharidis, and M. Shiripour. A new model to
mitigating random disruption risks of facility and transportation in supply
chain network design. The International Journal of Advanced Manufacturing Technology, 70(9-12):1757–1774, 2014.
[12] A. Azaron, K. Brown, S. Tarim, and M. Modarres. A multi-objective
stochastic programming approach for supply chain design considering risk.
International Journal of Production Economics, 116(1):129–138, 2008.
[13] M. Badri. Combining the analytic hierarchy process and goal programming for global facility location-allocation problem. International Journal
of Production Economics, 62(3):237–248, 1999.
[14] B. Beamon. Designing the green supply chain. Logistics Information
Management, 12(4):332–342, 1999.
[15] B. Beamon. Measuring supply chain performance. International Journal
of Operations & Production Management, 19(3):275–292, 1999.
[16] B. Beamon and B. Balcik. Performance measurement in humanitarian
relief chains. The International Journal of Public Sector Management,
21(1):4–25, 2008.
56
[17] J. Beaumont. Location-allocation problems in a plane a review of some
models. Socio-Economic Planning Sciences, 15(5):217–229, 1981.
[18] O. Berman, D. Krass, and M. Tajbakhsh.
A coordinated location-
inventory model. European Journal of Operational Research, 217(3):500–
508, 2012.
[19] E. Bottani and R. Montanari.
Supply chain design and cost analy-
sis through simulation. International Journal of Production Research,
48(10):2859–2886, 2010.
[20] K. Buccieri and S. Gaetz. Ethical vaccine distribution planning for pandemic influenza: Prioritizing homeless and hard-to-reach populations.
Public Health Ethics, 6(2):185–196, 2013.
[21] Y. Cardona-Valdés, A. Álvarez, and D. Ozdemir. A bi-objective supply
chain design problem with uncertainty. Transportation Research Part C:
Emerging Technologies, 19(5):821–832, 2011.
[22] G. Chen, M. Daskin, Z. Shen, and S. Uryasev. The α-reliable mean-excess
regret model for stochastic facility location modeling. Naval Research
Logistics (NRL), 53(7):617–626, 2006.
[23] S. Chen, B. Norman, J. Rajgopal, T. Assi, B. Lee, and S. Brown. A
planning model for the who-epi vaccine distribution network in developing
countries. IIE Transactions, 46(8):853–865, 2014.
[24] S. Chick, H. Mamani, and D. Simchi-Levi. Supply chain coordination and
influenza vaccination. Operations Research, 56(6):1493–1506, 2008.
[25] M. Christopher and H. Peck. Building the resilient supply chain. International Journal of Logistics Management, 15:1–13, 2004.
[26] R. Church and C. ReVelle. The maximal covering location problem. Papers of the Regional Science Association, 32(1):101–118, 1974.
57
[27] L. Cooper. Location-allocation problems. Operations Research, 11(3):331–
343, 1963.
[28] J. Current, H. Min, and D. Schilling. Multiobjective analysis of facility
location decisions. European Journal of Operational Research, 49(3):295–
307, 1990.
[29] M. Daskin. Network and Discrete Location: Models, Algorithms, and
Applications. Wiley, New York, 1995.
[30] M. Daskin and L. Dean. Location of health care facilities. In Margaret L.
Brandeau, Frans Sainfort, and William P. Pierskalla, editors, Operations
Research and Health Care, volume 70 of International Series in Operations
Research & Management Science, pages 43–76. Springer US, 2004.
[31] M. Daskin, S. Hesse, and C. Revelle. α-reliable p-minimax regret: A new
model for strategic facility location modeling. Location Science, 5(4):227–
246, 1997.
[32] M. Daskin, L. Snyder, and R. Berger. Facility location in supply chain
design. In André Langevin and Diane Riopel, editors, Logistics Systems:
Design and Optimization, pages 39–65. Springer US, 2005.
[33] C. Decouttere and N. Vandaele. A broader view on health care system
design and modelling. FBE Research Report KBI 1323, KU Leuven, Belgium, 2013.
[34] T. Demirel, N. Demirel, and C. Kahraman. Multi-criteria warehouse location selection using choquet integral. Expert Systems with Applications,
37(5):3943–3952, 2010.
[35] M. Dong and F. Chen. Performance modeling and analysis of integrated
logistic chains: An analytic framework. European Journal of Operational
Research, 162(1):83–98, 2005.
58
[36] F. Du and G. Evans. A bi-objective reverse logistics network analysis
for post-sale service. Computers & Operations Research, 35(8):2617–2634,
2008.
[37] S. Elhedhli and F. Gzara. Integrated design of supply chain networks
with three echelons, multiple commodities and technology selection. IIE
Transactions, 40(1):31–44, 2008.
[38] S. Elhedhli and R. Merrick. Green supply chain network design to reduce carbon emissions. Transportation Research Part D: Transport and
Environment, 17(5):370–379, 2012.
[39] G. Eppen. Effects of centralization on expected costs in a multi-location
newsboy problem. Management Science, 25(5):498–501, 1979.
[40] S. Erlebacher and R. Meller. The interaction of location and inventory in
designing distribution systems. IIE Transactions, 32(2):155–166, 2000.
[41] E. Eskigun, R. Uzsoy, P. Preckel, G. Beaujon, S. Krishnan, and J. Tew.
Outbound supply chain network design with mode selection and lead time
considerations. Naval Research Logistics, 54(3):282–300, 2007.
[42] B. Fahimnia, R. Farahani, R. Marian, and L. Luong. A review and critique
on integrated production-distribution planning models and techniques.
Journal of Manufacturing Systems, 32(1):1–19, 2013.
[43] Z. Firoozi, N. Ismail, S. Ariafar, S. Tang, M. Ariffin, and A. Memariani. Distribution network design for fixed lifetime perishable products: A
model and solution approach. Journal of Applied Mathematics, 2013:13
pages, 2013.
[44] M. Fisher. The lagrangian relaxation method for solving integer programming problems. Management Science, 50(12):1861–1871, 2004.
[45] R. Franca, E. Jones, C. Richards, and J. Carlson. Multi-objective stochastic supply chain modeling to evaluate tradeoffs between profit and qual59
ity. International Journal of Production Economics, 127(2):292–299, 2010.
Supply Chain Planning and Configuration in the Global Arena.
[46] G. Gatica, L. Papageorgiou, and N. Shah. Capacity planning under uncertainty for the pharmaceutical industry. Chemical Engineering Research
and Design, 81(6):665–678, 2003.
[47] E. Gebennini, R. Gamberini, and R. Manzini. An integrated productiondistribution model for the dynamic location and allocation problem with
safety stock optimization. International Journal of Production Economics,
122(1):286–304, 2009.
[48] A. Ghaderi, M. Jabalameli, F. Barzinpour, and R. Rahmaniani. An efficient hybrid particle swarm optimization algorithm for solving the uncapacitated continuous location-allocation problem. Networks and Spatial
Economics, 12(3):421–439, 2012.
[49] M. Goetschalckx, C. Vidal, and K. Dogan. Modeling and design of global
logistics systems: A review of integrated strategic and tactical models and
design algorithms. European Journal of Operational Research, 143(1):1–
18, 2002.
[50] J. Gosling, L. Purvis, and M. Naim. Supply chain flexibility as a determinant of supplier selection. International Journal of Production Economics,
128(1):11–21, 2010.
[51] S. Graves and S. Willems. Optimizing strategic safety stock placement in
supply chains. Manufacturing & Service Operations Management, 2(1):68–
83, 2000.
[52] S. Graves and S. Willems. Supply chain design: Safety stock placement
and supply chain configuration. In S.C. Graves and A.G. de Kok, editors, Supply Chain Management: Design, Coordination and Operation,
volume 11 of Handbooks in Operations Research and Management Science, pages 95 – 132. Elsevier, 2003.
60
[53] D. Griffith. Human capital in the supply chain of global firms. Organizational Dynamics, 35(3):251–263, 2006.
[54] I. Grossmann. Enterprise-wide optimization: A new frontier in process
systems engineering. AIChE Journal, 51(7):1846–1857, 2005.
[55] W. Gu, X. Wang, and E. McGregor. Optimization of preventive health
care facility locations. International Journal of Health Geographics, 9,
2010.
[56] G. Guillén, F Mele, M. Bagajewicz, A. Espuña, and L. Puigjaner. Multiobjective supply chain design under uncertainty. Chemical Engineering
Science, 60(6):1535–1553, 2005.
[57] G. Guillén-Gosálbez and I. Grossmann. Optimal design and planning of
sustainable chemical supply chains under uncertainty. AIChE Journal,
55(1):99–121, 2009.
[58] L. Haidari, D. Connor, A. Wateska, S. Brown, L. Mueller, B. Norman,
M. Schmitz, P. Paul, J. Rajgopal, J. Welling, J. Leonard, S. Chen, and
B. Lee. Augmenting transport versus increasing cold storage to improve
vaccine supply chains. PLoS ONE, 8(5)(5):e64303, 05 2013.
[59] S. Hamedani, M. Jabalameli, and A. Bozorgi-Amiri. A location-inventory
model for distribution centers in a three-level supply chain under uncertainty. International Journal of Industrial Engineering Computations,
4(1):93–110, 2013.
[60] S. Hamedani, M. Jabalameli, and A. Bozorgi-Amiri. A multi-objective
model for locating distribution centers in a supply chain network considering risk and inventory decisions. Management Science Letters, 3(4):1077–
1088, 2013.
[61] R. Hammami, Y. Frein, and A. Hadj-Alouane. Supply chain design in the
delocalization context: Relevant features and new modeling tendencies.
International Journal of Production Economics, 113(2):641–656, 2008.
61
[62] R. Hammami, Y. Frein, and A. Hadj-Alouane. A strategic-tactical model
for the supply chain design in the delocalization context: Mathematical
formulation and a case study. International Journal of Production Economics, 122(1):351–365, 2009.
[63] Y. Hinojosa, J. Kalcsics, S. Nickel, J. Puerto, and S. Velten. Dynamic
supply chain design with inventory. Computers & Operations Research,
35(2):373–391, 2008. Part Special Issue: Location Modeling Dedicated to
the memory of Charles S. ReVelle.
[64] M. Inuiguchi and J. Ramı̀k. Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets and Systems,
111(1):3–28, 2000.
[65] M. Inuiguichi, H. Ichihashi, and H. Tanaka. Stochastic versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty.
Kluwer, 1990.
[66] V. Jayaraman. Transportation, facility location and inventory issues in
distribution network design an investigation. International Journal of
Operations & Production Management, 18(5):471–494, 1998.
[67] V. Jayaraman and A. Ross. A simulated annealing methodology to distribution network design and management. European Journal of Operational
Research, 144(3):629–645, 2003.
[68] L. Kerbache and J. Smith. Queueing networks and the topological design
of supply chain systems. International Journal of Production Economics,
91(3):251–272, 2004.
[69] W. Klibi, A. Martel, and A. Guitouni. The design of robust value-creating
supply chain networks: A critical review. European Journal of Operational
Research, 203(2):283–293, 2010.
62
[70] Y. Kristianto, A. Gunasekaran, P. Helo, and Y. Hao. A model of resilient supply chain network design: A two-stage programming with fuzzy
shortest path. Expert Systems with Applications, 41(1):39–49, 2014. 21st
Century Logistics and Supply Chain Management.
[71] S. Kumar and M. Tiwari. Supply chain system design integrated with risk
pooling. Computers & Industrial Engineering, 64(2):580–588, 2013.
[72] S. Lee. Goal programming for decision analysis. Philadelphia, Auerbach,
1972.
[73] S. Lee, G. Green, and C. Kim. A multiple criteria model for the locationallocation problem. Computers & Operations Research, 8(1):1–8, 1981.
[74] A. Levis and L. Papageorgiou. A hierarchical solution approach for multisite capacity planning under uncertainty in the pharmaceutical industry.
Computers & Chemical Engineering, 28(5):707–725, 2004.
[75] R. Li, H. Lan, and J. Mawhinney. A review on deteriorating inventory
study. Journal of Service Science and Management, 3(1):117–129, 2010.
[76] K. Lieckens and N. Vandaele.
Reverse logistics network design with
stochastic lead times. Computers & Operations Research, 34(2):395–416,
2007.
[77] K. Lieckens and N. Vandaele. Multi-level reverse logistics network design under uncertainty. International Journal of Production Research,
50(1):23–40, 2012.
[78] M. Lim, M. Daskin, A. Bassamboo, and S. Chopra. A facility reliability
problem: Formulation, properties, and algorithm. Naval Research Logistics (NRL), 57(1):58–70, 2010.
[79] Y. Lin, R. Batta, P. Rogerson, A.Blatt, and M. Flanigan. A logistics
model for emergency supply of critical items in the aftermath of a disaster.
Socio-Economic Planning Sciences, 45(4):132–145, 2011.
63
[80] P. Longinidis and M. Georgiadis. Integration of financial statement analysis in the optimal design of supply chain networks under demand uncertainty. International Journal of Production Economics, 129(2):262–276,
2011.
[81] B. MacCarthy and W. Atthirawong. Factors affecting location decisions
in international operations a delphi study. International Journal of Operations & Production Management, 23(7):794–818, 2003.
[82] A. Madadi, M. Kurz, S. Mason, and K. Taaffe. Supply chain network
design heuristics for capacitated facilities under risk of supply disruptions.
2012.
[83] H. Mamani, S. Chick, and D. Simchi-Levi. A game-theoretic model of
international influenza vaccination coordination. Management Science,
59(7):1650–1670, 2013.
[84] M. Meixell and V. Gargeya. Global supply chain design: A literature review and critique. Transportation Research Part E: Logistics and Transportation Review, 41(6):531–550, 2005.
[85] M. Melo, S. Nickel, and F. Saldanha da Gama. A tabu search heuristic for
redesigning a multi-echelon supply chain network over a planning horizon.
International Journal of Production Economics, 136(1):218–230, 2012.
[86] P. Meyer and M. Roubens. On the use of the choquet integral with fuzzy
numbers in multiple criteria decision support. Fuzzy Sets and Systems,
157(7):927–938, 2006.
[87] P. Miranda and R. Garrido. Valid inequalities for lagrangian relaxation
in an inventory location problem with stochastic capacity. Transportation
Research Part E: Logistics and Transportation Review, 44(1):47–65, 2008.
[88] S. Mousavi and S. Niaki. Capacitated location allocation problem with
stochastic location and fuzzy demand: A hybrid algorithm. Applied Mathematical Modelling, 37(7):5109–5119, 2013.
64
[89] J. Mula, D. Peidro, M. Dı́az-Madroñero, and E. Vicens. Mathematical
programming models for supply chain production and transport planning.
European Journal of Operational Research, 204(3):377–390, 2010.
[90] A. Murray and T. Grubesic. Critical infrastructure reliability and vulnerability. Berlin; New York: Springer, 2007.
[91] A. Naimi Sadigh, H. Fallah, and N. Nahavandi. A multi-objective supply
chain model integrated with location of distribution centers and supplier
selection decisions. The International Journal of Advanced Manufacturing
Technology, 69(1-4):225–235, 2013.
[92] S. Narula.
Hierarchical location-allocation problems: A classification
scheme. European Journal of Operational Research, 15(1):93–99, 1984.
[93] L. Nozick and M. Turnquist. Integrating inventory impacts into a fixedcharge model for locating distribution centers. Transportation Research
Part E: Logistics and Transportation Review, 34(3):173–186, 1998.
[94] L. Nozick and M. Turnquist. Inventory, transportation, service quality
and the location of distribution centers. European Journal of Operational
Research, 129(2):362–371, 2001.
[95] L. Nozick and M. Turnquist. A two-echelon inventory allocation and distribution center location analysis. Transportation Research Part E: Logistics
and Transportation Review, 37(6):425–441, 2001.
[96] E. Olivares-Benitez, J. González-Velarde, and R. Rı́os-Mercado. A supply
chain design problem with facility location and bi-objective transportation
choices. TOP, 20(3):729–753, 2012.
[97] M. Ortuño, G. Tirado, and B. Vitoriano. A lexicographical goal programming based decision support system for logistics of humanitarian
aid. TOP, 19(2):464–479, 2011.
65
[98] L. Ozsen, C. Coullard, and M. Daskin. Capacitated warehouse location
model with risk pooling. Naval Research Logistics (NRL), 55(4):295–312,
2008.
[99] L. Ozsen, M. Daskin, and C. Coullard.
Facility location modeling
and inventory management with multisourcing. Transportation Science,
43(4):455–472, 2009.
[100] T. Paksoy, N.i Pehlivan, and E. Özceylan. Fuzzy multi-objective optimization of a green supply chain network with risk management that includes
environmental hazards. Human and Ecological Risk Assessment: An International Journal, 18(5):1120–1151, 2012.
[101] T. Paksoy, E. Özceylan, and G. Weber. A multi objective model for optimization of a green supply chain network. AIP Conference Proceedings,
1239(1):311–320, 2010.
[102] L. Papageorgiou, G. Rotstein, and N. Shah. Strategic supply chain optimization for the pharmaceutical industries. Industrial & Engineering
Chemistry Research, 40(1):275–286, 2001.
[103] C. Pappis and N. Karacapilidis. Applying the service level criterion in a
location-allocation problem. Decision Support Systems, 11(1):77–81, 1994.
[104] S. Park, T. Lee, and C. Sung. A three-level supply chain network design
model with risk-pooling and lead times. Transportation Research Part E:
Logistics and Transportation Review, 46(5):563–581, 2010.
[105] F. Persson and J. Olhager. Performance simulation of supply chain designs. International Journal of Production Economics, 77(3):231–245,
2002.
[106] M. Pishvaee, R. Farahani, and W. Dullaert. A memetic algorithm for biobjective integrated forward/reverse logistics network design. Computers
& Operations Research, 37(6):1100–1112, 2010.
66
[107] M. Pishvaee and S. Torabi. A possibilistic programming approach for
closed-loop supply chain network design under uncertainty. Fuzzy Sets
and Systems, 161(20):2668–2683, 2010.
[108] L. Qi and Z. Shen. A supply chain design model with unreliable supply.
Naval Research Logistics (NRL), 54(8):829–844, 2007.
[109] S. Rahman and D. Smith. Use of location-allocation models in health
service development planning in developing nations. European Journal of
Operational Research, 123(3):437–452, 2000.
[110] H. Rajabalipour Cheshmehgaz, M. Desa, and A. Wibowo. A flexible threelevel logistic network design considering cost and time criteria with a
multi-objective evolutionary algorithm. Journal of Intelligent Manufacturing, 24(2):277–293, 2013.
[111] J. Rice and F. Caniato. Building a secure and resilient supply network.
Supply Chain Management Review, pages 22–30, 2003.
[112] R. Rozek. Risk and regulatory factors affecting location decisions by
research-based pharmaceutical companies. European Journal of Risk Regulation, 1:92–103, 2011.
[113] E. Sabri and B. Beamon.
A multi-objective approach to simultane-
ous strategic and operational planning in supply chain design. Omega,
28(5):581–598, 2000.
[114] H. Sadjady and H. Davoudpour. Two-echelon, multi-commodity supply
chain network design with mode selection, lead-times and inventory costs.
Computers & Operations Research, 39(7):1345–1354, 2012.
[115] A. Sarmiento and R. Nagi. A review of integrated analysis of productiondistribution systems. IIE Transactions, 31(11):1061–1074, 1999.
[116] G. Schmidt and W. Wilhelm. Strategic, tactical and operational decisions
in multi-national logistics networks: A review and discussion of modelling
67
issues. International Journal of Production Research, 38(7):1501–1523,
2000.
[117] A. Scott. Location-allocation systems: A review. Geographical Analysis,
2(2):95–119, 1970.
[118] N. Shah. Pharmaceutical supply chains: key issues and strategies for
optimisation. Computers & Chemical Engineering, 28(6-7):929–941, 2004.
[119] N. Shah. Process industry supply chains: Advances and challenges. Computers & Chemical Engineering, 29(6):1225–1236, 2005.
[120] B. Shankar, S. Basavarajappa, J. Chen, and R. Kadadevaramath. Location and allocation decisions for multi-echelon supply chain network - a
multi-objective evolutionary approach. Expert Systems with Applications,
40(2):551–562, 2013.
[121] B. Shankar, S. Basavarajappa, R. Kadadevaramath, and J. Chen. A biobjective optimization of supply chain design and distribution operations
using non-dominated sorting algorithm: A case study. Expert Systems
with Applications, 40(14):5730–5739, 2013.
[122] S. Shariff, N. Moin, and M. Omar. Location allocation modeling for healthcare facility planning in malaysia. Computers & Industrial Engineering,
62(4):1000–1010, 2012.
[123] Z. Shen. Integrated supply chain design models: A survey and future
research directions. Journal of Industrial and Management Optimization,
3(1):1–27, 2007.
[124] Z. Shen, C. Coullard, and M. Daskin. A joint location-inventory model.
Transportation Science, 37(1):40–55, 2003.
[125] Z. Shen and M. Daskin. Trade-offs between customer service and cost
in integrated supply chain design. Manufacturing & Service Operations
Management, 7(3):188–207, 2005.
68
[126] J. Smith, M. Lipsitch, and J. Almond. Vaccine production, distribution,
access, and uptake. The Lancet, 378(9789):428–438, 2011.
[127] L. Snyder and M. Daskin. Reliability models for facility location: The
expected failure cost case. Transportation Science, 39(3):400–416, 2005.
[128] L. Snyder, M. Daskin, and C. Teo. The stochastic location model with risk
pooling. European Journal of Operational Research, 179(3):1221–1238,
2007.
[129] K. Sourirajan, L.Ozsen, and R. Uzsoy. A genetic algorithm for a single
product network design model with lead time and safety stock considerations. European Journal of Operational Research, 197(2):599–608, 2009.
[130] K. Sourirajan, L. Ozsen, and R. Uzsoy. A single-product network design
model with lead time and safety stock considerations. IIE Transactions,
39(5):411–424, 2007.
[131] S. Srivathsan and M. Kamath. An analytical performance modeling approach for supply chain networks. IEEE Transactions on Automation
Science and Engineering,, 9(2):265–275, 2012.
[132] M. SteadieSeifi, N. Dellaert, W. Nuijten, T. Van Woensel, and R. Raoufi.
Multimodal freight transportation planning: A literature review. European Journal of Operational Research, 233(1):1–15, 2014.
[133] M. Tamiz, D. Jones, and C. Romero. Goal programming for decision
making: An overview of the current state-of-the-art. European Journal of
Operational Research, 111(3):569–581, 1998.
[134] J. Tancrez, J. Lange, and P. Semal. A location-inventory model for large
three-level supply chains. Transportation Research Part E: Logistics and
Transportation Review, 48(2):485–502, 2012.
[135] C. Tang and B. Tomlin. The power of flexibility for mitigating supply
chain risks. International Journal of Production Economics, 116(1):12–
27, 2008.
69
[136] G. Tanonkou, L. Benyoucef, and X. Xie. Distribution network design with
random demand and unreliable suppliers. In IEEE International Conference on Automation Science and Engineering, pages 15–20, October 2006.
[137] E. Teimuory, F. Atoei, E. Mohammadi, and A. Amiri. A multi-objective
reliable programming model for disruption in supply chain. Management
Science Letters, 3(5):1467–1478, 2013.
[138] M. Tiwari, N. Raghavendra, S. Agrawal, and S. Goyal. A hybrid taguchiimmune approach to optimize an integrated supply chain design problem with multiple shipping. European Journal of Operational Research,
203(1):95–106, 2010.
[139] J. Torres-Soto and H. Üster. Dynamic-demand capacitated facility location problems with and without relocation. International Journal of
Production Research, 49(13):3979–4005, 2011.
[140] P. Tsiakis and L. Papageorgiou. Optimal production allocation and distribution supply chain networks. International Journal of Production
Economics, 111(2):468–483, 2008. Special Section on Sustainable Supply Chain.
[141] P. Tsiakis, N. Shah, and C. Pantelides. Design of multi-echelon supply chain networks under demand uncertainty. Industrial & Engineering
Chemistry Research, 40(16):3585–3604, 2001.
[142] G. Tzeng, H. Cheng, and T. Huang. Multi-objective optimal planning
for designing relief delivery systems. Transportation Research Part E:
Logistics and Transportation Review, 43(6):673–686, 2007. Challenges of
Emergency Logistics Management.
[143] B. Vahdani, R. Tavakkoli-Moghaddam, and F. Jolai. Reliable design of a
logistics network under uncertainty: A fuzzy possibilistic-queuing model.
Applied Mathematical Modelling, 37(5):3254–3268, 2013.
70
[144] V. Verter and S. Lapierre. Location of preventive health care facilities.
Annals of Operations Research, 110(1):123–132, February 2002.
[145] C. Vidal and M. Goetschalckx. Strategic production-distribution models:
A critical review with emphasis on global supply chain models. European
Journal of Operational Research, 98(1):1–18, 1997.
[146] N. Vidyarthi, E. Çelebi, S. Elhedhli, and E. Jewkes.
Integrated
production-inventory-distribution system design with risk pooling: model
formulation and heuristic solution. Transportation science, 41(3):392–408,
August 2007.
[147] B. Vitoriano, M. Ortuño, and G. Tirado. Hads, a goal programming-based
humanitarian aid distribution system. Journal of Multi-Criteria Decision
Analysis, 16(1-2):55–64, 2009.
[148] B. Vitoriano, M. Ortuño, G. Tirado, and J. Montero. A multi-criteria
optimization model for humanitarian aid distribution. Journal of Global
Optimization, 51(2):189–208, 2011.
[149] F. Wang, X. Lai, and N. Shi. A multi-objective optimization for green
supply chain network design. Decision Support Systems, 51(2):262–269,
2011. Multiple Criteria Decision Making and Decision Support Systems.
[150] D. Word, D. Cummings, D. Burke, S. Iamsirithaworn, and C. Laird. A
nonlinear programming approach for estimation of transmission parameters in childhood infectious disease using a continuous time model. Journal
Of The Royal Society Interface, 9(73):1983–1997, 2012.
[151] Z. Yao, L. Lee, W. Jaruphongsa, V. Tan, and C. Hui. Multi-source facility
location-allocation and inventory problem. European Journal of Operational Research, 207(2):750–762, 2010.
[152] S. Yazdian and K. Shahanaghi. A multi-objective possibilistic programming approach for locating distribution centers and allocating customers
71
demands in supply chains. International Journal of Industrial Engineering
Computations, 2(1):193–202, 2011.
[153] F. You and I. Grossmann. Optimal Design and Operational Planning of
Responsive Process Supply Chains, pages 107–134. Wiley-VCH Verlag
GmbH & Co. KGaA, 2007.
[154] F. You and I. Grossmann. Design of responsive supply chains under demand uncertainty. Computers & Chemical Engineering, 32(12):3090–3111,
2008.
[155] F. You and I. Grossmann. Mixed-integer nonlinear programming models and algorithms for large-scale supply chain design with stochastic
inventory management. Industrial & Engineering Chemistry Research,
47(20):7802–7817, 2008.
[156] F. You and I. Grossmann. Integrated multi-echelon supply chain design
with inventories under uncertainty: Minlp models, computational strategies. AIChE Journal, 56(2):419–440, 2010.
[157] F. You and I. Grossmann. Balancing responsiveness and economics in process supply chain design with multi-echelon stochastic inventory. AIChE
Journal, 57(1):178–192, 2011.
[158] F. You and I. Grossmann. Stochastic inventory management for tactical process planning under uncertainties: Minlp models and algorithms.
AIChE Journal, 57(5):1250–1277, 2011.
[159] M. Zaffran, J. Vandelaer, D. Kristensen, B. Melgaard, P. Yadav, K. AntwiAgyei, and H. Lasher. The imperative for stronger vaccine supply and
logistics systems. Vaccine, 31S(0):B73–B80, 2013. Decade of Vaccines.
[160] F. Zahedi. The analytic hierarchy process: A survey of the method and
its applications. Interfaces, 16(4):96–108, 1986.
72
[161] L. Zhang, S. Wang, F. Li, H. Wang, L. Wang, and W. Tan. A few measures
for ensuring supply chain quality. International Journal of Production
Research, 49(1):87–97, 2011.
[162] J. Zhou and B. Liu. Modeling capacitated location–allocation problem
with fuzzy demands. Computers & Industrial Engineering, 53(3):454–468,
2007.
73
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