The Design of a Responsive Sustainable Supply Chain Network
under Uncertainty
RameshwarDubey
Symbiosis Institute of Operations Management
(Constituent of Symbiosis International University)
Plot No. A-23,Shravan Sector
CIDCO
New Nashik-422008
India
E-mail: [email protected]
AngappaGunasekaran*
Charlton College of Business
University of Massachusetts Dartmouth
North Dartmouth, MA 02747-2300
USA
E-mail: [email protected]
Stephen J Childe
College of Engineering, Mathematics and Physical Sciences
University of Exeter
Harrison Building
EXETER
EX4 4QF
United Kingdom
Tel +44 1392 723653
E-mail: [email protected]
* Corresponding author
Submitted date: 16th October, 2014
Final acceptance: 24th February, 2015
2
The Design of a Responsive Sustainable Supply Chain Network
under Uncertainty
Abstract
There is growing interest among researchers in the concept of
sustainability.
Large
commercial
corporations
have
also
shown
responsibility for preserving planet and people while maintaining profit.
Our present paper is motivated by the three P’s People, Planet and
Profit. In our paper we have attempted to develop a responsive
sustainable supply chain network which can respond to a certain
degree of uncertainty due to uncontrollable forces. We have developed a
model using robust optimization based on three well-known robust
counterpart optimization formulations. Finally, this paper compares the
results of the three formulations using different test scenarios and
parameter-sensitive analysis in terms of final output, CPU time, and the
level of conservatism, the degree of closeness to the ideal solution, the
degree of balance involved in developing a compromise solution, and
satisfaction degree. Two further questions related to environmental
dimensions and social dimensions have been investigated using an
appreciative inquiry, a quasi-ethnographic study. In this way, we have
embraced mixed research design to address our research questions. We
have extended past research by incorporating uncertainty in a MixedInteger Linear Programming (MILP) model and qualitative research
methods to fill the voids. We have concluded our research with
limitations of our present study and outlined further research
directions.
Keywords: Responsive Supply Chain, Supply Chain Network Design, Closed
Loop Supply Chain, Robust Optimization, Case Research,
Appreciative Inquiry, Sustainable Supply Chain Network.
3
1
Introduction
In a globalized era where firms are focusing on optimizing product quality
and product cost, the average distance between markets and manufacturing
units has increased. For the last two decades we have seen increasing trends
among western countries to shift their manufacturing units from countries like
China, Malaysia, Vietnam, India to other Asian countries due to low cost of
production per unit. In recent years there has been increased competition
among these countries to attract Foreign Direct Investment (FDIs) as well as
conforming to global standards like stringent environmental norms, high
product quality and contribution to society. There is increased focus on
integrating forward and reverse logistics to reduce cost and decrease carbon
emissions in the entire supply chain network. Forward logistics encompasses
material supply, production, distribution, and consumption (Krikke et al.,
2003). In reverse logistics, the flow of used products includes the collection of
used products or products rejected due to failure, product inspection, parts
separation, parts recovery, waste disposal, and redistribution (Fleischmann et
al., 2001). The entire loop including forward production and reverse logistics is
known as a closed loop supply chain (CLSC).
In recent years, supply chain network design has attracted enormous
interest among academics and practitioners. However, there is lack of
consensus on sustainable supply chain network design (Melnyk et al., 2009;
Melnyk et al., 2013).
In real life, designing the sustainable supply chain
network is an herculean task which is driven by multiple and conflicting
objectives like maximizing supply chain surplus, reducing carbon emissions,
improving
supply
chain
network
reliability,
improving
supply
chain
responsiveness, improving supply chain flexibility and reducing the impacts of
supply chain risk (Nagurney and Nagurney, 2010; Nagurney, 2010). The life
cycle of products is getting shorter day by day and ever increasing customers’
expectations are the real challenges facing the designers of supply chain
networks that can increase customer satisfaction by providing fresh products
4
and minimize the cost. Optimizing such a network, in order to trade-off
between objectives, is not compatible with traditional methods.
Designing a closed loop supply chain network are made more difficult
where demand and supply are highly uncertain. As an alternative, the robust
optimization approach produces an uncertainty-immunized solution to an
optimization problem with uncertain data. Therefore the main objective of our
paper is to design a responsive sustainable supply chain network under
uncertainty.
From our objective, we have derived following research questions:
RQ1: What is the current state of research in closed loop supply chain network
design?
RQ2: How can the uncertainty dimension be included in a deterministic model?
RQ3: How environmental benefits be captured?
RQ4: How can social issues related to sustainable responsive supply chain
network be addressed?
RQ4: What are the options available for quantifying uncertainty in our model?
The paper is organized as follows. In this section we have outlined our
research strategies for answering research questions. The third section
provides a comprehensive review of literature on responsive supply chain,
sustainable supply chain, applications of operations research (OR) in supply
chain network design and identifies research gaps. The fourth section deals
with our case research and developed our theoretical model. The fifth section
discusses the various robust optimization techniques. The sixth section
presents the appreciative inquiry technique which we have used in our
research. Finally we have concluded our research findings and outlined the
limitations of our study and future research directions.
5
2. Research Strategy
To answer our research questions, as outlined in preceding section we adopt
both rationalist approach and qualitative research approach to answer first
three research questions. Dubey and Gunasekaran (2015) have attempted to
develop a sustainable supply chain network. However, that study did not
include social dimensions in their model. Second they have included only
carbon emissions for capturing environmental performance. We further argue
in our study that environmental performance should not be limited to carbon
emissions. In the model we need to embrace perspectives such as water
preservation, preservation of trees, recycling, reuse, remanufacture of products
after use. Third social perspectives in which we explore ethical practices in
supply chain network toward labor and the community.
To answer our first question we adopt extensive literature review. Seuring
et al. (2005) have argued that the literature review is an appropriate strategy
which fulfills two key functions. First, it summarizes the existing state of the
art of the current field of study. Second, to answer the question related to
“what?” the literature review helps to enfold the current literature against the
existing knowledge and theories.
To address our second research question which is hard pressed. Due to
globalization the level of uncertainty in demand and supply has increased.
Hence to address second research question we have adopt two prong strategies.
First, an extensive literature review to identify research gaps in current
literature and to further extend a rationalist approach is adopted.
The third and fourth research questions are the missing link in current
literature. In past researchers have attempted to factor in the carbon emission
factor in the objective function. However as we have argued that carbon
emission is only one perspective of environmental concerns. Second the social
issues were not addressed in past in empirical literature which have used
rationalist approach. Recently the operations management community has
realized the limitations of the rationalist approach (e.g. Voss et al. 2002;
6
Childe, 2011; Ketokivi and Choi, 2014). Hence they have suggested case
research approach to address questions which rationalist approach has failed
to offer (Markman and Krause, 2014). Ketokivi and Krause (2014) have argued
that in recent year’s operations management researchers have increasingly
embracing case research method. However, there are several shortcomings in
current case based studies. We further argue that there are other existing
qualitative research methods which can bridge the existing gaps which we see
in current case based research. Hence we propose to approaches to answer our
third and fourth research questions. First we will validate our model using data
gathered from an Indian based organization and to further draw insight into
current environmental friendly practices and ethical practices we adopt
appreciative inquiry (AI).
To answer our first research question, we have undertaken an extensive
literature review as discussed in our next section.
3. Literature Review
We consider the design of supply chain networks from the point of view of
responsiveness.
We introduce the concept of sustainability in supply chain
network management, and look at the development of thinking on the closedloop supply chain.
3.1 Responsive Supply Chain Network Design
In recent years the responsive supply chain has attracted a lot of interest
among academia and practitioners. According to Fisher (1997), the responsive
supply chain is designed to move innovative products which have many
product variants, short product life cycles and high forecast error. Lee (2002)
defined responsive supply chain network design as the ability of a supply chain
network which enables the supply chain to respond to high demand
uncertainties. However, in responsive (to demand) supply chain network design
the supply uncertainty is assumed to be low. The responsive supply chain is
regarded as a networked economy strategy as pointed out by Gunasekaran et
al. (2008). However in spite of so many definitions, we found a simple definition
which defines responsive supply chain as the ability of a supply chain to
7
respond quickly to changes in demand, in terms of both volume and mix of
products (Christopher, 2000; Holweg, 2005). You and Grossmann (2008) tried
to analyze the responsive supply chains under uncertainty using a quantitative
model. In our paper we have attempted to extend the work using robust
optimization.
3.2 Evolution of sustainable supply chain management and practices
In recent years, sustainable supply chain management and practices have
attracted huge interest among academia and practitioners. There are some
cases which have indicated how a company has earned huge profitability,
through sustainable supply chain practices, such as Wal-Mart, Nike, IKEA,
Boeing, CISCO, Siemens, Nestle, Herman Miller, Holcim, Lafarge, Dell and
many others. In the early 2000s, supply chain network design was guided by
single objective, i.e. to reduce supply cost or to maximize supply chain surplus
(e.g. Simpson et al., 2007; Sarkis et al., 2011).
However, due to rapid change in climate and increased awareness among
customers the firms have now embraced sustainability as one of their goals
(Naustdalslid, 2011) under institutional pressures such as coercive pressure,
peer pressure or mimetic pressure (Gavronski et al., 2008; Guide Jr. and van
Wassenhove, 2009; Gunasekaran and Spalanzani, 2012). Lee (2010) suggested
that sustainability as a guiding philosophy involves each member of the supply
chain network. The benefits of a sustainability program revolve around
innovation, collaboration and transparency (Schifrin et al., 2013). Plambeck et
al. (2013) reflected the experience of some companies who have achieved
superior environmental performance, with proper incentive alignment and
collaboration. However, the objective is not only to improve environmental
performance. Carter and Rogers (2008), in their seminal paper, extended the
“green supply chain management” concept to “sustainable supply chain
management (SSCM)” in which sustainability can only be achieved by finding
an optimal balance between three objectives, “profit, planet and people”.
In
8
Table 1 we have identified some of the recent works, related to sustainable
supply chain management (SSCM) practices and their characteristics.
Table 1: Sustainable Supply Chain Management Practices
Reference
SSCM practices
Amann et al. (2014)
Public procurement enterprises who have integrated
social and environmental parameters in their
procurement policies, have experienced better
sustainability.
Ortas et al. (2014)
Sustainability should not be simply viewed as a CSR
activity; rather it is a tool for gaining competitive
advantage over competitors.
Clark et al. (2014)
Sustainability is defined in terms of market
orientation, green purchasing and logistics
performance.
Coordination among supply chain actors or partners
is important for achieving sustainability, i.e. social,
economic and environmental performance.
A firm can outperform their competitors in terms of
sustainability by implementing four checklists as:
 Sourcing checklist;
 Manufacturing checklist;
 Distribution checklist;
 Consumption checklist;
Sustainability can be achieved by protecting forests.
Supply chain network design must consider
responsibility towards the natural environment.
Supply chain sustainability cab be achieved
through:
 Alignment;
 Collaboration;
 Transparency.
Sustainable operational practices can be defined as
operations strategies, tactics and techniques, and
operational policies to support both economic and
environmental objectives and goals.
Optimizing energy consumption in a closed loop
supply chain network is one of the way of achieving
sustainability.
The participation of suppliers is an important
antecedent of sustainable supply chain management.
The sustainable supply chain considers both
economic and carbon emissions as important
dimensions.
d’Angelo and Brunstein (2014)
Lowitt (2014)
Bennett-Curry et al. (2013)
Plambeck et al. (2013)
Gunasekaran et al. (2013)
Jain et al. (2013)
Caniels et al. (2013)
Chaabane et al. (2012)
9
Ageron et al. (2012)
Gunasekaran and Spalanzani,
(2012)
Proposed a sustainable business development
framework.
A sustainable development framework for both
manufacturing and services sectors. Sustainability is
regarded as an integration of product design, sourcing
& purchasing, production or operations, distribution
and managing reverse logistics.
The above table presents a non-exhaustive list of recent articles from
reputable journals. Sustainability can be now perceived as an organizational
philosophy. We can conclude that the concept of the sustainable supply chain
has evolved from convergence of the ideas of supply chain and sustainability.
3.3 The evolution of closed loop supply chain network (CLSC)
In recent years, the subject of sustainable network design has attracted lot of
attention from OR professionals both academia and consultants (Tang and
Zhou, 2012). In recent years European Journal of Operational Research,
Journal of the Operational Research Society, Annals of Operations Research
and Computers and Operations Research have published dedicated special
issues and some journals are yet to come out with their special issues on the
sustainability theme.
The concept of CLSC is not new but the nomenclature is barely 15 years
old. Corominas (2013), argues that SCM is as old as human civil civilization,
but the formal name was only coined in 1981. Similarly, CLSC was used in
past literature e.g. (Thierry et al., 1995; Guide Jr. and Srivastava, 1998; Shear
et al., 2002; Souza et al., 2002), however the concept of CLSC has mainly
attracted the serious attention of academia after the seminal contributions of
Savaskan et al. (2004) and Guide Jr. and van Wassenhove (2006).
Guide Jr.and van Wassenhove (2009) defined CLSC as the design, control,
and operation of a system to maximize value creation over the entire life cycle of
a product with dynamic recovery of value from different types and volumes of
returns over time. The definition focuses on the maximization of value recovery,
which is only an economic perspective. Neither did the definition consider the
environmental dimension or the social perspective. In recent years, CLSC
10
network design and its convergence with sustainability has attracted lot of
contributions (e.g. Zarandi et al. 2011; Soleimani et al. 2013). Supply chain
network design has attracted huge attraction from academia and practitioners,
due to supply chain risks resulting from market volatility and natural
disasters. Zipkin (2012) & Naslud and Williamson (2010) were both pessimistic
about supply chain and the way the subject has been dealt with in recent
years. Corominas (2013), argued that supply chain or SCM should be replaced
by a more comprehensive term, “supply chain network” together with “supply
chain network management”.
3.4 Operational Research in sustainable supply chain network design
We have reviewed articles prior to the time of writing (2014), to understand
the recent use of operations research (OR) tools in sustainable supply chain
network design. A summary of this literature is presented in Table 2.
Table 2: Operations Research in sustainable supply chain network design
Reference
Dubey
and
Techniques
Gunasekaran
(2015)
Used Mixed Integer Linear Programming (MILP) to develop
sustainable supply chain network to address multiple objectives
using goal programming techniques.
In this paper the researcher has used interactive fuzzy multi-
Mirakhorli (2014)
objective linear programming (IFMOLP) method to solve fuzzy biobjective reverse logistics network design problems.
Govindan et al. (2014)
The barriers to green supply chain management implementation
are further analyzed using Analytic Hierarchy Process (AHP).
Reviews mathematical models focusing on environmental and
Brandenburg et al. (2014)
social factors in the forward supply chains. Concluded that AHP,
ANP and LCA were commonly used tools for developing the models.
Mathiyazhagan et al. (2014)
Muduli et al. (2013)
The barriers are further analyzed using AHP process.
In this article researchers used Graph Theory and Matrix Approach
(GTMA).
de Sousa et al.(2013)
Statistical analysis
Muduli et al. (2013a)
ISM methodology
11
Yusuf et al. (2013)
Chaabane et al.(2012)
Zailani et al.(2012)
De Giovanni and Vinzi
(2012)
Kannan et al. (2012)
Rahman and Subramanian
(2012)
Statistical analysis
Mixed Integer Linear Programming (MILP)
Statistical analysis
Statistical analysis
Mixed integer linear program model
DEMATEL ( a cognitive mapping process)
The competitive supply chain model for fashion firms is network-
Nagurney and Yu (2012)
based and variational inequality theory is utilized for the
formulation of the governing Nash equilibrium as well as for the
solution of the case study examples.
Amin and Zhang (2012)
Govindan et al. (2010)
Mixed Integer Linear Programming (MILP)
Genetic algorithm applied to MILP problem
Govindan et al. (2010) pointed out the growing importance among firms of
reducing carbon emissions using “Green” SCM practices. According to Zhu and
Sarkis (2006), environmental impacts at all stages of a product’s life cycle from
raw material extraction to environmentally friendly disposal of the product after
consumption can be achieved through adopting a closed loop supply chain
(CLSC) network. Andic et al. (2012) suggested the CLSC network was highly
suitable as a bi-objective problem which involves striking balance between
profit and environmental performance. The emerging concept of supply chain
sustainability required an identification of the closed-loop supply chain model
(Frota Neto et al. 2008; Solvang and Hakam, 2010). One of the objectives of
sustainable supply chain design is to accommodate the needs of future
generations (Wilkinson et al. 2001).
3.5 Research Gaps
In many papers, the minimization of total costs is treated as a single
objective by summing the different types of costs according to the set of
decisions modeled. In contrast, multi-objective approaches have received much
less attention from researchers. Most of them use fuzzy goal programming as a
12
whole or part of their solution approach (Lee et al. 2007; Pishvaee and Torabi,
2010; Vahdani et al., 2012). Pishvaee et al. (2010) and Ramezani et al. (2013)
obtained a set of solutions by using, respectively, a memetic algorithm and the
 -constraint method to deal with a multi-objective problem.
The deterministic model is the most common framework used by
researchers in past (e.g. Marin and Pelegrin 1998; Jayaraman et al. 1999;
Fleischmann et al. 2001; Krikke et al. 2003; Lu and Bostel 2007; Ko and Evans
2007; Min and Ko 2008; Lee and Dong 2008; Easwaran and Uster 2009; Wang
and Hsu 2010; Zarei et al. 2010; Easwaran and Uster 2010). Recently, because
of the significance of uncertainty, more researchers have incorporated
uncertain parameters into CLSC networks. Lee et al. (2007) explored a
stochastic approach for a dynamic and multi-product problem. To solve the
proposed
model,
a
solution
approach
integrating
a
sample
average
approximation method with a simulated annealing-based heuristic algorithm
was
developed.
Listes
(2007)
developed
a
generic
stochastic
integer
programming model to solve a problem involving uncertainties in reverse
logistics network. Lee et al. (2010) presented a two-stage stochastic model that
accounts for a number of alternative scenarios. The model was constructed
based on stochastic demand and used products with known distribution. Wang
and Hsu (2010) proposed a generalized model in which stochastic demand, the
reusable rate of used products, and the disposal rate were all expressed by
fuzzy numbers. Pishvaee et al. (2009 & 2011) developed CLSC networks in a
stochastic programming and a robust counterpart optimization formulation,
respectively. In 2010, a mixed integer programming model was proposed to
address multi-period closed-loop logistics under uncertainty by Pishvaee and
Torabi (2010). El-Sayed et al. (2010) developed a CLSC network under risk in a
stochastic MILP formulation as a multi-stage stochastic program. Vahdani et
al. (2012) developed a hybrid solution approach by combining Ben-Tal’s robust
optimization, queuing theory, and fuzzy programming to solve a multi-objective
CLSC model.
13
4. Case Research
The research strategies to be adopted in a study depends upon three
fundamental questions: research objectives or research questions, the control
an investigator has over actual behavioral events, and the focus on
contemporary, as opposed to historical, phenomena. However, the first and
most important condition for differentiating among the various research
strategies is to identify the type of research questions being asked (Yin,
1989).The case study method has its strength in its ability to deal with a full
variety of evidence such as documents, artifacts, interviews, and observations
(Yin, 1989).Yin (1989), has further argued that when research question poses
“how” and “why”, then in such situation case research methodology is the most
appropriate strategy (Dubey and Gunasekaran, 2015).
4.1 Case Study Background
ABC Ltd. is a Uttar Pradesh (Indian state) based industrial unit which has been
in the business of manufacturing industrial air conditioners for 20 years. It
started its operation as a small venture catering to local demand and gradually
built its sales volume until becoming the third-largest supplier of industrial air
conditioners in the Delhi-National Capital Region. Rising demand for residential
and commercial infrastructure, including facilities for healthcare, education,
shopping in the vicinity of residential areas has generated a need for more and
more air conditioning units.
Initially the company had only one production center; it now boasts 3
production centers, with its products supplying a large area including Delhi,
Faridabad, Ghaziabad, NOIDA, Gurgaon, Samlakha and Panipat. Of these three
sites, two are big production centers in Ghaziabad and Gurgaon and the third is
a relatively newer setup in Panipat. The cities of Ghaziabad and Gurgaon have
seen tremendous industrial growth since the last ten years and it is sensible for
the organization to have major production centers in these areas, while the
Panipat center is focused on supplying the neighboring states of Punjab and
Himachal for future growth. The organization has seven major distribution
14
organizations spread across the entire coverage area, with a strong logistics
chain and efficient marketing team for the proper distribution and positioning of
its product. The business has seen tremendous growth and sustainable profits
in recent years.
As the business grew, the issues of logistics and transportation started
giving some trouble to the organization. Since the individual product unit is
expensive and heavy, the organization cannot take the risk of damage, theft or
any other problem, so it has given the responsibility of transporting units from
the production centers to the respective distribution centers to a trusted service
supplier BHL Ltd. The company one has one repair center where attempts are
made to repair the defected or damaged goods. This sometime takes a lot of time
which creates the problem of customer grievance and satisfaction. The company
has a policy “Goods once sold will not be taken back”.
4. 2. Theoretical Model
The model presented in Figure 1 is applied to Air Conditioners in a reverse
logistics network. This case includes many features of practical relevance, such
as a multi-period setting, reverse Bill-of-Materials (BOM), maximum throughput
at the facilities, operational costs are variable, and there are finite demands in
the secondary market. In the multi-period setting, all network design decisions
are taken over a planning horizon which is set regularly either at the beginning
or end of a period. The model (see Figure 1) shows that used products are
collected at collection centers (CC) and sent to reprocessing centers (RPC) for
inspection and dismantling; then inspected components are shipped to sellers as
spare parts, a remanufacturing plant (RMP), a recycling center (RC) or a disposal
site (DS) accordingly.
Missing components for remanufacturing is assumed to be tackled by
purchasing through pre-qualified suppliers. High price difference between the
new and remanufactured product with almost similar quality creates demand for
the remanufactured product. If the number of components available is in excess
15
of demand, they are stored in the remanufacturing point until the next period.
The design of such a network is a strategic matter as it involves decisions on the
number of facilities, their locations and the allocation of the flow of used
products and components at an optimal cost for a given market demand in the
network flows. The network used for the analysis involves eight echelons: CC,
RPC,
RMP,
RC,
remanufactured
DS,
spare
products)
and
parts
markets,
pre-selected
secondary
new
markets
component
(for
suppliers.
Assumptions are as follows:
1. Unlimited numbers of used products are collected at pre-specified
collection centers. No holding cost is incurred as goods collected in each
CC are transported to the reprocessing centers as soon as possible.
2. At the RPC, components are disassembled, cleaned, tested and sorted for
re-use, remanufacture, spare parts, recycling and dismantling operations.
Spares market demands are met by selling spare parts at a high price. The
RPC will recycle or store components until required.
3. Some new components and old components may be required for the
remanufacturing and final assembly of the product at the RMP. There is
an inventory carrying cost for used components while Just-In-Time
delivery is used for new components. CC’s, RPC’s and RMP’s are
considered to have a monthly fixed cost. Transport cost is calculated with
respect to the distance. The cost of new components ordered from preselected suppliers includes transportation cost.
4. Secondary market shortages are assumed to occur with no loss.
5. We consider a decision horizon that includes multi-periods and multiproducts in the proposed model. Regarding cost minimization which
includes setting cost, capacity expansion cost and processing cost and
the second objective is reducing delivery and collection time related to
improving supply chain responsiveness (Ravi et al. 2005).
16
Supplier
Components
flow
Manufacturing
Unit
Distribution
Centre or
Warehouse
Product
flow
Delivery of product to
customers
C
o
m
p
o
n
e
n
t
s
Product flow
Secondary market
Customers
Reuse
Remanufacturing
Centre
Mixing Centre
Decomposition
Centre
Dismantling
Centre
Disposal of
waste
Forward flow
Reverse flow
Fig. 1: CLSC network structure
Repair Centre
17
The following notation is used in the formulation of the CLSC problem.
Notations:
I, i : represent the set of plants;
J, j: represent the set of distribution centers;
K, k: represent the set of retailers;
L, l: represent the set of collection centers;
S, s: represents the set of recycling centers;
P, p: Set and index of products
T, t: Set and index of time periods
Parameters:
Storage capacity by unit product p;
AC p
t
Rate of return of the product p from retailer k at period t;
ARkp
AS tp Rate of unrecoverable of product p at period t
CD/CC Cost of delay in product delivery/collection for per product in per unit
of time
CI ip Maximum plant capacity for product p
CJ j / CLl / CRr / CS s Maximum capacity of center j/l/r/s




Dt  j TD jkp  EDkp and C t l TCklp  ECkp for a given time t
DP kp Product p demand at retailer k at a given time t
t
t
t
Expected collection/delivery time of product p for retailer k at period
ECkp
/ EDkp
t
EJ tj / ELtl / ERrt Operating cost of expanding standard size in distribution center
j/collection center l /recovery center r at period t
FH ht FJ tj / FLtl / FRrt / FSst Fixed cost of opening center h/j/l/r/s at period t
,
GJ j / GLl / GRr Standard expansion size of center j/l/r
MJ tj / MLtl / MRrt Maximum number for standard expansion size of distribution
center j/collection center l /recovery center r at period t
PI ip Manufacturing cost per unit of product p at plant i
PJ jp / PLlp Processing cost per unit of product p at center j/l
18
PRrp Remanufacturing cost per unit of product p at recovery center r
TCklp Collection time of product p from retailer k by collection center l
TD jkp Delivery time of product p from distribution center j to retailer k
TI ijp / TJ jkp / TK klp / TLlrp / TSlsp / TRrjp Transportation cost per unit of product p from i to
j/ j to k / k to l / l to r / l to s / r to j
Decision Variable:
t
t
t
t
Quantity of product p shipped from center
QIijp
/ QJ tjkp / QKklp
/ QLtlrp / QRrjp
/ QSlsp
i/j/k/l/r/l to center j/k/l/r/j/s at period t
XJ tj / XLtl / XRrt / XSst  1if a distribution/collection/recovery/recycling center is
opened at location j/l/r/s at period t, zero otherwise
ZJ tj / ZLtl / ZRrt
Number of standardized expansion in distribution center j/
collection center l/recovery center r at period t
The CLSC problem can be formulated as follows:
MinZ1  Setting cost + Capacity expansion cost + Transportation cost +
Processing cost


 
t 1
j
FJ 1j XJ 1j   t  2  j FJ tj XJ tj 1  XJ tj 1 
 
t 1
l
FL1l XL1l   t  2  l FLtl XLtl 1  XLtl1 
 
t 1
r
FRr1 XRr1   t  2  r FRrt XRrt 1  XRrt 1 
 
s
FS s1 XS s1   t  2  s FS st XS st 1  XS st 1 
 
h  j l
t 1
t 1







FH h1 XJ h1 XL1h   t  2  h  j l FH ht XJ ht XLth 1  XJ ht 1 XLth1

  t  j EJ tj ZJ tj   t  l ELtl ZLtl   t  r ERrt ZRrt
t
t
  t  p  j  i TI ijp QI ijp
  t  p  k  j TJ jkp QJ tjkp   t  p  l  k TK klpQK klp
t
t
t
  t  p  r  l TLlrp Qllrp
  t  p  s  l TSlsp QSlsp
  t  p  j  r TRrjp QRrjp
t
t
  t  p  j  i PI ip QI ijp
  t  p  k  j PJ jp QJ tjkp   t  p  r  l PLlpQllrp
19
t
t
  t  p  s  l PLlp QSlsp
  t  p  j  r PRrp QRrjp

Min Z2 = Delivery time + Collection time
t
t
t
CD  t  p  k  jDt (TD jkp  EDkp
)QJ tjkp  CC  t  p  k  lC t (TCklp  ECkp
)QK klp
Subject to:

QJ tjkp  DPkpt
j
 QK
l
 QI
i
t
klp
t
ijp
(1)
t , p, k
t
 ARkp
DPkpt
(2)
t , p, k
t
  r QRrjp
  k QJ tjkp
t
(1  AS tp ) k QK klp
  r QLtlrp
t
t
AS tp  k QK klp
  s QSlsp
(3)
t , p, j
(4)
t , p, l
(5)
t , p, l
(6)

l
t
QLtlrp   j QRrjp

j
t
QI ijp
 CI ip

t
t
AC p ( i QI ijp
  r QRrjp
)  CJ j XJ tj   GJ j ZJ j
p

t
AC p  k QK klp
 CLl XLtl   GLl ZLl
p

AC p  l QLtlrp  CRr XRrt   GRr ZRr
p

p
t , p, r
(7)
t , p, l
t
t , j
(8)
 1
t
t , l
(9)
 1
t
t , r
(10)
 1
t
AC p  l QSlsp
 CS s XS st
XJ tj1  XJ tj
t , s
t , j
(11)
(12)
XLtl1  XLtl
t , l
(13)
XRrt 1  XRrt
t , r
(14)
XS st 1  XS st
t , s
(15)
ZJ tj  MJ tj * XJ tj
t , j
(16)
ZLtl  MLtl * XLtl
t , l
(17)
ZRrt  MRrt * XRrt
t , r
(18)
XJ tj , XLtl , XRrt , XSst {0,1} t , j, r, l , s
(19)
t
t
t
t
QIijp
, QJ tjkp , QKklp
, QLtlrp , QSlsp
, QRrjp
 0 t , p, i, j, k , l , r, s
(20)
20
ZJ tj , ZLtl , ZRrt int eger
(21)
t , p, j, l , r
Constraint (1) assumes zero unmet demand. Constraint (2) ensures complete
collection of returned products from consumers. Constraints (3-6) impose flow
balance at the distribution, collection, recovery and recycling centers.
Constraints (7-11) are capacity constraints on facilities, including that on
expansion size over the time period, prohibiting a certain number of products,
returned products and recoverable and recyclable products from being
transferred to facilities that are not open. Constraints (12-15) guarantee that
the open facilities cannot be closed during the following periods. Constraints
(16-18) ensure that the expansion of a facility is only possible if the facility has
already been opened and impose a maximum standardized expansion for each
type of facility at each time period. Finally, Constraints (19-21) enforce binary,
non-negativity, and integer restrictions on decision variables.
In the objective function, there are several nonlinear terms to be
considered. These are associated with the fixed cost of opening distribution,
collection, recovery, and recycling centers and the fixed savings cost of a hybrid
facility. Each of them involves the multiplication of two binary variables as:
t
t 1
t
t 1
t
t 1
( XJ tj , XJ tj1 ) , ( XLl , XLl ) , ( XRr , XRr ) , ( XS s , XS s ), and ( XJ ht , XLth ) .
Therefore,
the
above model is linearized by defining new variables as follows.
First, using X J tj  XJ tj 1  XJ tj 1  , the following constraints are added to the
model:
XJ tj  XJ tj 1  X J tj  2
t  2, j
(22)
XJ tj  XJ tj 1  X J tj  0
t  2, j
(23)
2 XJ tj  XJ tj 1  X J tj  1
t  2, j
(24)
2 XJ tj  XJ tj 1  X J tj  1
t  2, j
(25)
Constraint (22) ensures that if XJ tj  1 and XJ tj 1  1 , X J tj should be zero; constraint
(23) ensures that if XJ tj  0 and XJ tj 1  0 , X J tj should be zero; constraint (24)
ensures that if XJ tj  1 and XJ tj 1  0 , X J tj should be one; and constraint (25)
ensures that if XJ tj  0 and XJ tj 1  1 , X J tj should be zero.
21
Second, using X Ltl 

XLtl 1  XLtl1
,

X Rrt  XRrt 1  XRrt 1
 , and

X S st  XS st 1  XS st 1
 , based
on the same logic as applied for the fixed cost of opening a distribution center,
the following constraints should also be added to the model:
XLtl  XLtl1  X Ltl  2
t  2, l
(26)
XLtl  XLtl1  X Ltl  0
t  2, l
(27)
2 XLtl  XLtl1  X Ltl  1
t  2, l
(28)
2 XLtl  XLtl1  X Ltl  1
(29)
t  2, l
XRrt  XRrt 1  X Rrt  2
t  2, r
(30)
XRrt  XRrt 1  X Rrt  0
t  2, r
(31)
2 XRrt  XRrt 1  X Rrt  1
2 XRrt  XRrt 1  X Rrt  1
t  2, r
(32)
t  2, r
(33)
XS st  XS st 1  X S st  2
t  2, s
(34)
XS st  XS st 1  X S st  0
t  2, s
(35)
2 XS st  XS st 1  X S st  1
t  2, s
(36)
2 XS st  XS st 1  X S st  1
(37)
t  2, s
Finally, the nonlinear terms, with respect to the fixed savings cost of a hybrid
facility, are linearized through following two steps.
In the first step, a new variable XH ht  j l  XJ tj XLtl is defined as
XH ht  j l  1if a distribution center and a collection center are opened at location
h
in period t and zero otherwise. According to the new variable, the
transformed terms are
 
t 1
h  j l

FH h1 XH h1   t  2  h  j  l FH ht XH ht 1  XH ht 1

However, though the objective function minimizes costs, it has a tendency to
make the value of the variable
value of
XH ht
XH ht
equal to 1, and we should only limit the
to 1 when both XJ tj and XLtl are equal to 1. This can be achieved
by adding the following constraints to the model.
2 XH ht  j l  XJ tj  XLtl
t , j, l
(38)
22
(39)
 XH ht  j l  XJ tj  XLtl  1 t , j, l
In the second step, using X H ht  XH ht 1  XH ht 1  , based on the same logic that was
applied for the fixed cost of opening other centers, the following constraints
should be added to the model:
XH ht  XH ht 1  X H ht  2
t  2, h
(40)
XH ht  XH ht 1  X H ht  0
t  2, h
(41)
2 XH ht  XH ht 1  X H ht  1
(42)
t  2, h
2 XH ht  XH ht 1  X H ht  1
t  2, h
(43)
5. Solutions approaches for uncertainty in sustainable supply chain
network
The proposed sustainable supply chain network is a multi-objective MILP
formulation under uncertainty. The original model is formulated into a robust
counterpart optimization problem by applying three well-known robust
optimization formulations: a) Soyster’s formulation, b) Lin’s formulation, and c)
Bertsimas’ formulation.
5.1Robust Optimization Formulations
Ben-Tal and Nemirovski (2002) have argued that robust optimization (RO)
is among the recent trends for optimization under uncertainty. In contrast to
stochastic optimization, RO does not require uncertainty data with a known
probability distribution and chance constraints. Unlike SO, RO generates a
solution that is optimal for all possible ranges of uncertain data. In the
following section, we present the three most well-known RO formulations based
on the nominal mixed integer linear model:
Minimize cx
s.t
a x
ij
j
 bi
j
L  x U
i
(ii)
23
x j binary or continuous
j
In this paper, we assume that data uncertainty affects only the elements of the
right-hand-side (RHS) column coefficients. To address the assumption in
Soyster’s and Bertsimas’ RO formulations, we can introduce a new variable xn 1 ,
which is a binary variable with a fixed value of 1, and rewrite model (ii) as
follows:
Minimize cx
s.t
a x
ij
j
 bi xn 1  0
i
j
(iii)
L  x U
x j binary or continuous j
1  xn1  1
The uncertainty parameter, bi , takes on values according to a symmetric
distribution with a mean equal to the nominal value bi in the interval
[bi  bi , bi  bi ] , where b i represents the variation amplitude.
5.1.1 Soyster’s formulation
Soyster (1973) was one of the first researchers to propose a RO formulation to
produce a solution that is feasible for any realization of uncertain data that
belong to a convex set.
Minimize cx
s.t
 a x   aˆ u
ij
j
j
jJ i
ij
j
 bi
i
(iv)
L  x U
 uj  xj  uj
j
uj  0
j
where J i is the set of coefficients in row i that are subject to uncertainty. Each
entry aij , j  J i is formulated as a symmetric and bounded random variable
aij , j  J i (Ben-Tal and Nemirovski, 2000) that takes on values  aij  aˆij , aij  aˆij  .
Based on the above formulation, model (iii) adopts the following form:
24
Minimize cx
s.t
a x
ij
j
 bi xn 1  bˆi un 1  0 i
j
(v)
L  x U
x j binary or continuous j
1  xn 1  1,  un 1  xn 1  un 1
As seen, in this formulation, the maximum variation is considered that affords
the highest protection against uncertainty.
5.1.2 Lin’s formulation
A significant contribution in the area of RO was provided by Ben-Tal and
Nemirovski (2000). To address the extreme conservatism in Soyster’s
formulation, they developed a number of RO formulations and applications and
presented a detailed analysis of the RO framework in linear programming. In
2004, Lin et al. (2004) extended Ben-Tal’s formulation to mixed integer
programming problems as follows:
Minimize cx
s.t

a
x


aij uij  
j ij j  
 jJi

2 2
2
a
z

b

ij ij
i 
jJ i

 bi   max 1, bi  i
 uij  x j  zij  uij i, j
(vi)
L  x U
Where the coefficient and the right-hand-side parameters (respectively aij and bi )
in row i are subject to uncertainty.
In the following, we present model (i) according to the Lin’s formulation for
bounded and symmetric uncertainty:
Minimize cx
s.t
a x
ij
j
j
 bi  bi   max 1, bi  i
L  x U
x j binary or continuous j
(vii)
25
where δ and ε are infeasibility tolerance and uncertainty level, respectively.
Assume that the uncertain data are distributed as follows:
bi  1  i  bi
(viii)
where ξi are random variables that are distributed symmetrically over the
interval [-1,1]. As shown by the authors (Lin et al., 2004), in this formulation,
the probability that the i constraint is violated is at most k=exp( i2 2 ), where
 is a positive parameter that depends on the decision maker in order to
tradeoff robustness and quality of the solution.
5.1.3 Bertsimas’ formulation
Because Ben-Tal’s formulation leads to a non-linear model and no guarantee
regarding the probability that the robust solution is feasible, it is highly
desirable to develop a method that addresses these drawbacks. Bertsimas and
Sim (2004) proposed a new RO formulation with a parameter i for every
constraint. In this formulation, each uncertainty parameter is assumed to take
on a value from within a symmetric interval around a nominal value, and the
parameter i for each constraint limits the uncertainty parameters that can
simultaneously take on their worst-case value. The parameter i controls the
trade-off between the probability of violation and the effect to the objective
function of the nominal problem, which is what they call “the price of
robustness” (Bertsimas and Sim 2004). They proposed the following non-linear
formulation:
Minimize cx
s.t
a x
ij
j

j




a ij u j  (i  i  )aiti uti   bi


Si ti  Si  Ji , Si  i  ,ti Ji \ Si  
 jSi


L  x U
max
 uj  xj  uj
j
uj  0
j
i (ix)
26
Where

J i  j a ij

0 ,
i  0, J i  and
can also take non-integer value,
Si
represents the subset that contains i  uncertain parameters in the constraint,
and ti is an index used to describe an additional uncertain parameter if i is not
an integer. Thus, when i  0 , model (viii) is equivalent to that of the nominal
problem. Similarly, if i  J i , we have Soyster’s formulation. Therefore, this
allows for an adjustment between the robustness of the formulation and the
level of conservatism of the solution. The above robust formulation has an
equivalent linear formulation on whose basis model (iii) is rewritten as follows:
Minimize cx
s.t
a x
ij
j
 bi xn 1  zi i   pij  0 i
jJ i
j
zi  pij  bi un 1 i, j
 un 1  xn 1  un 1
pij  0 i, j
(x)
zi  0 i
un 1  0
1  xn 1  1
L  x U
x j binary or continuous j
For this robust counterpart formulation, Bertsimas and Sim calculated the
probability of violation of the i-th constraint. Specifically, if the uncertain
coefficient parameter bi follows a symmetric distribution and takes values in
the range [bi  bi , bi  bi ] , then the probability that the i-th constraint is violated
satisfies the following constraint: as follows:

 1 

P   aij x j  bi xn*1  0   n 1   
 j
 2 

 1    C  n,    
where n  J i , 
n
 C  n, l 
l    1
i  n
, and      
2

    
n
 

n
l    1
n
l

(xi)
27



C (n, l )  
 1
 2

1
(if l  0 or l  n)
2n




n
n

 n  l 
.exp n log 
  l log 
  otherwise
(n  l )l
 l 

 2n  l  


5.2 Computational experiments
To assess the performance of the three robust counterpart’s optimization
formulations in the sustainable supply chain network, all three EACSCMs are
solved in CPLEX 12.2 using a PC with a 2.3-GHZ CPU and 1 GB of RAM. They
are examined in two steps. In the first step, the EACSCMs are tested on 8 test
scenarios with different sizes, uncertainty, and reliability levels by fixing the
coefficient of compensation and relative importance. In the second step, the
EACSCMs are examined based on the various coefficients of compensation and
relative importance for one scenario. We set a bounded and symmetric
uncertainty in demand and return products. Let us consider a demand with
40% variability; it takes on values in the range [80,190] and has a nominal
value of 135. The other parameters are generated randomly using the uniform
distribution specified in Table 3.
Table 3: The values used in the test scenarios
Parameter
Range
Parameter
Range
Parameter
Range
U(250,350)
t
DPkp
U(80,190)
TIijp ,TJ jkp ,TKklp
U(4,10)
t
CIip
U(500,750)
t
ARkp
U(0.6,0.7)
TLlrp ,TSlsp ,TRrjp
U(4,10)
t
CSsp
U(80,150)
AS tp
U(0.15,0.20)
FJ j , FLl
U(1800,2600)
t
CRrp
FRr
U(3000,4000)
FSs
U(1500,2200)
FH h
U(600,1000)
PRrp
U(2,4)
ERrt
U(300,700)
PIip
U(3,5)
EJ tj , ELtl
U(200,500)
AC p
CJ tjp ,CLtlp
GJ j ,GLl ,GRr
U(0.8,1)
U(200,350)
U(50,100)
MJ tj , MLtl , MRrt
TD jkp ,TCklp
t , EC t
EDkp
kp
PJ jp , PLlp
U(1,5)
U(5,8)
U(4,6)
U(1.5,3)
5.3 Different Scenarios
Through EACSCM, Bertsimas’ formulation is solved based on four uncertainty
levels (0, 0.2, 0.5, 1) and four reliability levels (50%, 62.5%, 70%, 75%), which
28
indicate the probability that the constraint is violated. Under Lin’s formulation,
we assume three uncertainty levels (0, 0.2, 0.5), three reliability levels with a
minimum of 62.5% (because a smaller amount causes the model to be
infeasible), and an infeasibility tolerance level equal to zero. By supposing that
the first objective function is the most important objective, we consider that
  0.4 and   0.6 .
Table 4 shows that the results of the deterministic formulation are the
same as those of Bertsimas’ and Lin’s formulations presented in Tables 4 and 5
when the uncertainty and reliability levels are zero and 75%, respectively. In
Table 5, Soyster’s formulation shows the same results obtained using
Bertsimas’ formulation (Table 3) when the uncertainty level is 1 and the
reliability level is 50%. This means that for scenario 1, the cost is guaranteed to
be below 33903 with a probability of 50% in the presence of 100% uncertainty
in the amount of demand and return products.
Table 4 Results of deterministic and Soyster’s formulations
Scenario
Scenario Specifications
Deterministic formulation
Soyster’s formulation
No.
p/t/i/j/k/l/r\s
Objective
CPU time
Objective
CPU time
1
4/3/2/3/5/3/1/1
24016
624
33903
1029
2
6/2/5/8/10/5/2/1
27390
2028
39223
1997
3
3/2/20/15/35/13/6/3
31276
5445
44764
5709
4
2/2/30/20/50/17/8/4
35657
7394
50421
7598
5
2/2/30/30/70/25/15/7
40098
14096
56654
14103
6
3/3/30/40/80/30/25/15
101944
36692
143913
36707
7
4/3/30/50/100/40/30/20
163504
82222
230788
95301
8
5/3/30/70/150/50/35/20
304410
179728
429663
189899
Comparing Bertsimas’ and Lin’s formulations in terms of the objective reveals
that Bertsimas’ formulation outperforms Lin’s for all scenarios and different
uncertainty and reliability levels, as shown in Tables 5 and 6. These tables
show the gap between the two formulations, which widens as the scenario size
29
and uncertainty level increase along with a decrease in reliability level.
Furthermore, in Bertsimas’ formulation, the increase in CPU time with the
scenario size is smaller than that in Lin’s formulation.
Table 5 Results of Bertsimas’ formulation
Scenario
No.
β= 75%, Γ = 0
Objective
β= 70%, Γ = 0.2
CPU
Objective
CPU time
β= 62.5%, Γ = 0.5
Objective
β= 50%, Γ = 1
CPU time
Objective
CPU time
time
1
24016
1279
25994
982
28960
1170
33903
1014
2
27390
2309
29756
2590
33306
2637
39223
2511
3
31276
6692
33954
9396
37985
6614
44764
5913
4
35657
7535
38603
7347
43034
7987
50421
7659
5
40098
14898
43405
14774
48366
14462
56654
14194
6
101944
39516
110333
37877
122917
37658
143913
38017
7
163504
86210
176956
103849
197133
87428
230788
84209
8
304410
184861
329460
192005
367036
190492
429663
198738
Table 6 Results of Lin’s formulation
Scenario
No.
β= 75%, Γ = 0
β= 70%, Γ = 0.2
β= 62.5%, Γ = 0.5
Objective
CPU time
Objective
CPU time
Objective
CPU time
1
24016
811
28099
2699
35699
1061
2
27390
1981
32046
2231
infeasible
infeasible
3
31276
6209
36601
5772
infeasible
infeasible
4
35657
6973
41735
7979
53029
7831
5
40098
13775
46914
14087
59587
14836
6
101944
39236
119275
38345
151428
38891
7
163504
83881
191300
81588
242878
85332
8
304410
237558
356159
333029
452051
260498
As summarized in Table 7, we can conclude that Soyster’s formulation, with
the highest level of conservatism, is not flexible to adjust the degree of
robustness. In Lin’s formulation, this adjustment is made by changing the
uncertainty level or probability of constraint violation (reliability level) or both.
The combination of uncertainty and reliability levels makes Lin’s model more
30
conservative and more likely to obtain infeasible solutions. Bertsimas’
formulation is able to adjust the degree of conservatism through the
uncertainty level (level of robustness).
Table 7 Comparison of Bertsimas’ and Lin’s formulations
Formulation
Objective
CPU
Level of
Feasible
Type of
Model Dimensions
time
Conservatism
Solution
Uncertainty
(K= No. uncertain
parameter)
Bertsimas
Lin
Better
Less
Less
Solution
Time
Conservatism
---
---
---
Guarantee
Bounded &
n+k+1 variables
Symmetric
m+k+n Constraints
No
Bounded
n+2k variables
Guarantee
with/without
m+2k Constraints
Symmetric
5.4 Different compromise solutions
In this step, EACSCMs are evaluated based on the different coefficients of
compensation   0 1 and relative importance   0 1 for one scenario
(Table 8). Due to space limitations, the details of the compromise solutions
obtained using the different parameters are not presented here, but can be
made available upon request.
Table 8 The size of the test scenario and value of some parameters
Scenario Specifications
Uncertainty
Reliability
Coefficient of
Relative
Level
Level
Compensation
Importance
0.2
0.7
0-1
0-1
p / t / i / j / k / l / r /s
2/3/5/8/20/5/2/1
The solutions show that in approximately 85% of cases, Bertsimas’ EACSCM
presents a better satisfaction degree for the first objective. However, this
amount decreases to approximately 60% for the second objective. For a better
assessment, we analyze and compare the performance of the EACSCMs using
the following distance and dispersion measures.
To determine the degree of closeness of each EACSCM to the ideal solution,
we define the following family of distance functions (Torabi and Hassini 2008,
Steuer 1986):
31
K p
Dp  Z  x   =  θ k 1-μ k  Zk  x  
 k=1

k

1
p



p  1 and integer (xiv)
where the power p is a distance parameter, p = 1, 2 indicate the longest and
shortest distances, in the geometrical sense, respectively, and p = ∞ is the
shortest distance, in the numerical sense. Thus, the best approach producing a
preferred compromise solution is that in which the minimum D p  Z k  x   is
achieved by the solution with respect to some p.
The range of satisfaction degrees (ARSD) is a dispersion index that is
computed as follows [21]:



RSD  Zk  x   = max μ k  Zk  x   - min μ k  Zk  x  
k
k

(xv)
This index helps us measure the degree of balance involved in developing a
compromise solution by considering the maximum difference between the
satisfaction degrees of objectives.
By comparing the EACSCMs of Soyster, Bertsimas and Lin based on the
above two measures over the change in γ and θ values, we can derive the
following information:

Table 9 shows the minimum distance measure over the change in γ and
θ. It is clear that Bertsimas’ EACSCM presents minimum distance values
for all distance parameters (p) when θ ≥ 0.3. Otherwise Soyster’s
EACSCM provides a better degree of closeness to the ideal solution than
the other EACSCMs.

Table 10 shows that all three EACSCMs present almost the same
dispersion measure over the change in γ and θ values for both objectives.
32
Table 9 Performance comparison based on the minimum distance measure
Coefficient of
Distance
Relative Importance
Compensation
Parameter
θ ≤ 0.2
0.3 ≤ θ ≤ 0.5
θ ≥ 0.6
γ ≤ 0.2
p=1
Soyster
Bertsimas
Bertsimas
p=2
Soyster
Bertsimas
Bertsimas
p=∞
Soyster
Bertsimas
Bertsimas
p=1
Soyster
Bertsimas
Bertsimas
p=2
Soyster
Bertsimas
Bertsimas
p=∞
Soyster
Bertsimas
Bertsimas
p=1
Soyster
Bertsimas
Bertsimas
p=2
Soyster
Bertsimas
Bertsimas
p=∞
Soyster
Bertsimas
Bertsimas
0.3 ≤ γ ≤ 0.5
γ ≥ 0.6
Table 10 Performance comparison based on the minimum dispersion measure
Coefficient of
Objective
Compensation
function
γ ≤ 0.2
0.3 ≤ γ ≤ 0.5
γ ≥ 0.6
Relative Importance
θ ≤ 0.2
0.3 ≤ θ ≤ 0.5
θ ≥ 0.6
Obj 1
Soyster
All of them
All of them
Obj 2
All of them
All of them
Bental
Obj 1
All of them
All of them
All of them
Obj 2
All of them
All of them
All of them
Obj 1
All of them
All of them
All of them
Obj 2
All of them
All of them
All of them
Considering the same dispersion measure for all EACSCMs, Bertsimas’
EACSCM is the best choice, with a minimum degree of closeness to the ideal
solution and nearly the highest satisfaction degree with respect to both
objectives for decision makers, except when θ ≤ 0.2.
Overall it can be concluded that Bertsimas’ EACSCM presents the most
effective and efficient robust counterpart formulation at least for locationallocation problems.
6. Appreciative Inquiry
To understand the reasons for management actions in a field such as
sustainability, case research is often the norm. In India where a majority of
the organizations are in the process of assimilation of sustainability or thinking
33
about sustainability, action research may be the best methodology
(Meyer,
2000; Coughlan and Coghlan, 2002). However Cooperrider and Srivastva
(1987) have argued that action research because of its critique nature has
failed to embrace the appreciation perspective. Cooperrider and Srivastva
(1987) have suggested the appreciative enquiry methodology to provide deeper
insight through positive and constructive discussions with actors. Ludema et
al. (2006) have argued the importance of appreciative inquiry to generate
theories as alternative methods to other established methods like case research
and action research. Appreciative inquiry is a four stage methodology
(Cooperrider and Srivastava, 1987), which includes discovering, dreaming,
designing, and doing (4D’s). In the discovery phase we have attempted to
unearth the silver lining in the cloud; in the dreaming phase we have
encouraged our participants to dream of ideal scenarios; in the design phase a
blue print is prepared to achieve dreams and in the fourth phase the actual
action is taken to translate the blueprints into desired outcomes. In our
current paper we have included only first three phases (i.e. discover, dream,
and design). The final phase which is about action has been excluded from our
discussion which is still under progress and in future we may report in
extended work.
The current research is an attempt by us to adopt ethnographic studies in
operations management field, which in past has not been exploited by the
operations management community. The ethnographic research allows for
detailed actors-researchers encounters in actual settings as events and
behaviors transpire, with a focus on how people live their lives (Williams and
George, 2013). Hence we argue that appreciative inquiry is a quasiethnographic research used in current study as a microcosmic reflection of the
data-richness embodied in full-scale ethnographic studies in business.
6.1 The study
The study was conducted in three manufacturing units of ABC Limited which
we have discussed in preceding sections, plus a tier 1 supplier of parts to ABC,
34
and a distribution center. The locations were chosen after consulting the chief
executive officer (CEO) of ABC Limited. To achieve the study objectives, one of
our research team members spent one day at each location with the respective
manager, observing their conversations and behavior, taking notes from their
dairies, and contacting their other team members for additional information
and input. Over the time of the study member of the research team built an
excellent rapport with the respondents and their staff. The relationship
facilitated the process and the information was shared very comfortably. We
were able to exercise our control over the quality of the data gathered during
the study. The questions were communicated in the regional language by
providing examples and explanations. The research questions and ensuing
conversations addressed 7 key issues broadly classified under two sections.
First, environmental related questions, and second, the ethical practices
related questions.
6.2 Environmental related questions
6.2.1 Carbon emissions control related practices
When we asked about carbon emissions control practices, many of the
respondents had no proper explanation. However, we further assured them
that the data which we are gathering were for academic purposes and not
related to any government or NGO related projects. The respondents
highlighted key issues such as:
(i) The transporters’ rate is negotiated at lower rate than current market rate.
Hence in response to the current situation truck operators are forced to
overload the truck. The supreme court of India has strictly prohibited transport
operators from loading beyond 9 metric tons for six-wheelers and 15 metric
tons for ten-wheelers but in reality six-wheelers are carrying up to 20 metric
tons and 10 wheelers are carrying loads from 25 to 30 metric tons.
(ii) Most of the truck operators were using trucks over 7 years old. Hence the
old trucks which are used for transportation are emitting more carbon than
new trucks.
35
(iii) The police menace and poor infrastructure have further worsened the
conditions.
However, beside these concerns they identified some recent advancement in
latest technologies.
An awareness program related to reducing carbon
footprints in association with Confederation of Indian Industries (CII), has
helped in achieving significant success in reducing carbon emissions generated
within manufacturing units. The observations conform to past studies (e.g. Kim
and Van Wee, 2009; Huang et al. 2009). Hence we can argue that in the
absence of human agency, the institutional pressures are not translated into
desired actions.
6.2.2 Water recycling
One of the research questions probed the water preservation initiative by the
organization. Many of the respondents have expressed that in recent years the
organization has taken some positive steps towards recycling waste water and
rain harvesting to reduce excessing reliant on water supply. However, they
expressed the view that more initiatives need to be taken to further improve the
quality of the water.
6.2.3 Recycling of product after use
Our observation suggests that many respondents are positive about recycling
initiatives. The organizations have experienced significant growth in recycled
parts and product. This has helped to boost the company performance in terms
of revenue and significant reduction in direct materials cost.
6.3 Ethical practices
This question was probed with caution. We posed seven questions related to
the ethical practices towards labor and community.
6.3.1 Compensation
The research findings suggest that the compensation structure of the staff in
the organization is adequate. However, when we further intensified the
discussions, some interesting findings emerged. There is concern among the
staff regarding increasing difference in compensation offered to the various
grades of staff. Some of the respondents have even identified the unequal
36
treatment among staff as the major cause of rifts between team members and
jealousy which may be the major cause behind failure of several initiatives. The
inequality among staffs is on the rise. The case gets even worse when the
salaries of the staff employed with the suppliers and working in the
distribution center are even lower than the staffs of the principal organization.
This has further explained the poor alignment between supply chain partners.
6.3.2 Working hours
The research findings show that working hours in most of the organizations are
more than 8 hours. Some of the respondents even expressed that the excessive
working hours have disturbed their family life.
6.3.3 Lack of proper health checkup facilities
Most of the respondents have responded that the medical checkup conducted
within their organization suggests that most of the activities are for
documentation purpose. Second the medical checkups conducted outside the
organization are costly. Hence their expenses are not reimbursed which further
discourages middle level staffs or labor to undergo regular medical checkup.
6.3.4 Bribing
We made an interesting observation in our study. The respondents have
indicated that in recent years the bribery culture is fading away. However, still
the bribing is
a
major concern
within government departments
and
organizations still need to bribe pollution control board to prevent any further
strict action against violation of guidelines.
6.4 Discussion
To provide a holistic view, we have synthesized our findings using a rationalist
approach and alternative methods. The organizations studied have a long way
still to go to achieve a responsive sustainable supply chain network. In the
past, literature has attempted to address cost and carbon emissions using the
goal programming technique. However other environmental initiatives were not
addressed using quantitative approach. Social issues were usually not included
in previous studies. Hence, we have adopted mixed research strategies to
address economic, environmental and social aspects of sustainable supply
37
chain network. The social dimensions are still ignored and suggest the need for
a more holistic framework which can address social issues along with economic
issues and environmental issues.
7. Conclusion
In this section, we will now try to conclude our research attempt to answer our
research questions, which we posed in our introduction section. In response to
our first question, we have undertaken an extensive review of literature. We
have attempted to provide a theoretical background of responsive supply chain
and sustainable supply chain and further reviewed literature from the
operational research perspective. In this we way we have highlighted the role of
OR in sustainable supply chain network design. The review of literature has
provided a direction and clarity in our research objective. Second to answer our
second research question we have used robust optimization techniques and
presented our computation results. To answer our third and fourth research
questions we adopted qualitative research methods. In our study we have used
appreciative inquiry to highlight environmental and social issues which were
not included in our robust optimization model in our preceding discussions.
Hence, we found that in developing economies, the sustainability in supply
chain network is still a nascent concept. However, like the silver lining in a
cloud; we can see an awareness level among these organizations towards
sustainable development and most of the organizations have started embracing
sustainability as a corporate philosophy.
7.1 Unique Contributions
Unlike previous research, which considers only a single product or single
period
in
multi-objective
function
problems,
this
paper
proposed
a
mathematical model for multi-period multi-product CLSC problems. We
considered the issue of balancing cost and delivery/collection times by using a
multi-objective model. Moreover, the model supported facility expansion for
each facility except for plants and recycling centers and also considered cost
savings associated with hybrid centers.
38
By considering multiple objectives and unknown parameters, the above
CLSC network was studied by developing a hybrid solution approach based on
the interactive fuzzy goal programming (IFGP) model and three robust
counterpart optimization formulations proposed by Soyster, Bertsimas and Lin.
The numerical results show that Soyster’s EACSCM is the most conservative
formulation without the ability to adjust the degree of robustness, which
means it gives up too much optimality for the nominal problem, which is our
unique contribution in the present paper. Between the other two with the
ability to adjust the level of conservatism, Bertsimas proposed a more
appropriate formulation based on modeling and numerical aspects. Bertsimas’
EACSCM does not increase the problem size considerably and preserves
linearity. The numerical results showed that it outperforms Lin’s and Soyster’s
EACSCM in terms of the final solutions obtained, the degree of closeness to the
ideal solution, satisfaction degree and the level of conservatism, in addition to
guaranteeing the feasibility of the RO formulation. Additionally, the results
indicated that in Bertsimas’ EACSCM, the growth in CPU time with increasing
scenario size is less than that exhibited by Lin’s EACSCM. Second, we have
used alternative methods like appreciative inquiry to address environmental
and social issues. Hence we can argue that we have attempted to answer the
pending research calls for use of qualitative research methods in operations
management field. In our study we have used mixed research approach to
highlight the relative importance of each method for advancing current
operations management research to next level. Hence our present research
further corroborate with the observations of scholars who have stressed on the
use of alternative methods in operations management field to take the research
to the next level (e.g. Childe, 2011; Ketokivi and Choi, 2014; Markman and
Krause, 2014).
39
7.2 Limitations of present study and further research directions
Our model does not consider environmental as well as social parameters, due
to unavailability of accurate data which is our present limitations.
There are several possible extensions to this work that may be interesting
lines of future research. These include:

In the objective function of our model, carbon emissions and social
performance dimensions can be added.

A comparative study between the proposed hybrid solution approach and
other solution approaches used to solve multi-objective models under
uncertainty.

Considering the model proposed in this paper under different types of
uncertainties and risk.

To
add
richness
to
further
research
opportunities,
longitudinal
ethnographic research design offer considerable promise.
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