International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 5 (2016) pp 3728-3732
© Research India Publications. http://www.ripublication.com
A Combined Approach for Workspace Location Selection Decision
Problem: A Linguistic-Mathematical Modeling Methodology
Sara Haddou Amar
Ph.D. Student, National School of Applied Sciences Kenitra-Systems Engineering Laboratory,
Ibn Tofail University, Kénitra, Morocco.
Team of Modelling, Optimization of Industrial Systems and Logistics,
Abdellah Abouadellah
Professor, National School of Applied Sciences, Kenitra-Systems Engineering Laboratory,
Ibn Tofail University, Kénitra, Morocco.
Team of Modelling, Optimization of Industrial Systems and Logistics,
performances of the options and the criteria in order to select
the most optimal location.
Abstract
Industrial workspace location selection is a complex problem
involving several criteria. It is an important and strategic
decision to make that requires the consideration of various
quantitative and qualitative factors on both national and
international level. In this paper, we propose à multi-criteria
decision making approach to solve the selection problematic of
a workspace location. In fact, the proposed methodology is a
combination between linguistic and mathematical modeling of
the decision criteria and the potential options. The objective is
to study and analyze the locations in order to select the most
optimal location choice.
Literature Review
The location decision problem is very important issue in the
conception process of supply chain network. It is highly studied
because of its big importance and deep impact on the work
flow. A lot of papers and books were dedicated to this
problematic. In fact, The American Mathematical Society
known by AMS did create a special code of the location
problem (90B80 for discrete location and assignment, and
90B85 for continuous location).
There is a multitude of study fields of location decision
problem, it depends on the objective and the interest of the
study but generally the workspace location has a strong link
with the global implementation of the supply chain process [5].
Keywords: Decision making, International location, Linguistic
evaluation,
Multi-criteria,
Polynomial
interpolation,
Workspace location.
Introduction
The facility location selection is an important decision
significantly affecting the company [1] [2] [15]. It has a deep
impact on the efficiency of the supply chain process and the
future of the industrial site in a way that any bad decision leads
to excessive costs, poor customer service, incompetent labor
and the failure of the company's strategy [3][5].
The location choice has an important role in the effective and
efficient traffic flow, for example: The transportation of raw
material to the manufacturing centers, the sourcing of
manufacturing components, the parts final assembly and the
delivery to the distribution centers and warehouses [1]. In fact,
the decision should be based on different criteria and factors in
order to illustrate the needed characteristics in the workspace
location. The preferences of the decision maker are also an
important factor to be considered. These preferences represent
the perspectives and the strategy of the organization in the
decision making process [4].
The analyzed problematic in this paper can be represented in
the selection of workspace location. The objective is to choose
a location among several potential locations noted as "potential
options". The choice is based on different criteria previously
determined and the decision process consist on the evaluation,
the comparison and the analysis of the characteristics and
Figure 1: Architecture supply chain implementation
Figure 2: The proposed approach diagram
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 5 (2016) pp 3728-3732
© Research India Publications. http://www.ripublication.com
There are many objectives that are usually considered by
organizations in location problems. Some of them can be as
follows [12][13]:
 Minimizing the total setup cost.
 Minimizing the longest distance from the existing
facilities.
 Minimizing fixed cost.
 Minimizing total annual operating cost.
 Maximizing service.
 Minimizing average time/ distance traveled.
 Minimizing maximum time/ distance traveled.
 Minimizing the number of located facilities.
 Maximizing responsiveness.
be divided into four important categories: Market factors,
Production factors, Economic risks and Transportation [9].
The description of the methodology is shown in the figure 2
(Fig 2) above.
The proposed approach is based on four steps:
Structuring step: This step consists on defining the main
component of the problematic; the decision criteria which we
will base our analysis on, and the potential options. The
approach is based on the comparison aspect, so we need a
comparison reference therefore we introduce the ideal option
concept:
"The ideal option is an option that best describes the
expectations of the decision maker in a location for the new
workspace; this option is imaginary and only serves as a
comparative reference"
Evaluating step: In order to measure the priority index of the
decision criteria, we established a genetic program. As follows
the details:
{Cr0 , Cr1 , … , Crn }.The
Let's consider
n+1
criterion
measurement process consists on the following steps:
 Organize the criteria from the least to the most important.
 Assign to the least important criterion the weight x0 = 0.
 Pair-wise comparison of criteria based on the following
scale*:
Among supply chain studies, many papers on facility location
problem have been published. Hamad (2008) developed an
approach to solve the warehouse location problem with the
objective of minimizing the total logistic cost. He brought a
new perspective by integrating the cost "take or pay", and the
constraints of tax benefits.
Colson and Dorigo (2004) proposed a software to support the
selection of public warehouse (public warehouses carrier
selection system-PWSS) to help decision makers to operate a
public warehouse database where more information is given on
each warehouse in a certain country.
Michel and Hentenryck (2004) did present a very simple tabusearch algorithm which performs amazingly well on the
uncapacitated warehouse location problem. The algorithm is
based on linear neighborhood.
Vahidnia et al (2009) did use AHP method (analytic hierarchy
process) to select a location for a hospital network. They base
their study on three objectives: minimizing the travelled time,
pollution degree and costs. Moreover they compared three
resolution approaches: the center of area, the α-cut and the
fuzzy extended method. The results show that the fuzzy extend
method is the least effective one; in fact It would appear that
three consistent sets of priorities are sufficient to have a firm
conclusion about the alternatives. However, The total weights
that represent an average score is meaningful only if the
weights acquired from fuzzy extent analysis do not include any
zero values. In such situations,
The workspace location problem complexity lies in the fact of
choosing the best location among a multitude of proposals.
Those proposals should be evaluated and compared regarding
the decision criteria. Therefore our paper seeks to design a
support system for multi-criteria decision making based on
linguistic and mathematical modeling using distance
measurement with polynomial interpolation.
Table 1. Measure allocation scale for priority factor
Weighting Linguistic terms
1
Similar, equal importance
2
Slightly important
3
Medium importance
4
Important
5
Very important
*NB: The weight measurement can be modified according to
decision maker perspective.
 Determine the weight xj of the criterion Crj , ∀j ∈ ⟦0. n⟧ as
follows:
We consider the criterion Cri less important than the
criterion Crj , and Mij the pair-wise comparison weight given by
the decision maker to these criteria.
So the priority weight xj is calculated by:
∀i, j ∈ ⟦0. n⟧ xj = xi + Mij
(1)
The potential and the ideal options should be also evaluated
regarding the decision criteria. For each potential option
POj ∀j ∈ ⟦0. n⟧ we evaluate its performances regarding the
criteria Cri , ∀i ∈ ⟦0. n⟧. The measurement allocation is noted
yij . As for the ideal option the measurement allocation is noted
zi . The following table shows the linguistic allocation scale for
the options evaluation:
The problematic and steps of the methodology
In this paper, we propose to solve the workspace location
selection problem. The aim is to analysis the potential options
regarding the decision criteria in order to choose the best option
that describes the decision maker expectations. There is
multitude of criteria involved in the decision making process.
In the case of workspace location selection, these criteria can
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 5 (2016) pp 3728-3732
© Research India Publications. http://www.ripublication.com
decision lies in the selection of the potential option with the
smallest value of the closeness index CIj .
Table 2: Measure allocation scale for options performances
Measure
allocation
scale
1
2
3
4
5
6
7
8
9
Label Linguistic Terms
x
CIj = ∫x n (Pj (x) − Pid (x))
0
EV
VL
L
SL
M
H
SL
VH
EH
Workspace location selection: international location case
International facility location selection decision is influenced
by several factors. Economical, cultural and political
differences should be taken into account. There are five main
factors that strongly influence the decision makers to take their
activities across national borders: costs, infrastructure, labor
characteristics, government and political factors and economic
factors [10] [14]. The most major sub-factors involved in
international location decision are: quality of labor force,
existence of modes of transportation, quality and reliability of
modes of transportation, availability of labor force, quality and
reliability of utilities, wage rates, motivation of workers,
telecommunication systems, record of government stability and
industrial relations laws. As for the managerial part of the
influencing factors, decision makers are commonly concerned
by; protection of patents, availability of management resources
and specific skills and system and integration costs.
It is clear that additional criteria should be added to the decision
making process to properly illustrate the differences of
international workspace location selection. Pin (2009)
summarized those criteria in six important axes:
 Availability production inputs at low prices
 Proximity and access to markets
 Attitude of the host government to foreign investment
 The economic and political stability
 Taxes: the exchange rate policy of the host government
 The existence of other competitors
Table 3: Evaluation step data collection
Cr0
Cr1
⋯
Cri
⋯
Crn
Priority
Option
"j" Ideal
measurements (x) performances (y) option (z)
y0j
x0
z0
y1j
x1
z0
⋯
⋯
⋯
yij
xi
z0
⋯
⋯
⋯
y
xn
z0
nj
For each potential option we have a set of pairs "point-image"
[xi , yij ] ∀i, j ∈ ⟦0. n⟧. So according to Lagrange interpolation
polynomials theorem, there is a unique polynomial that respect
the following rule:
Pj (x) = ∑n0 yij × Li (x)
(2)
Study case: application to an industrial workspace location
selection
A big industrial company wants to decide on where it will
locate its new facility. The criteria were chosen and presented
by the managerial consultant of the company (Table 4). The
alternative locations have been determined by the experts of the
company, they reduce the number of options into three location
site noted as: S1; S2 and S3.
The expert's team generated the priority index for the selected
decision criteria and developed their perspective of the ideal
option along with the potential location's linguistic evaluation
(See table 4).
The modeling step using Lagrange interpolation is
accomplished using Python software. The figure 2 is the
presentation of the polynomial function's curves. As well as for
the closeness index values, we used Simpson calculation
method (table 5).
With Li noted as Lagrange base:
Li (x) = ∏nm=0
m≠i
=
x−x0
xi −x0
×… ×
x−xi−1
xi −xi−1
x−xm
(3)
xi −xm
×
x−xi+1
xi −xi+1
×…×
x−xn
xi −xn
(4)
As for the ideal otion, the representing Lagrange polynomial is
the following:
Pid (x) = ∑n0 zi × Li (x)
(5)
The closeness index represents the distance between the two
polynomial functions. In fact, if the closeness index value is
small, it means that the distance between the potential option
and the ideal option is small. And in consequences the potential
option related to the smallest value of CIj is the most
representing one of the decision maker expectations.
Extra low
Very low
Low
Slightly low
Middle
High
Slightly high
Very high
Extra high
Modeling step:
This step consists on converting the evaluation data into
polynomials by using Lagrange interpolation polynomials
(Haddou Amar and Abouabdellah, (2015)). The output of the
evaluation step is represented in the following table:
Criteria
2
(4)
Analyzing step: The objective of mathematical modeling is to
have an over mixed view on the criteria priority and the
potential option performances. Moreover the interpolation step
is a simple way to compare the options with the decision maker
expectations represented as the ideal option. The location
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 5 (2016) pp 3728-3732
© Research India Publications. http://www.ripublication.com
modeling. It takes into consideration quantitative and
qualitative criteria and information fusion between criteria's
priority factor and linguistic evaluation terms. This study uses
the Lagrange interpolation polynomials to present the
numerical evaluation data. The interpolation is a simple way to
have a large and global perspective on the criteria priority index
and the potential options performances.
The proposed methodology is based on the comparison
technique. It takes into account the needs and the preferences
of the decision maker. Indifference curves can be used to
enhance the linguistic evaluation assignment and improve the
accuracy of the numerical values for future research.
References
[1]
Figure 3: Lagrange polynomials curves
Table 4: Initial data for the case study
Criteria priority
Cr0 Competitiveness
Cr1 Quality of labor
Cr2 Reliability of transportation
Cr3 Availability of transportation
Cr4 Availability of labor force
Cr5 Skilled labor
Cr6 Proximity to customers
Cr7 Proximity to suppliers
Cr8 Cost of labor
Cr9 Transportation Cost
Ideal Option
0 5
1 5
3 6
6 7
7 7
10 5
12 8
13 6
15 7
16 4
[2]
S1 S2
5 7
6 5
5 7
6 7
8 6
6 4
8 6
5 4
8 7
7 4
S3
7
6
4
6
5
6
5
4
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[6]
Sites Closeness index
S1 16.4080277494
[7]
S2
S3
19.687531675
50.4747133529
[8]
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transportation cost, it has the best performances on a global
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Conclusion
We propose in this paper a multi-criteria decision making
method to solve the workspace location selection problem. The
approach is based on linguistic evaluation and mathematical
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