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Saldanha-da-Gama et al., (2009) reviewed facility location models in the context of supply
chain management and identified
basic features that such models must capture to support decision-making
involved in strategic supply chain planning. In particular, the integration of
location decisions with other decisions relevant to the design of a supply
chain network has been discussed. Furthermore, aspects related to the structure
of the supply chain network, including those specific to reverse logistics has
been addressed. Significant contributions to the current state-of-the-art have
been surveyed taking into account numerous factors. Also, supply chain
performance measures and optimization techniques have been reviewed. Finally, a
list of issues requiring further research has been highlighted.

Farahani ?and Arabani, (2012)
investigated the dynamics of facility location
problems (FLPs) ought to be taken into account so as to efficiently deal with
changing parameters such as market demand, internal and external factors, and
populations. A trade-off should be set between
benefits brought by facility location changes and costs incurred by possible
modifications. They reported
on literature pointing out some aspects and characteristics of the dynamics of
FLPs. In fact, they aimed not only to review most variants of these problems,
but also to provide a broad overview of their mathematical formulations as well
as case studies that have been studied by the literature. Finally, based on
classified research works and available gaps in the literature, some possible
research trends have been pointed out.

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Park? et al., (2017) investigated how firms make plant location and
inventory level decisions to serve global markets. In their analysis, they
considered not only differences in wages, transportation costs, and subsidies
across countries but also exchange rate changes and competition between firms.
They presented that the degree of risk exposure of firms and the benefit of
relocating plants to the final consumption market played a critical role in firms’
plant location decisions, especially when the global economy is highly
uncertain. Furthermore, they provided conditions under which a firm relocates
its plant from one country to another, and empirically validates the results.
Also, they investigated how a firm manages inventory when its plant is located
in a foreign country. Finally, they confirmed the predictions of the theory
empirically by using a unique firm-level dataset drawn from Korean firms.


Diabat et al., (2017) presented a joint location-inventory model for the
network design of a supply chain with multiple Distribution Centers (DCs) and
retailers. The developed model determined the number and location of DCs, the
assignment of retailers to DCs, and the size and timing of orders for each DC.
The uncertain natures of demands and replenishment lead times have been
incorporated into the model utilizing a queuing approach. To solve the
presented model for large size problems, a hybrid solution algorithm based on
simulated annealing and direct search method has been adopted. The comparative
analysis of the numerical results provided important modeling insights.
Particularly, they demonstrated numerically that the cost savings obtained from
the queuing approach could be significant.

Nagurney?(2010) proposed a framework for supply chain network design
and redesign that allows for the determination of the optimal levels of
capacity and operational product flows associated with supply chain activities
of manufacturing, storage, and distribution at minimal total cost and subject
to the satisfaction of product demands. He formulated both the design and
redesign problems as variational inequalities and displayed that the same
algorithm, which exploits the underlying network structure, can be used for the
solution of either problem. Moreover, he illustrated the new framework with
numerical examples that demonstrated the practicality and flexibility of the

Meng? et al., (2009) addressed a novel competitive facility location
problem about a firm that intends to enter an existing decentralized supply
chain comprised of three tiers of players with competition: manufacturers,
retailers and consumers. Firstly they proposed a variational inequality for the
supply chain network equilibrium model with production capacity constraints,
and then employed the logarithmic-quadratic proximal prediction–correction
method as a solution algorithm. Based on this model, they developed a generic
mathematical program with equilibrium constraints for the competitive facility
location problem, which can simultaneously determine facility locations of the
entering firm and the production levels of these facilities so as to optimize
an objective. Subsequently, a hybrid genetic algorithm that incorporates with
the logarithmic-quadratic proximal prediction–correction method has been
developed for solving the proposed mathematical program with an equilibrium
constraint. Finally, they carried out some numerical examples to evaluate
proposed models and solution algorithms.

Farahani et al., (2012)
reviewed the covering problems in facility
location. Here, besides a number of reviews on covering problems, a
comprehensive review of models, solutions and applications related to the
covering problem have been presented. They outlined the covering problems and
then investigated solutions and applications. 

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