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Saldanha-da-Gama et al., (2009) reviewed facility location models in the context of supplychain management and identifiedbasic features that such models must capture to support decision-makinginvolved in strategic supply chain planning. In particular, the integration oflocation decisions with other decisions relevant to the design of a supplychain network has been discussed. Furthermore, aspects related to the structureof the supply chain network, including those specific to reverse logistics hasbeen addressed. Significant contributions to the current state-of-the-art havebeen surveyed taking into account numerous factors. Also, supply chainperformance measures and optimization techniques have been reviewed.

Finally, alist of issues requiring further research has been highlighted.Farahani ?and Arabani, (2012)investigated the dynamics of facility locationproblems (FLPs) ought to be taken into account so as to efficiently deal withchanging parameters such as market demand, internal and external factors, andpopulations. A trade-off should be set betweenbenefits brought by facility location changes and costs incurred by possiblemodifications. They reportedon literature pointing out some aspects and characteristics of the dynamics ofFLPs. 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 wellas case studies that have been studied by the literature. Finally, based onclassified research works and available gaps in the literature, some possibleresearch trends have been pointed out.Park? et al., (2017) investigated how firms make plant location andinventory level decisions to serve global markets.

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In their analysis, theyconsidered not only differences in wages, transportation costs, and subsidiesacross countries but also exchange rate changes and competition between firms.They presented that the degree of risk exposure of firms and the benefit ofrelocating plants to the final consumption market played a critical role in firms’plant location decisions, especially when the global economy is highlyuncertain. Furthermore, they provided conditions under which a firm relocatesits plant from one country to another, and empirically validates the results.

Also, they investigated how a firm manages inventory when its plant is locatedin a foreign country. Finally, they confirmed the predictions of the theoryempirically by using a unique firm-level dataset drawn from Korean firms. Diabat et al., (2017) presented a joint location-inventory model for thenetwork design of a supply chain with multiple Distribution Centers (DCs) andretailers. The developed model determined the number and location of DCs, theassignment of retailers to DCs, and the size and timing of orders for each DC.The uncertain natures of demands and replenishment lead times have beenincorporated into the model utilizing a queuing approach.

To solve thepresented model for large size problems, a hybrid solution algorithm based onsimulated annealing and direct search method has been adopted. The comparativeanalysis of the numerical results provided important modeling insights.Particularly, they demonstrated numerically that the cost savings obtained fromthe queuing approach could be significant.Nagurney?(2010) proposed a framework for supply chain network designand redesign that allows for the determination of the optimal levels ofcapacity and operational product flows associated with supply chain activitiesof manufacturing, storage, and distribution at minimal total cost and subjectto the satisfaction of product demands. He formulated both the design andredesign problems as variational inequalities and displayed that the samealgorithm, which exploits the underlying network structure, can be used for thesolution of either problem.

Moreover, he illustrated the new framework withnumerical examples that demonstrated the practicality and flexibility of theapproach.Meng? et al., (2009) addressed a novel competitive facility locationproblem about a firm that intends to enter an existing decentralized supplychain comprised of three tiers of players with competition: manufacturers,retailers and consumers.

Firstly they proposed a variational inequality for thesupply chain network equilibrium model with production capacity constraints,and then employed the logarithmic-quadratic proximal prediction–correctionmethod as a solution algorithm. Based on this model, they developed a genericmathematical program with equilibrium constraints for the competitive facilitylocation problem, which can simultaneously determine facility locations of theentering firm and the production levels of these facilities so as to optimizean objective. Subsequently, a hybrid genetic algorithm that incorporates withthe logarithmic-quadratic proximal prediction–correction method has beendeveloped for solving the proposed mathematical program with an equilibriumconstraint.

Finally, they carried out some numerical examples to evaluateproposed models and solution algorithms.Farahani et al., (2012)reviewed the covering problems in facilitylocation. Here, besides a number of reviews on covering problems, acomprehensive review of models, solutions and applications related to thecovering problem have been presented. They outlined the covering problems andthen investigated solutions and applications. 

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