Pareto Optimal Solution Selection for a Multi-Site Supply Chain Planning Problem Using the VIKOR and TOPSIS Methods

Pareto Optimal Solution Selection for a Multi-Site Supply Chain Planning Problem Using the VIKOR and TOPSIS Methods

Houssem Felfel, Omar Ayadi, Faouzi Masmoudi
DOI: 10.4018/IJSSMET.2017070102
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In this paper, a multi-objective, multi-product, multi-period production and transportation planning problem in the context of a multi-site supply chain is proposed. The developed model attempts simultaneously to maximize the profit and to maximize the product quality level. The objective of this paper is to provide the decision maker with a front of Pareto optimal solutions and to help him to select the best Pareto solution. To do so, the epsilon-constraint method is adopted to generate the set of Pareto optimal solutions. Then, the technique for order preference by similarity to ideal solution (TOSIS) is used to choose the best compromise solution. The multi-criteria optimization and compromise solution (VIKOR), a commonly used method in multiple criteria analysis, is applied in order to evaluate the selected solutions using TOPSIS method. This paper offers a numerical example to illustrate the solution approach and to compare the obtained results using TOSIS and VIKOR methods.
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1. Introduction

In the face of today’s highly competitive and global markets, manufacturing enterprises no longer operate as independent entities, but rather as multi-site supply chain. Thus, these enterprises are required to develop an integrated multi-site planning approach that takes into account the coordination between the different entities of the supply chain. Since the manufacturing sites are situated in different places, the planners need to define the amounts of products to be produced at each site as well the flow of products from one site to another.

The supply chain planning problem can be classified following the time horizon into three major categories: strategic, tactical, and operational (Fox et al. 2000). The strategic level concerns the design and the structure of the supply chain over a long time horizon that could last more than five years. The operational level is related to short term decisions lasting from few days to a few weeks. It deals with issues such as lot sizing, scheduling, and sequencing. The tactical planning model is between these two extremes including procurement, production, storage and distribution decisions. The focus of this work addressed the tactical level of the supply chain planning.

The profit and the cost represent the most used objectives for supply chain performance. The majority of the works in the literature focus on the maximization of the profit or the minimization of the cost as a single objective. One can refer to Moon et al. (2002), Gnoni et al. (2003), Leung et al. (2006), Lin and Chen (2006), Shah and Ierapetritou (2012), Lin et al. (2011) and Felfel et al. (2015b). Besides, the product quality level represents another important performance metric of the supply chain in a highly competitive market environment. This objective is rarely treated in the literature on supply chain planning problems. It is worthwhile noting that profit and product quality conflict with each other. In fact, the best product quality corresponds usually to a higher cost, which means a less profit.

Several multi-objective optimization problems and solution approaches have been proposed in the literature on multi-site supply chain. Leung et al. (2007) developed a robust optimization model to deal with a multi-site production problem under uncertainty for a multinational lingerie company located in Hong Kong. The proposed model attempted simultaneously to minimize the total cost as well as the variance of the total cost. The proposed model was solved as a single objective model using LINDO software. Torabi and Hassini (2009) dealt with a multi-site multi-echelon supply chain production planning model integrating procurement and distribution plans.

The authors considered four objective functions simultaneously, which are the minimization of the cost, the minimization of the late deliveries, the minimization of the volume of defective products and the maximization of the value of purchasing. A novel fuzzy approach was proposed to solve the developed multi-objective model and to find an efficient compromise solution. Mirzapour Al-e-Hashem et al. (2011) proposed a multi-site, multi-product, multi-period aggregate production planning problem. A novel robust multi-objective mixed integer nonlinear programming model was developed considering two conflicting objectives simultaneously. The first objective function consists on the minimization of the total losses of the supply chain and the second consists on the maximization of the customer satisfaction level. The proposed multi-objective model was solved then as a single-objective model by means of the LP-metrics method.

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