A genetic algorithm approach for multi-objective optimization of supply chain networks

Abstract

Supply chain network (SCN) design is to provide an optimal platform for efficient and effective supply chain management. It is an important and strategic operations management problem in supply chain management, and usually involves multiple and conflicting objectives such as cost, service level, resource utilization, etc. This paper proposes a new solution procedure based on genetic algorithms to find the set of Pareto-optimal solutions for multi-objective SCN design problem. To deal with multi-objective and enable the decision maker for evaluating a greater number of alternative solutions, two different weight approaches are implemented in the proposed solution procedure. An experimental study using actual data from a company, which is a producer of plastic products in Turkey, is carried out into two stages. While the effects of weight approaches on the performance of proposed solution procedure are investigated in the first stage, the proposed solution procedure and simulated annealing are compared according to quality of Pareto-optimal solutions in the second stage.

Introduction

A supply chain is a set of facilities, supplies, customers, products and methods of controlling inventory, purchasing, and distribution. The chain links suppliers and customers, beginning with the production of raw material by a supplier, and ending with the consumption of a product by the customer. In a supply chain, the flow of goods between a supplier and customer passes through several stages, and each stage may consist of many facilities (Sabri & Beamon, 2000). In recent years, the supply chain network (SCN) design problem has been gaining importance due to increasing competitiveness introduced by the market globalization (Thomas & Griffin, 1996). Firms are obliged to maintain high customer service levels while at the same time they are forced to reduce cost and maintain profit margins. Traditionally, marketing, distribution, planning, manufacturing, and purchasing organizations along the supply chain operated independently. These organizations have their own objectives and these are often conflicting. But, there is a need for a mechanism through which these different functions can be integrated together. Supply chain management (SCM) is a strategy through which such integration can be achieved. Illustration of a supply chain network is shown in Fig. 1.

The network design problem is one of the most comprehensive strategic decision problems that need to be optimized for long-term efficient operation of whole supply chain. It determines the number, location, capacity and type of plants, warehouses, and distribution centers to be used. It also establishes distribution channels, and the amount of materials and items to consume, produce, and ship from suppliers to customers. SCN design problems cover wide range of formulations ranged from simple single product type to complex multi-product one, and from linear deterministic models to complex non-linear stochastic ones. In literature, there are different studies dealing with the design problem of supply networks and these studies have been surveyed by Vidal and Goetschalckx, 1997, Beamon, 1998, Erenguc et al., 1999, Pontrandolfo and Okogbaa, 1999.

An important component in SCN design and analysis is the establishment of appropriate performance measures. A performance measure, or a set of performance measures, is used to determine efficiency and/or effectiveness of an existing system, to compare alternative systems, and to design proposed systems. These measures are categorized as qualitative and quantitative. Customer satisfaction, flexibility, and effective risk management belong to qualitative performance measures. Quantitative performance measures are also categorized by: (1) objectives that are based directly on cost or profit such as cost minimization, sales maximization, profit maximization, etc. and (2) objectives that are based on some measure of customer responsiveness such as fill rate maximization, customer response time minimization, lead time minimization, etc. (Beamon, 1998). In traditional supply chain management, the focus of the integration of SCN is usually on single objective such as minimum cost or maximum profit. For example, Jayaraman and Pirkul, 2001, Jayaraman and Ross, 2003, Yan et al., 2003, Syam, 2002, Syarif et al., 2002, Amiri, 2006, Gen and Syarif, 2005, Truong and Azadivar, 2005 had considered total cost of supply chain as an objective function in their studies. However, there are no design tasks that are single objective problems. The design/planning/scheduling projects are usually involving trade-offs among different incompatible goals. Recently, multi objective optimization of SCNs has been considered by different researchers in literature. Sabri and Beamon (2000) developed an integrated multi-objective supply chain model for strategic and operational supply chain planning under uncertainties of product, delivery and demand. While cost, fill rates, and flexibility were considered as objectives, ε-constraint method had been used as a solution methodology. Chan and Chung (2004) proposed a multi-objective genetic optimization procedure for the order distribution problem in a demand driven SCN. They considered minimization of total cost of the system, total delivery days and the equity of the capacity utilization ratio for manufacturers as objectives. Chen and Lee (2004) developed a multi-product, multi-stage, and multi-period scheduling model for a multi-stage SCN with uncertain demands and product prices. As objectives, fair profit distribution among all participants, safe inventory levels and maximum customer service levels, and robustness of decision to uncertain demands had been considered, and a two-phased fuzzy decision-making method was proposed to solve the problem. Erol and Ferrell (2004) proposed a model that assigning suppliers to warehouses and warehouses to customers. They used a multi-objective optimization modeling framework for minimizing cost and maximizing customer satisfaction. Guillen, Mele, Bagajewicz, Espuna, and Puigjaner (2005) formulated the SCN design problem as a multi-objective stochastic mixed integer linear programming model, which was solved by ε-constraint method, and branch and bound techniques. Objectives were SC profit over the time horizon and customer satisfaction level. Chan, Chung, and Wadhwa (2004) developed a hybrid approach based on genetic algorithm and Analytic Hierarch Process (AHP) for production and distribution problems in multi-factory supply chain models. Operating cost, service level, and resources utilization had been considered as objectives in their study. The studies reviewed above have found a Pareto-optimal solution or a restrictive set of Pareto-optimal solutions based on their solution approaches for the problem. Our purpose in this paper is to present a solution methodology to obtain all Pareto-optimal solutions for the SCN design problem and enable the decision maker for evaluating a greater number of alternative solutions.

During the last decade, there has been a growing interest using genetic algorithms (GA) to solve a variety of single and multi-objective problems in production and operations management that are combinatorial and NP hard (Gen and Cheng, 2000, Dimopoulos and Zalzala, 2000, Aytug et al., 2003). In this study, we proposed a new approach based on GA for multi-objective optimization of SCNs which is one of the NP hard problems. Three objectives were considered: (1) minimization of total cost comprised of fixed costs of plants and distribution centers (DCs), inbound and outbound distribution costs, (2) maximization of customer services that can be rendered to customers in terms of acceptable delivery time (coverage), and (3) maximization of capacity utilization balance for DCs (i.e. equity on utilization ratios). The proposed GA was designed to generate Pareto-optimal solutions considering two different weight approaches. To investigate the effectiveness of the proposed GA, an experimental study using actual data from a company, which is a producer of plastic products in Turkey, was carried out into two stages. While the effects of weight approaches on the performance of proposed GA were investigated in the first stage, the proposed GA and multi-objective simulated annealing (MO_SA) proposed by Ulungu, Teghem, Fortemps, and Tuyttens (1999) were compared according to quality of Pareto-optimal solutions in the second stage.

The paper is organized as follows: In Section 2, multi-objective SCN design problem is formulated and discussed. Comprehensive explanation of the proposed GA is given in Section 3. Section 4 gives the computational results to show the performance of the GA using actual data obtained from a company in Turkey. Finally, concluding remarks are outlined and future research directions highlighted in Section 5.