Applying nonlinear MODM model to supply chain management with quantity discount policy under complex fuzzy environment

Journal of Industrial Engineering and Management JIEM, 2014 – 7(3): 660-680 – Online ISSN: 2013-0953 – Print ISSN: 2013-8423 http://dx.doi.org/10.3926/jiem.1079 Applying Nonlinear MODM Model to Supply Chain Management with Quantity Discount Policy under Complex Fuzzy Environment Zhe Zhang1, Jiuping Xu2* 1 School Economics & Management, Nanjing University of Science and Technology (CHINA) Uncertainty Decision-Making Laboratory, Sichuan University (CHINA) 2 , Received: January 2014 Accepted: May 2014 Abstract: Purpose: The aim of this paper is to deal with the supply chain management (SCM) with quantity discount policy under the complex fuzzy environment, which is characterized as the bifuzzy variables. By taking into account the strategy and the process of decision making, a bifuzzy nonlinear multiple objective decision making (MODM) model is presented to solve the proposed problem. Design/methodology/approach: The bi-fuzzy variables in the MODM model are transformed into the trapezoidal fuzzy variables by the DMs's degree of optimism α1 and α2, which are de-fuzzified by the expected value index subsequently. For solving the complex nonlinear model, a multi-objective adaptive particle swarm optimization algorithm (MO-APSO) is designed as the solution method. Findings: The proposed model and algorithm are applied to a typical example of SCM problem to illustrate the effectiveness. Based on the sensitivity analysis of the results, the bifuzzy nonlinear MODM SCM model is proved to be sensitive to the possibility level α1. Practical implications: The study focuses on the SCM under complex fuzzy environment in SCM, which has a great practical significance. Therefore, the bi-fuzzy MODM model and MOAPSO can be further applied in SCM problem with quantity discount policy. -660- Journal of Industrial Engineering and Management – http://dx.doi.org/10.3926/jiem.1079 Originality/value: The bi-fuzzy variable is employed in the nonlinear MODM model of SCM to characterize the hybrid uncertain environment, and this work is original. In addition, the hybrid crisp approach is proposed to transferred to model to an equivalent crisp one by the DMs's degree of optimism and the expected value index. Since the MODM model consider the bi-fuzzy environment and quantity discount policy, so this paper has a great practical significance. Keywords: bi-fuzzy variable, nonlinear, multi-objective programming, sensitivity analysis, particle swarm optimization 1. Introduction A supply chain (SC) is a system of facilities and activities that functions to procure, produce, and distribute goods to the customers. Basically, supply chain management (SCM) is a set of approaches utilized to efficiently integrate suppliers, manufacturers, warehouses, and stores, so that merchandise is produced and distributed at the right quantities, to the right locations, and at the right time, in order to minimize system-wide costs (or maximize profits) while satisfying service level requirements (Simchi-Levi , Kaminsky & Simchi-Levi, 2000). In this situation, SCM has become the foundation for the operations management nowadays (Al-e-hashem, Malekly & Aryanezhad, 2011). In traditional SCM, the focus of the integration of supply chain network is usually on single objective, i.e., minimum cost or maximum profit. However, in practice, there are no design tasks that are single objective problems. In SC, different members have different conflicting objectives, such as cost and quality, on time delivery and quality, and so on. Chen and Lee (2004) presented a multi-product, multi-stage, and multi-period scheduling model to deal with multiple incommensurable goals for a multi-echelon supply chain network with uncertain market demands and product prices. Altiparmak, Gen, Lin and Paksoy (2006) designed a new solution procedure based on genetic algorithms to find the set of Pareto-optimal solutions for multi-objective supply chain network problem. In addition, to deal with the multiple objectives and enable the decision maker for evaluating a greater number of alternative solutions, two different weight approaches are implemented in the proposed solution procedure. Torabi and Hassini (2008) proposed a multiobjective possibilistic mixed integer linear programming model (MOPMILP) for integrating procurement, production and distribution planning considering various conflicting objectives simultaneously as well as the imprecise nature of some critical parameters such as market demands, cost/time coefficients and capacity levels. Arikan (2013) considered three objective functions, which were minimization of costs, maximization of quality and maximization of ontime delivery, in the suppliers selection problems of SCM. The application of MODM in SCM will become increasingly extensive and in-depth because SCM has made managers and analysts to shift their focuses from only manufacturing plant to the entities process. -661- Journal of Industrial Engineering and Management – http://dx.doi.org/10.3926/jiem.1079 Another key issue which also worth our attention in SCM is the inevitable uncertainty. Actually, the variables in SCM, such as the market demands, availabilities of raw materials, buyer's cost, are usually uncertain. Traditionally, the subjective uncertainty, i.e. the perception and dissension of decision makers (DMs), in SCM is assumed to be fuzzy. The fuzzy set theory, which was initialized by Zadeh in 1965, can be used to handle the uncertain issues such as demands, e x t e r n al raw m at e r ia l s up p l y de l i ve r y, i nve n t o r y c o s t, a n d s o o n . Giannoccaro, Pontrandolfo and Scozzi (2003) applied the fuzzy sets theory to characteristic the uncertainties associated with both market demand and inventory cost. Wei, Liang and Wang (2007) adopted the fuzzy set theory to resolve the ambiguities involved in assessing SCM alternatives and aggregating the linguistic evaluations. Wang and Shu (2008) developed a fuzzy decision methodology that provided an alternative framework to handle supply chain uncertainties and to determine supply chain inventory strategies, while there was lack of certainty in data or even lack of available historical data. Tabrizi and Razmi (2013) proposed a mixed-integer non-linear mathematical model in which the uncertainties were represented by the fuzzy set theory, and applied an interactive resolution method to provide the decision maker with alternative decision plans in regard to the different satisfaction degrees. In practice, however, we may face a complex fuzzy environment in the practical SCM. For example, in order to collect the data of inventory cost, some investigations and surveys are made to the different experienced managers (i.e., m = 1, 2, …, M, where m is the index of managers). Instead of the exact parameters, the managers can describe the parameters as an interval [lm, rm] with the most possible value pm (i.e., a fuzzy variable (lm, pm, rm)), such as “the maximal i (...truncated)