Bi-objective optimization of a multi-product multi-period three-echelon supply chain problem under uncertain environments: NSGA-II and NRGAby Seyed Hamid Reza Pasandideh, Seyed Taghi Akhavan Niaki, Kobra Asadi

Information Sciences

Text

Accepted Manuscript

Bi-objective optimization of a multi-product multi-period three-echelon supply chain problem under uncertain environments: NSGA-II and NRGA

Seyed Hamid Reza Pasandideh, Seyed Taghi Akhavan Niaki, Kobra Asadi

PII: S0020-0255(14)00873-1

DOI: http://dx.doi.org/10.1016/j.ins.2014.08.068

Reference: INS 11098

To appear in: Information Sciences

Received Date: 23 February 2014

Revised Date: 10 August 2014

Accepted Date: 29 August 2014

Please cite this article as: S.H. Reza Pasandideh, S.T. Akhavan Niaki, K. Asadi, Bi-objective optimization of a multiproduct multi-period three-echelon supply chain problem under uncertain environments: NSGA-II and NRGA,

Information Sciences (2014), doi: http://dx.doi.org/10.1016/j.ins.2014.08.068

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Bi-objective optimization of a multi-product multi-period three-echelon supply chain problem under uncertain environments: NSGA-II and NRGA

Seyed Hamid Reza Pasandideh, Ph.D.

Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

Phone: +98 (21) 88830891, Fax: +98 (21) 88329213, e-mail: shr_pasandideh@tmu.ac.ir

Seyed Taghi Akhavan Niaki1

Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran , Ph.D.

Phone: +98 21 66165740, Fax: +98 21 66022702, e-mail: Niaki@Sharif.edu

Kobra Asadi, M.Sc.

Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

Phone: +98 (21) 88830891, Fax: +98 (21) 88329213, e-mail: asadi_kb@yahoo.com

Abstract

Bi-objective optimization of a multi-product multi-period three-echelon supply-chain-network problem is aimed in this paper. The network consists of manufacturing plants, distribution centers (DCs), and customer nodes. To bring the problem closer to reality, the majority of the parameters in this network including fixed and variable costs, customer demand, available production time, set-up and production times, all are considered stochastic. The goal is to determine the quantities of the products produced by the manufacturing plants in different periods, the number and locations of the warehouses, the quantities of products transported between the supply chain entities, the inventory of products in warehouses and plants, and the shortage of products in periods such that both the expected and the variance of the total cost are minimized. The problem is first formulated into the framework of a single-objective stochastic mixed integer linear programming model. Then, it is reformulated into a bi-objective deterministic mixedinteger nonlinear programming model. To solve the complicated problem, a non-dominated sorting genetic algorithm (NSGA-II) is utilized next. As there is no benchmark available in the literature, another

GA-based algorithm called non-dominated ranking genetic algorithm (NRGA) is used to validate the results obtained. In both algorithms, a modified priority-based encoding is proposed. Some numerical illustrations are provided at the end to not only show the applicability of the proposed methodology, but also to select the best method using a t-test along with the simple additive weighting (SAW) method.

Keywords: Supply chain management; Uncertainty; Mixed-integer nonlinear programming; NRGA &

NSGA-II; SAW 1 Corresponding Author 2 1. Introduction

The concept of supply chain management (SCM), one of the most important managerial practices manifested in the early 1990s, has recently been the focus of many researchers. A supply chain is an integrated network consisting of suppliers, manufacturing plants, warehouses, customers, and distribution channels that are organized efficiently to receive raw materials, to convert them to finished products, to locate distribution centers, to select proper transportation channels, and finally to distribute products to customer nodes at the right quantities, to right locations, and at right time. In SCM, the entire components that work all together to provide products or services for customers are taken into account. Supply chain managers always seek the best decisions at different levels of strategic design, tactical planning, and operational planning.

In most of the classical supply chain network designs, the goal has been to send products from one layer to another in order to supply demands such that sum of strategic and tactical/operational cost is minimized. For instance, Amiri [4] developed a SC model to obtain the best strategic decisions on locating production plants and distribution warehouses in order to dispatch the products from plants to customers with the goal of minimizing the total costs of the distribution network. Gebennini et al. [14] suggested a three-stage production–distribution system to minimize costs.

Intricacy involved in mutual relations between various supply chain components together with risks and uncertainties throughout the chain have turned the SC decision-making process into a challenging problem, where newer goals are propound. The uncertainties involved in supply chain networks are divided into three classes based on the supplier layer, receiver layer, and in the middle layers. Because reversing the decisions in relation to the SC network configuration is very costly and difficult, the importance of the interactions between these decisions is largely enhanced under uncertainty.

Bidhandi and Yusuff [7] modeled a stochastic supply chain network as a two-stage program under strategic and tactical decisions. They also mentioned that customer demands, operational costs, and the capacity of the facilities might be highly uncertain as all of them can severely affect the strategic decisions. In the strategic level, Snyder [38] investigated a problem called the "reliable facility location 3 problem (RFLP)" to locate facilities at distributer level of a SC under uncertainty when facilities were subject to random failures. Murthy et al. [29] pointed out that the uncertainty at the strategic level is the most important and difficult issue to be considered. In the tactical level, Van Landeghem and Vanmaele [42] worked on a supply chain planning problem that involved the distribution of raw materials and products. Moreover, Jamshidi et al. [23] proposed a bi-objective multi-echelon SCN design model considering several transportation options at each level of the chain with different costs and a capacity constraint.