A Three-Level Supply Chain Network Design Model with Risk-Pooling and Lead Times

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Transportation Research Part E 46 (2010) 563–581

Contents lists available at ScienceDirect

Transportation Research Part E
journal homepage: www.elsevier.com/locate/tre

A three-level supply chain network design model with risk-pooling and lead times Sukun Park, Tae-Eog Lee *, Chang Sup Sung
Department of Industrial and Systems Engineering, KAIST, 373-1, Guseong-dong, Yuseong-gu, Daejeon, Republic of Korea

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This paper considers a single-sourcing network design problem for a three-level supply chain consisting of suppliers, distribution centers (DC’s) and retailers, where risk-pooling strategy and DC-to-supplier dependent lead times are considered. The objective is to determine the number and locations of suppliers and DC’s, the assignment of each location-fixed DC to a supplier and that of each retailer to a DC, which minimizes the system-wide location, transportation, and inventory costs. The problem is formulated as a nonlinear integer programming model, for which a two-phase heuristic solution algorithm is derived based on the Lagrangian relaxation approach. Numerical experiments show that the proposed heuristic is effective and also efficient. Ó 2009 Elsevier Ltd. All rights reserved.

Article history: Received 21 April 2009 Received in revised form 29 August 2009 Accepted 17 November 2009

Keywords: Location-inventory model Risk-pooling Lead time Lagrangian relaxation Supply chain management

1. Introduction Under today’s increasingly competitive business environment with product life cycles being shortened, customer demands become more uncertain and keep varying greatly. The ‘‘risk-pooling” strategy has been proposed as one of the effective ways to manage such demand uncertainty (Eppen, 1979; Chen and Lin, 1989), for which inventory needs to be centralized at distribution centers (DC’s) for achieving appropriate service levels. Lead time is one of the critical factors substantially affecting the level of safety stock under the environment of random customer demands (Eppen and Martin, 1988; Karmarkar, 1993; Yang and Geunes, 2007). In the real field, lead times are often dependent on customer-to-supplier pairs due to various factors including physical distance, transportation mode, production capability, and manufacturing technology. Thereupon, total amount of the safety stock to be maintained at DC’s for achieving risk-pooling benefits depends not only on DC locations and their associated retailer assignments, but also on supplier (plant) locations and their associated DC assignments to the suppliers. However, none of the papers in the literature incorporating the risk-pooling strategy have considered DC-to-supplier dependent lead times on the network design decision yet. This provides the motivation of considering the proposed three-level supply chain network design problem with risk-pooling strategy and DC-to-supplier dependent lead times allowed. The proposed problem considers a three-level supply chain network composed of multiple number of suppliers, DC’s and retailers for single-item products for which customer demands occur randomly at each retailer. Each DC with finite capacity carries on-hand inventory to satisfy demands from its assigned retailers, along with taking care of safety stock to cope with demand variations from its assigned retailers under the risk-pooling strategy. Supply/order lead times from DC’s to suppliers are dependent on DC-to-supplier pairs. In the problem, the network design decisions on the number and the locations of suppliers and DC’s, and the assignment of each DC located and retailer, as well as the associated inventory control decisions * Corresponding author. Tel.: +82 42 350 3122; fax: +82 42 350 3110. E-mail addresses: waterut@kaist.ac.kr (S. Park), telee@kaist.ac.kr (T.-E. Lee), cssung@kaist.ac.kr (C.S. Sung). 1366-5545/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.tre.2009.12.004

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