Collaboration for a closed-loop deteriorating inventory supply chain with multi-retailer and price-sensitive demand P.C. Yang a , S.L. Chung b , H.M. Wee c,n , E. Zahara a , C.Y. Peng d a Marketing and Logistics Management Department, St. John’s University, Tamsui, Taipei 25135, Taiwan, ROC b Information Management Department, St. John’s University, Tamsui, Taipei 25135, Taiwan, ROC c Industrial and Systems Engineering Department, Chung Yuan Christian University, Chungli 32023, Taiwan, ROC d Industrial Engineering and Management Department, St. John’s University, Tamsui, Taipei 25135, Taiwan, ROC article info Article history: Received 6 September 2010 Accepted 24 July 2012 Available online 1 August 2012 Keywords: Collaboration Closed-loop supply chain Deteriorating item Price sensitive demand Price discounts abstract In this paper, a closed-loop logistics system with manufacturing and remanufacturing cycle is analyzed using three optimization methods. They are: (i) sequential optimization, (ii) centralized optimization without benefit sharing, and (iii) centralized optimization with benefit sharing. In the first method, the decisions of sequential optimization are made initially by the retailers, and then by the manufacturer. In the second method, the decision of the centralized optimization is made simultaneously by the whole logistics system. The second method is not favorable to the retailers because the retailers’ profit will become smaller as a result of collaboration. Therefore a third method with benefit sharing is investigated. The logistics system includes a manufacturer and multi-retailer considering price- sensitive demand and deterioration. Industrial examples of such products are IC chips, computers and mobile phones that usually outdate or decrease in value due to technological innovation. The decrease in value is considered as a form of deterioration. In order to add value, these outdated products can be remanufactured and resold to market. Four key effects are investigated in this study: (i) recycling in supply chain, (ii) deterioration, (iii) collaboration effect between manufacturer and retailers using three optimization methods, and (iv) price sensitive demand. & 2012 Elsevier B.V. All rights reserved. 1. Introduction One of the keys to successful supply chain management is system integration. Clark and Scarf (1960) presented a concept of serial multi-echelon structures to determine the optimal policy. Banerjee (1986) derived a joint economic lot size model for a single vendor, single buyer system when the vendor has a finite production rate. Goyal (1988) extended Banerjee’s model by relaxing the lot-for-lot production assumption. Wee and Jong (1998) studied the integration between parts and finished product with multi-lot size and deterioration. Yang et al. (2007, 2008) derived a collaborative vendor–buyer inventory system with different patterns of purchase cost, products price and market situations. Wee (1993) considers product deterioration as decay, damage, spoilage, evaporation, obsolescence, pilferage, loss of utility or loss of marginal value of a commodity that results in decreasing usefulness from the original one. Ghare and Shrader (1963) were the first authors to consider on-going deterioration of inventory. Other authors such as Kang and Kim (1983) and Raafat et al. (1991) assumed either instantaneous or finite production with different assumptions on the patterns of deterioration. Many enterprises have focused their attention on reverse supply chain to meet environmental concerns/regulations and social liability. Product remanufacturing such as transforming used items into marketable products through refurbishment, repair and upgrading can also yield substantial cost benefits. Schrady (1967) was the earliest author to propose a deterministic model with instantaneous production rate for manufacturing and remanufacturing. Schrady (1967) argued that optimal lot sizes for manufacturers and remanufacturers can be determined by the classical EOQ formula. Teunter and Laan (2002) used an average cost approach to derive inventory models with remanufacturing. Chung et al. (2008) developed a closed-loop model with single manufacturing and single remanufacturing cycles. Jaber and Saadany (2009) developed a manufacturing and remanufacturing inventory system under the condition of lost sale. Hsu et al. (2010) considered preservation technology investment for deteriorating inventory. Wee et al. (2011) and Chung and Wee (2011) considered deteriorating green products and supply chains inventory systems. Feng and Viswanathan (2011) derived a new lot-sizing heuristic with remanufacturing. Recently, Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/ijpe Int. J. Production Economics 0925-5273/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ijpe.2012.07.020 n Corresponding author. Tel.: þ886 3 2654409. E-mail address: weehm@cycu.edu.tw (H.M. Wee). Int. J. Production Economics 143 (2013) 557–566