A multi-echelon inventory management framework for stochastic and fuzzy supply chains Alev Taskin Gumus * , Ali Fuat Guneri Department of Industrial Engineering, Yildiz Technical University, 34349 Besiktas-Istanbul, Turkey article info Keywords: Supply chain management Multi-echelon inventory management Stochastic cost model Neural networks Neuro-fuzzy approximation abstract In this paper, for effective multi-echelon supply chains under stochastic and fuzzy environments, an inventory management framework and deterministic/stochastic-neuro-fuzzy cost models within the context of this framework are structured. Then, a numerical application in a three-echelon tree-structure chain is presented to show the applicability and performance of proposed framework. It can be said that, by our framework, efficient forecast data is ensured, realistic cost titles are considered in proposed mod- els, and also the minimum total supply chain cost values under demand, lead time and expediting cost pattern changes are presented and examined in detail. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Supply chain inventory management (SCIM) is an integrated ap- proach to the planning and control of inventory, throughout the entire network of cooperating organizations from the source of supply to the end user. SCIM is focused on the end-customer de- mand and aims at improving customer service, increasing product variety, and lowering costs (Giannoccaro, Pontrandolfo, & Scozzi, 2003). Most manufacturing enterprises are organized into networks of manufacturing and distribution sites that procure raw material, process them into finished goods, and distribute the finish goods to customers. The terms ‘‘multi-echelon” or ‘‘multi-level” produc- tion/distribution networks are also synonymous with such net- works (or supply chains (SCs)), when an item moves through more than one step before reaching the final customer (Ganeshan, 1999; Rau, Wu, & Wee, 2003). Fig. 1 shows a multi-echelon system consisting of a number of suppliers, plants, warehouses, distribu- tion centers and customers (Andersson & Melchiors, 2001; Axsater, 1990; Axsater, 2003). The analysis of multi-echelon inventory systems that pervades the business world has a long history (Chiang & Monahan, 2005). Given the importance of these systems, many researchers have studied their operating characteristics under a variety of condi- tions and assumptions (Moinzadeh & Aggarwal, 1997). Since the development of the economic order quantity (EOQ) formula by Harris in 1913, researchers and practitioners have been actively concerned with the analysis and modeling of inventory systems under different operating parameters and modeling assumptions (Routroy & Kodali, 2005). Research on multi-echelon inventory models has gained importance over the last decade mainly because integrated control of supply chains consisting of several processing and distribution stages has become feasible, through modern infor- mation technology (Diks & de Kok, 1998; Kalchschmidt, Zotteri, & Verganti, 2003; Rau et al., 2003). Clark and Scarf (1960) were the first to study the two-echelon inventory model (Bollapragada, Akella, & Srinivasan, 1998; Chiang & Monahan, 2005; Diks & de Kok, 1998; Dong & Lee, 2003; Rau et al., 2003; Tee & Rossetti, 2002; van der Vorst, Beulens, & van Beek, 2000). They proved the optimality of a base stock policy for the pure serial inventory sys- tem and developed an efficient decomposing method to compute the optimal base stock ordering policy. Bessler and Veinott (1965) extended the Clark and Scarf (1960) model to include gen- eral arborescent structures. The depot-warehouse problem was ad- dressed by Eppen and Schrage (1981) who analysed a model with stockless central depot (van der Heijden, 1999). Several authors have also considered this problem in various forms (Bollapragada et al., 1998; Dong & Lee, 2003; Moinzadeh & Aggarwal, 1997; Parker & Kapuscinski, 2004; Tee & Rossetti, 2002; van der Heijden, 1999; van der Vorst et al., 2000). Sherbrooke (1968) constructed the METRIC (Multi-Echelon Technique for Recoverable Item Control) model, which identifies the stock levels that minimize the expected number of backorders at the lower echelon subject to a budget constraint. Thereafter, a large set of models that generally seek to identify optimal lot sizes and safety stocks in a multi-echelon framework were produced by many researchers. In addition to analytical models, simulation models have also been developed to capture the complex interac- tions of the multi-echelon inventory problems. For detailed 0957-4174/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2008.06.082 * Corresponding author. Tel.: +90 2122597070/2242; fax: +90 2122585928. E-mail address: ataskin@yildiz.edu.tr (A.T. Gumus). Expert Systems with Applications 36 (2009) 5565–5575 Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa