Supply chain modeling in uncertain environment with bi-objective approach Mehdi Mahnam * , Mohammad Reza Yadollahpour, Vahid Famil-Dardashti, Seyed Reza Hejazi Department of Industrial and Systems Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran article info Article history: Received 22 September 2007 Accepted 23 September 2008 Available online 30 September 2008 Keywords: Supply chain management Uncertainty Fuzzy sets Multi-objective decision making Simulation optimization Particle swarm optimization abstract Supply chain is viewed as a large-scale system that consists of production and inventory units, organized in a serial structure. Uncertainty is the main attribute in managing the supply chains. Managing a supply chain (SC) is very difficult, since various sources of uncertainty and complex interrelationships among various entities exist in the SC. Uncertainty may result from customer’s demand variability or unreliabil- ity in external suppliers. In this paper we develop an inventory model for an assembly supply chain net- work (each unit has at most one immediate successor, but any number of immediate predecessors) which fuzzy demand for single product in one hand and fuzzy reliability of external suppliers in other hand affect on determination of inventory policy in SCM. External supplier’s reliability has determined using a fuzzy expert system. Also the performance of supply chain is assessed by two criteria including total cost and fill rate. To solve this bi-criteria model, hybridization of multi-objective particle swarm optimi- zation and simulation optimization is considered. Results indicate the efficiency of proposed approach in performance measurement. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Supply chain (SC) consists of all steps which, directly or indi- rectly, fulfill customer’s requirements. The objective of any SC is to maximize total created value which is, in fact, the difference be- tween value of final product to customer and costs incurred during SC steps to fulfill customer’s requirements. Supply chain manage- ment generally includes management of data, money and product flow among chain steps (customers, retailers, distributors, manu- facturers, and suppliers) to maximize final profitability. Ap- proaches to model SC designing and analyzing problems are studied in four categories which are deterministic analytical, sto- chastic analytical, economical and simulation models. A specific modeling approach is applied in each category according to the nature of input information and study objectives (Beamon, 1998). Various deterministic and stochastic models have been devel- oped to study supply chain control and management (Ishii, Takah- ashi, & Muramatsu, 1988; Williams, 1981). Moreover, extensive research has been conducted to study demand uncertainty as a sto- chastic factor in SC inventory models. Cohen and Lee (1988) devel- oped a stochastic analytical model which covers the entire SC network. Svoronos and Zipkin (1991) considered multi-echelon SC systems with stochastic demand following Poisson distribution and provide a model to determine average inventory level and average backorder in each stock keeping unit (SKU). Lee and Bil- lington (1993) developed a heuristic stochastic model for material flow management. In their model, review period and order quan- tity is determined as model outputs. Lee, Billington, and Carter (1993) studied a stochastic model based on periodic review policy whose objective is to maximize customer service level. Van Hou- tum, Inderfurth, and Zijm (1996) reviewed the numerical and the- oretical models of stochastic multi-echelon systems with periodic review inventory policy. Supplier reliability (delivery tardiness), manufacturing process (machine failures and reliability of transportation), and customer’s demand (quantity and composition) are generally three major sources of uncertainty in a supply chain. Uncertainty also exists in estimates of inventory cost elements, e.g., cost of backorders. Many researchers modeled uncertainty in order to develop SC inventory strategies using probability distributions which are de- rived from analysis of previous experiences. However, past data are not always available or reliable (e.g. due to market turbulence and decreasing product life time as a result of increasing innova- tion level). Hence, it is claimed that probability theory is not suit- able for evaluating market demand and relevant inventory costs (Giannoccaro, Pontrandolfo, & Scozzi, 2003). In addition, when uncertainty exists as a result of difficulties in measuring market demand and inventory costs, possibility is applied in modeling uncertainty more often than probability. Fuzzy sets theory (Zadeh, 1978) can be an alternative approach to deal with uncertainty in supply chains. Few researchers have ap- plied fuzzy sets theory in supply chain management. Petrovic, Roy, and Petrovic (1998), Petrovic, Roy, and Petrovic (1999) modeled supplier’s reliability using fuzzy sets and presented a fuzzy model to determine the order-up-to level in each SKU independently on 0360-8352/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2008.09.038 * Corresponding author. Tel.: +98 311 3912550; fax: +98 311 3915526. E-mail address: mahnam@in.iut.ac.ir (M. Mahnam). Computers & Industrial Engineering 56 (2009) 1535–1544 Contents lists available at ScienceDirect Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie