On-line supplement On the Integrated Production and Distribution Problem with Bi-directional Flows Lei Lei Department of Supply Chain Management and Marketing Sciences, Rutgers University, 180 University Avenue, Newark, New Jersey 07102, USA, llei@business.rutgers.edu Hua Zhong Economics & Business Division, SUNY College at Oneonta, Ravine Parkway, Oneonta, New York 13820, USA, zhongh@oneonta.edu W. Art Chaovalitwongse Department of Industrial and Systems Engineering, Rutgers University, 96 Frelinghuysen Rd, Piscataway, New Jersey 088554, USA, wchaoval@rci.rutgers.edu In the literature, there have been several streams of research on problems involving reverse flows: network design for reverse flows, inventory control for returns, closedloop supply chains, and green supply chains. The studies on network design for reverse flows mainly focus on the decision with respect to facility locations and the design of logistics structures for shipping used/returned products back to the facilities. Among the recent results in network design, Fleischmann et al. (2000, 2001) analyzed the impact of reverse flows on network designs and operational performance of a supply chain. Nakashimay et al. (2002) introduced a discrete time Markov chain model for evaluating the performance of a product recovery system with stochastic demand. Schultmann et al. (2003) studied a two-stage facility-location problem and solved the problem via branchand-bound. The solution was then integrated into a simulation model to design a closedloop supply chain of spent batteries. Jayaraman et al. (2003) presented mathematical models for locating the recycling facilities and proposed heuristics to solve the location problem. More recently, Salema et al. (2007) introduced a general framework for the design of networks to support reverse flows. Real life applications of network designs for reverse flows can be found in the studies by Kroon and Vrijens (1995), Spengler et al. (1997), Barros et al. (1998), Louwers et al. (1999), Krikke et al. (1999a), Biehla el al. (2007), and Lee and Dong, (2008). Two excellent reviews on related work can be found
in Fleischmann (1997) and Carter (1998). In contrast to the work in this area, our study focuses on the integrated planning and scheduling of production, inventory, and shipping operations for a given network with bi-directional flows. There have also been many studies on inventory control for reverse flows, aiming at integrating the reverse flow into the manufacturers' materials planning. Cohen et al. (1980) showed the optimality of a periodic review order-up-to policy for a special case of such inventory problems. Heyman (1977) studied an inventory model with stochastic demand and returns, assuming negligible fixed cost, and procurement and repair times. This work was later extended by Muckstadt and Isaac (1981), and Kelle and Silver (1989). Van der Laan and Salomon (1997) empirically studied the average long-run behavior of different inventory control policies. Inderfurth (1997) analyzed the replenishment policies under non-zero lead-times for orders and recovery. Fleischmann et al. (2002) introduced a new inventory model and the optimal policy for managing the product to be reused, and Kiesmuller (2003) studied the inventory policies in a stochastic recovery system. Inderfurth (2005) studied the behavior of a product recovery system to find the optimal recovery and production policy and the impact of cost-efficient decision making. Different from our study, the main focus of inventory control is on inventory replenishment policies, not operations scheduling. Most existing studies on closed-loop supply chains and green supply chains are concerned with the development of managerial strategies and policies for environmental protection and sustainability. The research on green supply chains focuses heavily on environmental issues, the linkages between the operations policies of supply chain partners, and the activities (collaboration and evaluation) performed by plant managers, suppliers, and customers. Murphy et al. (1995) reported that 60% of the managers (interviewed in their study) considered the environmental issues to be very important in the business of their companies. Handfield and Nichols (1999) indicated that green issues will play an important role in future supply chain management. Van Hoek (1999) examined the differences between reverse logistics and green supply chain management. The term green supply chain management is coined to refer to management practices that aim at reducing sources of waste and consumption of resources, which, however, are not the main focus of reverse logistics processes. Beamon (1999) investigated
environmental factors and analyzed performance measures for the design of green supply chains. A general procedure towards achieving and maintaining green supply chains was then proposed. Lakhal and H Mida (2003) suggested a framework for developing quantitative models to manage the process of greening a supply chain, and to assess the greenness of an existing supply chain. On the other hand, the studies on managing closedloop supply chains have focused on the sustainability of a system by making sure that the society (plants and customers) efficiently and effectively uses and reuses all the resources invested in the products. Representative work in this area can be found in the studies by Fleischmann et al. (2000), Fleischmann et al. (2001), Van Hillegersberg et al. (2001), Guide and Van Wassenhove (2003), Krikke et al. (2003), Spengler and Schröter (2003), Ketzenberg et al. (2003), Ferguson et al. (2005), Schultmann et al. (2006), and Sheu (2008). Reference for Online Supplement Barros, A. I., R. Dekker, V. Scholten. 1998. A two-level network for recycling sand: A case study. European Journal of Operational Research 110 199-214. Beamon, B. M. 1999. Designing the green supply chain. Logistics Information Management 12 (4) 332-342. Biehla, M., E. Praterb, M.J. Realff. 2007. Assessing performance and uncertainty in developing carpet reverse logistics systems. Computers & Operations Research 34 443-463. Carter, C. R. 1998. Reverse logistics: A review of the literature and framework for future investigation. Journal of Business Logistics 19 85-102. Cohen, M.A., W.P. Pierskalla, S. Nahmias. 1980. A dynamic inventory system with recycling. Naval Research Logistics Quarterly 27(1) 289-296. Ferguson, M., V.D. Guide, Jr., G.C. Souza. 2005. Supply chain coordination for false failure returns. Penn State Working Paper, November 2005. Fleischmann, M., R. Kuik, R. Dekker. 2002. Controlling inventories with stochastic item returns: A basic model. European Journal of Operational Research 138 63-75.
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