Optimization of a Reverse Manufacturing System with Multiple Virtual Inventories Kenichi Nakashima* and Surendra M. Gupta** *Kanagawa university, Yokohama, Kanagawa 221-8686 JAPAN (Tel: +81-45-481-5661(ext.3721); e-mail: nakasima@ kanagawa-u.ac.jp). **Northeastern University, Boston, MA 02115 USA (e-mail: gupta@neu.edu) Abstract: This paper deals with a cost management problem of a remanufacturing system with stochastic variability such as demand. We model the system with consideration for two types of inventories. One is the actual product inventory in a factory. The other is the virtual inventory that is used by customer. For this virtual inventory, it should be required to consider an operational cost that we need in order to observe and check the quantity of the inventory. We call it the virtual inventory cost and model the system including it. We define the state of the remanufacturing system by the both of the inventory levels. It is assumed that the cost function is composed of various cost factors such as holding, backlog and some kinds of manufacturing costs etc. We obtain the optimal production policy that minimizes the expected average cost per period. Numerical results show the effects of the factors on the optimal policy. Keywords: Optimal control, MDP, Virtual inventory 1. INTRODUCTION The escalating growth in consumer waste in recent years has started to threaten the environment. Product recovery is mainly driven by the escalating deterioration of the environment and aims to minimize the amount of waste sent to landfills by recovering materials and parts from old or outdated products by means of recycling and remanufacturing. Product recovery includes collection, disassembly, cleaning, sorting, repairing and reconditioning broken components, reassembling and testing (Brennan et al.(1994), Gupta and Taleb(1994)). Managing reverse manufacturing or reverse supply chain includes activities necessary to acquire end of life products from customers to recover value and eventually dispose it (Prahinski and Kocabasoglu (2006)). In recent years, reverse supply chains have been garnering increased attention for various institution- and market-based mechanisms (Meyer (1999), Thierry et al. (1995), Toffel (2003)). Institution-based mechanisms include considerations such as limited landfill capacity, take-back laws, concerns of increasing carbon footprint, FRQVXPHU¶V backlash, etc. In contrast, market-based mechanisms include considerations such as increasing proportion of product returns, consumer preferHQFH IRU ‡JUHHQ· SURGXFWV KLJKHU UHYHQXHV WKURXJK secondary sales in global markets, second life for discarded products, etc. Within reverse supply chains, product recovery activities seek to reduce scrap by recovering materials and components from end-of-life or prematurely discarded/returned product from consumers. Here we focus on the product inventory which is taken back from the consumers in a reverse manufacturing system under stochastic variability stemming from the customer demand of the products. This paper deals with an optimal control problem of a remanufacturing system under stochastic variability such as demand. The system is formulated into a Markov Decision Process (MDP) (Howard(1960), Puterman(1994)). The MDP is a class of stochastic sequential processes in which the reward and transition probability depend only on the current state of the system and the current action. The MDP models have gained recognition in such diverse fields as economics, communications, transportation and so on. Each model consists of states, actions, rewards, and transition probability. In the engineering field, for example, the approach is used for controlling the production system (Ohno and Ichiki(1987), Ohno and Nakashima(1995)). Choosing an action as production quantity in a state generates rewards and/or costs, and determines the state at the next decision epoch through a transition probability function. Then, we can obtain the optimal production policy that minimizes the expected average cost per period in the optimal production control problem. We here consider two types of inventories. One is the actual product inventory in a factory, the other is the virtual inventory which is used by customer. We define the state of the remanufacturing system by the both of the inventory levels. We can obtain the optimal production policy that minimizes the expected average cost per period. We also consider some scenarios under various conditions using design of experiments. In section 2, we describe a brief review of the literature on the remanufacturing systems. In section 3, we consider a single-item remanufacturing system under stochastic demand. 7th IFAC Conference on Manufacturing Modelling, Management, and Control International Federation of Automatic Control June 19-21, 2013. Saint Petersburg, Russia 978-3-902823-35-9/2013 © IFAC 99 10.3182/20130619-3-RU-3018.00109