435 CHIU et al: OPTIMAL COMMON CYCLE TIME FOR MULTI-ITEM PRODUCTION Journal of Scientific & Industrial Research Vol. 72, July 2013, pp. 435-440 *Author for correspondence E-mail: hwangmh@cyut.edu.tw Optimal common cycle time for a multi-item production system with discontinuous delivery policy and failure in rework Yuan-Shyi Peter Chiu 1 , Hong-Dar Lin 1 , Feng-Tsung Cheng 2 and Ming-Hon Hwang 3 * 1 Department of Industrial Engineering & Management, Chaoyang University of Technology, Taiwan 2 Department of Industrial Engineering and Systems Management, Feng Chia University, Taiwan 3 Department of Marketing and Logistics Management, Chaoyang University of Technology, Taiwan Received 25 August 2012; revised 12 January 2013; accepted 01 May 2013 This study is concerned with the optimal common cycle time for a multi-item production system with discontinuous delivery and failure in rework. In real life manufacturing environments, managements often plan to produce multiple products in turn on a single machine in order to maximize machine utilization. Also, dealing with random defective items during production seems to be an inevitable task, and the multi-delivery policy is commonly adopted to distribute the finished products to buyers. The objective of this study is to determine the optimal common production cycle that minimizes the total production-inventory- delivery costs per unit time for a multi-item production system with failure in rework and multi-delivery policy. Mathematical modeling along with an optimization procedure is used to derive the optimal common cycle time for the aforementioned production problem. Keywords: multi-item production, optimization, common cycle time, failure in rework, scrap, multi-shipment Introduction A mathematical technique was first introduced 1 to solve the economic production quantity (EPQ) problem for single product under the assumption of perfect production and the policy of continuous inventory issuing. However, in real life production environments, managements often plan to produce multiple products in turn on a single machine in order to maximize machine utilization. Gordon and Surkis 2 presented a simple and practical approach to determine the control policies for a multi-item inventory environment where the items are ordered from a single supplier and the demand for items are subject to severe fluctuations. The time between the orders can either be fixed or based on a system of accumulating a fixed order quantity for all products. Their model balanced the stock carrying and stock-out costs. An operational system structure was developed and a simulation procedure adopted to determine the appropriate value of their inventory factor in the model. Zahorik et al . 3 investigated a multi-item, multi-level production scheduling problem with linear costs and production and inventory constraints at a key facility. Two multi-item problems were considered, one where the constraint was on shipping capability and the other where there was a final stage bottleneck machine. A multi-item Facilities-in-series problem was formulated as a linear program, and a three-period result was used as the basis for a rolling heuristic for T-period problems. They discussed the conditions under which this heuristic fails to find optimal solutions, and provide computational comparisons to standard linear programming. Rosenblatt 4 compared two policies for the joint replenishment problem with a general ordering cost function. The fixed-cycle policy used a dynamic programming approach, resulting in partitioning the items into groups. The basic-cycle policy used a heuristic approach to partition the items into only two groups. A simulation model was developed to compare the effectiveness of the two policies and the economic order quantity approach. Leachman and Gascon 5 proposed a heuristic scheduling policy for multi- item, single-machine production systems facing stochastic, time-varying demands. Their dynamic cycle length heuristic, integrated feedback control based on the monitoring of inventory levels with the maintenance of economic production cycles. The policy could be applied time period by time period to decide on which items to produce and in what quantities during the next time period. Extensive studies related to various aspects