Optimal Order Policies in Assembly Systems with Random Demand and Random Supplier Delivery

Abstract

In this paper we consider an assembly problem where two critical components are required for assembly of the final product, the demand for which is stochastic. The components can be ordered separately from individual suppliers or in a set (a set refers to the components in the required ratio) from a joint supplier. We consider the case where the assembly stage is free, i.e., the firm procures and stores the components and sells complete sets. The supplier delivery process may be random owing to uncertainty in the production process (e.g., semiconductor industries). We assume that a supplier, with probability β (say), supplies 100% of the order quantity in the current period, and with probability (1 – β supplies nothing. If there is no delivery during this period, the order is delivered in the next period. The added complexity of coordinating shipments of different components requires careful planning in placing the orders. In the single-period problem, if no order is placed with the joint supplier, the order quantities from the individual suppliers follows an order-up-to policy structure with identical order levels. However, it is optimal to diversify (i.e., order from the joint supplier as well) when the inventory level is below a certain threshold (determined in this paper). With lower initial inventory levels, the firm cannot risk the cost of stockouts if the individual supplier(s) fail to deliver in the current period. With certain conditions on the cost and delivery parameters of the suppliers, we show that the policy structure for the multi-period problem is similar to that of the single-period problem, except that the order up-to-levels are not the same. Intuitively, it might be optimal to order extra components for use in the future. This is a direct consequence of the uncertainty in the delivery timing of the suppliers. Finally we conduct a computational study of the two-period problem and determine the effect of supplier costs and the probability of delivery on the optimal order policy. The policies are intuitive and offer a better understanding of the effect of supply and demand uncertainty on the assembly problem.

Additional information

Notes on contributors

Haresh Gurnani

Haresh Gurnani is an Assistant Professor of Information and Systems Management in the School of Business and Management at the Hong Kong University of Science and Technology. He received the bachelor’s degree in Mechanical Engineering from the Indian Institute of Technology, the M.S. in Operations Research and the Ph.D. in Operations Research and Operations Management, from Carnegie Mellon University, Pittsburgh, USA. His primary research interests are in enterprise supply chain management and multi-plant coordination, total quality management, logistics development and the analysis of the management of logistics projects, stochastic modeling and the impact of uncertainties on manufacturing systems, and manufacturing/marketing strategy. He has received several awards, including The William W. Cooper Award for the Best Doctoral Dissertation in the area of Business and Economics, The William Larimer Fellowship and President Richard Cyert Fellowship nomination. He has interacted extensively with industries, including such corporations as IBM, AT&T, and Texas Instruments, along with various Asian companies.

John Lehoczky

John Lehoczky is Professor of Statistics at Carnegie Mellon University, Pittsburgh, PA. He received the B.A. degree in mathematics from Oberlin College, Overlin, Ohio in 1965, and the M.S. and Ph.D. degrees in Statistics from Stanford University, Stanford, California in 1967 and 1969, respectively. He has been on the faculty of Carnegie Mellon University since 1969 and served as Head of the Department of Statistics from 1984 until 1995. His research interests involve applied probability theory with emphasis on models in the area of computer, communication and manufacturing systems. In addition, he is the senior member of the CMU Advanced Real-Time Technology (ART) Project and is doing research in distributed real-time systems. Dr. Lehoczky is a member of Phi Beta Kappa, a fellow of the Institute of Mathematical Statistics and the American Statistical Association and is an elected member of the International Statistical Institute. He is also a member of IEEE, ACM, AAAS and INFORMS. He served as area editor of Management Science from 1981 to 1986 and is associate editor of IEEE Transactions on Computers and Real-Time Systems.