Stochastic Allocation of Inspection Capacity to Competitive Processes Wooseung Jang, 1 J. George Shanthikumar 2 1 Department of Industrial and Manufacturing Systems Engineering, University of Missouri-Columbia, Columbia, Missouri 65211 2 Department of Industrial Engineering and Operations Research, Walter A. Hass School of Business, University of California at Berkeley, Berkeley, California 94720 Received October 1998; revised April 2001; accepted 30 April 2001 Abstract: Optimal allocation and control of limited inspection capacity for multiple produc- tion processes are considered. The production processes, which operate independently but share inspection capacity, are subject to random failures and are partially observed through inspection. This study proposes an approach of stochastic allocation, using a Markov decision process, to minimize expected total discounted cost over an infinite time horizon. Both an optimal model and a disaggregate approximation model are introduced. The study provides some structural results and establishes that the control policy is of a threshold type. Numerical experiments demonstrate a significantly decreased amount of computational time required for the disaggregate approach when compared to the optimal solution, while generating very good control policies. c  2002 John Wiley & Sons, Inc. Naval Research Logistics 49: 78–94, 2002; DOI 10.1002/nav.1049 1. INTRODUCTION Consider a system that consists of multiple production processes, operating independently of one another, while sharing a common inspection capacity. The objective is to find optimal control and allocation of limited inspection capacity among several competing multiple production processes for the purpose of minimizing total operation costs. This study was motivated by the production-inspection procedures in semiconductor manufacturing. While active statistical process control is being conducted throughout the wafer fabrication processes, it is also quite common to have limited capacity for wafer inspection, primarily due to the high cost of equipment (see Leachman [7] and Nurani [11] for related discussions). Hence, it becomes crucial to develop process control policies that consider inspection capacity allocation. Although there are many studies on general capacity allocation or process control problems (see Porteus and Angelus [13] and Valdez-Flores and Feldman [22] for reviews and references), it appears that there is a lack of literature on multiple process control under inspection capacity constraints. Recently, Yao and Zheng [24] investigated the inspection process of multistage batch manufacturing, focusing on interstage coordination under capacity constraints. Assaf and Shan- thikumar [1] considered a two-state multiple process problem very similar to that presented in Correspondence to: W. Jang c  2002 John Wiley & Sons, Inc.