Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027 2
School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853 3
School of Management, University of Texas at Dallas, Richardson, Texas 75083
Received 29 October 2003; revised 24 August 2005; accepted 30 September 2005 DOI 10.1002/nav.20128 Published online 12 December 2005 in Wiley InterScience (www.interscience.wiley.com).
Abstract: Capacity planning decisions affect a signiﬁcant portion of future revenue. In equipment intensive industries, these decisions usually need to be made in the presence of both highly volatile demand and long capacity installation lead times. For a multiple product case, we present a continuous-time capacity planning model that addresses problems of realistic size and complexity found in current practice. Each product requires speciﬁc operations that can be performed by one or more tool groups. We consider a number of capacity allocation policies. We allow tool retirements in addition to purchases because the stochastic demand forecast for each product can be decreasing. We present a cluster-based heuristic algorithm that can incorporate both variance reduction techniques from the simulation literature and the principles of a generalized maximum ﬂow algorithm from the network optimization literature. © 2005 Wiley Periodicals, Inc. Naval Research Logistics 53: 137–150, 2006 Keywords: capacity planning; stochastic demand; simulation; submodularity; semiconductor industry
Because highly volatile demands and short product life cycles are commonplace in today’s business environment, capacity investments are important strategic decisions for manufacturers. In the semiconductor industry, where the proﬁt margins of products are steadily decreasing, manufacturers may spend up to 3.5 billion dollars for a state-of-the-art plant [3, 23]. The capacity decisions are complicated by volatile demands, rising costs, and evolving technologies, as well as long capacity procurement lead times. In this paper, we study the purchasing and retirement decisions of machines (or interchangeably, “tools”). The early purchase of tools often results in unnecessary capital spending, whereas tardy purchases lead to lost revenue, especially in the early stages of the product life cycle when proﬁt margins are highest. The process of determining the sequence and timing of tool purchases and possibly retirements is referred to as strategic capacity planning. Our strategic capacity planning model allows for multiple products under demand uncertainty. Demand evolves over time and is modeled by a set of scenarios with associated Correspondence to: W.T. Huh (firstname.lastname@example.org) © 2005 Wiley Periodicals, Inc.
probabilities. We allow for the possibility of decreasing demand. Our model of capacity consumption is based on three layers: tools (i.e., machines), operations, and products. Each product requires a ﬁxed, product-speciﬁc set of operations. Each operation can be performed on any tool. The time required depends on both the operation and the tool. In our model time is a continuous variable, as opposed to the more traditional approach of using discrete time buckets. Our primary decision variables, one for each potential tool purchase or retirement, indicate the timing of the corresponding actions. In contrast, decision variables in typical discrete-time models are either binary or integer and are indexed by both tool groups and time periods. Our objective is to minimize the sum of the lost sales cost and the capital cost, each a function of tool purchase times and retirement times. Our continuous-time model has the advantage of having a smaller number of variables, although it may be difﬁcult to ﬁnd global optimal...