This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: Robust Capacity Planning in Semiconductor Manufacturing Francisco Barahona * Stuart Bermon * Oktay G¨unl¨uk * Sarah Hood † October, 2001 (Revised February, 2005) Abstract We present a stochastic programming approach to capacity planning under demand uncertainty in semiconductor manufacturing. Given multiple demand scenarios together with associated prob- abilities, our aim is to identify a set of tools that is a good compromise for all these scenarios. More precisely, we formulate a mixed-integer program in which expected value of the unmet demand is minimized subject to capacity and budget constraints. This is a difficult two-stage stochastic mixed-integer program which can not be solved to optimality in a reasonable amount of time. We instead propose a heuristic that can produce near-optimal solutions. Our heuristic strengthens the linear programming relaxation of the formulation with cutting planes and performs limited enumeration. Analyses of the results in some real-life situations are also presented. * IBM T. J. Watson Research Center, Yorktown Heights, NY 10598 † IBM Microelectronics Division 1 1 Introduction In the semiconductor industry, the determination of the number of manufacturing tools needed to manufacture forecasted product demands, is particularly difficult because of its sensitivity to product mix, the uncertainty in future demand, the long lead time for obtaining tools and large tool costs. Tools used in the manufacturing process are highly customized and made to order with delivery lead times up to 18 months and costs ranging from below $1 million to over $13 million. The total capital investment for a plant is typically several billion dollars. The product demand is highly volatile and therefore it is difficult to predict the demand profile for the mix of products over several months or years. Planning for a single demand profile can result in a large gap between planned and needed capacity when the actual demand materializes. Our goal in this paper is to explore a stochastic programming approach to produce a tool set that is robust with respect to demand uncertainty. To achieve this, we consider multiple demand scenarios instead of a single one. We associate a probability with each scenario and formulate a mixed-integer programming model in which the expected value of the unmet demand is minimized subject to capacity and budget constraints. We solve the resulting two-stage stochastic mixed-integer program to near-optimality using a heuristic based on cutting planes and limited enumeration. Capacity planning in the semiconductor industry is typically implemented using spreadsheets [3, 16, 19] or when considerations of cycle time are important, using discrete- event simulation . These methods do not involve the application of optimization tech- niques and require multiple runs to find a solution which may effectively use the tools to “maximize” profit, revenue or throughput. Linear programming based techniques have...
View Full Document
This note was uploaded on 04/11/2011 for the course ECE 357 taught by Professor Subjolly during the Spring '11 term at National University of Ireland, Galway.
- Spring '11
- C Programming