ISE Graduate Seminar Series

Optimal Control of a Make-to-Stock System with Adjustable Production Rate

Maria E. Mayorga*
Department of Industrial Engineering and Operations Research
University of California at Berkeley

Date: Friday, October14th, 2005
Time: 9:00am
Location: Room 09-2139 (Kate Gleason Engineering Building)

Abstract:

The ability to meet uncertain deman efficiently is one of the most important goals for managers in manufacturing and service firms. One way for firms to cope with uncertain demand is to develop an ability to adjust capacity (or production rate) according to changing deman. Practices such as using overtime, floaters, and part-time workforce enable firms to adjust capacity to meet uncertain demand at additional costs. On the other hand, practices such as inventory rationing and prioritizing production according to the importance of an order, allow the firm to find a way to allocate limited production resources in a cost-effective manner. Although many firms use both practices simultaneously, very little work has been done to examine how to optimally adjust production capacity and allocate this capacity to various tasks.

We consider a multi-class make-to-stock production facility, served by a single server with adjustable production rate. Deman for each class arrives randomly and independent of each other. Each order is fulfilled with one unit of finished goods from on-hand inventory. An order which is not immediately satisfied from on-hand inventory is backordered, and a backorder cost rate is incurred. The facility produces finished goods one at a time according to an adjustable production rate. When an item is produced, it can immediately satisfy a backorder order in either queue or it can be stocked in inventory and incur a holding cost rate. We assume preemptions are allowed. Thus, at each order arrival and production completition time the decision maker must determine production rate and choose a prodcuction decision (i.e., whether to produce an item to stock or satisfy a backorder in either queue) and a rationing decision upon order arrival (i.e., whether to satisfy a new order from stock or backorder).

We formulate this problem as a Markov decision process using iniformization and characterize the structure of optimal capacity adjustment, production, and stock rationing policy. We show that the optimal capacity policy is monotone in current inventory and backorder levels. Furthermore, the choice of capacity can be characterized through exclusion criteria, which reduces the number of capacity settings considered when computing the optimal policy. To characterize the optimal production and rationing policy, we analyze the structure of the value functions and identify a set of properties that the optimality equation must satisfy if the optimal policy is employed. Using these results, we show that the optimal production control and stock-rationing policy can be represented by a single monotone switching curve. We further extend these results to the infinite horizon case under discounted and average cost criteria. Through a comprehensive numerical study, we show that the savings from joint decision making are significant.

Questions?
Contact Dr. Michael Kuhl at 475-2134 or mekeie@rit.edu

* Co-authored with Hyun-soo Ahn, Ross School of Business, University of Michigan at Ann Arbor and J. George Shanthikumar, Department of Industrial Engineering and Operations Research, University of California at Berkeley