Capacity reservation in a cyclic planning environment

Edith Katherine Schmidt, Purdue University

Abstract

This thesis considers the reservation of capacity in a cyclic planning environment. We develop analytical models for the single-period, one-family, two-item, one- two- and m-machine problem in which capacity must be reserved before item demand for that period is known. These problems have two stages: first capacity is reserved for the family, then after demand is realized a cost minimizing production decision is made for the family. The joint demand distribution for the items in the family is known. For the one-machine model, we show the capacity reservation decision can be viewed as an extension to the classic newsboy problem. The two-machine and m-machine problems give rise to the concept of a demand region for each machine. Generally, a machine's demand region is that subset of possible demands that results in production decisions that fully utilize the reserved capacity for that machine. A key property is that in an optimal solution to the capacity reservation problem, each machine has a positive probability of being a bottleneck, and that for m-2 of the machines this probability is not dependent on the demand distribution. We give optimality conditions for the capacity reservation problem. We then present a case study of the cyclic planning problem at ALCOA, an aluminum tube manufacturer. In the case study demand is known prior to capacity allocation but actual realized capacity is random due to machine breakdowns. Further, we consider multiple families in this application. The resulting problem is a single-period, rolling-horizon multiple family, multiple item problem in which the amount of capacity we reserve for each family attempts to equalize the customer due date tardiness by product family. We then describe how cyclic planning resulted in lower work-in-process inventory, enhanced production and workforce planning, improved customer order promising, and a substantial reduction in customer backlog.

Degree

Ph.D.

Advisors

Ward, Purdue University.

Subject Area

Management|Operations research|Industrial engineering

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