(A) capacity expansion planning of equipment with conversion possibility

Abstract

This thesis describes a deterministic capacity expansion planning problem in which a firm has to meet demands for the services of two distinct but related equipments over a finite number of discrete time periods. Each equipment supplies two kinds of service demand devised into a fixed ratio. These service demands occurred at both equipments are similar so that capacity conversion from only one of the two equipments into the other can be made to fulfill the similar service roll. Therefore, such demands can be met by dircet capacity addition (installation) of capacity conversion from the other equipment in idle(exess). In other words, capacity expansions can be initiated by either installation or conversion at the associated costs. And once converted, the capacity becomes an integral part of the new equipment. All the cost functions including installation cost, conversion cost and holding cost are assumed to be nondecreasing and concave. The objective is to find a policy(plan) of capacity installation and conversion at each period over the whole planning horizon such that the total cost is minimized. Using a network flow approach, the optimal solution properties are characterized. And a dynamic programming algorithm is then developed, which can be used to solve the problem efficiently. Thereafter the model is extended to the cases with capacity bounds and short-term capacity leasing allowed, respectively.