Dynamic programming solutions to deterministic machine replacement models
Abstract
In this thesis we consider three different machine replacement models. The replacement or upgrade of productive resources over time is an important decision for an organization, and the type of technology used in the productive resources determines how effectively the manufacturing operations can support the product and marketing strategy of the organization. In the models proposed here, machines will be replaced due to increasing operating costs for aging machines and the emergence of newer technologies that are less expensive to operate. We first consider a single machine replacement problem in which the effects of learning cause the sequence of keep/replace decisions made over time to become interdependent. A forward dynamic programming algorithm is developed which can be used to solve finite horizon problems. Decision and forecast horizon results ensure that choices made during the decision horizon based only on information over the forecast horizon are also optimal for any longer horizon problem. The second model we propose deals with the parallel machine replacement problem, in which a population of machines of various ages are in operation and in each period decisions must be made whether to keep or replace each machine. Economies of scale effects make the decisions for separate machines interdependent, and this problem is therefore much more complex than the single machine problem. An efficient forward-time branch-and-search algorithm is developed for optimally solving the problem as formulated. The aim of the final model is to integrate the machine replacement and capacity expansion decisions. By considering these decisions jointly some economies of scale may be gained which would not be realized if the decisions were made separately. In this model, demand is nonstationary and capacity expansion therefore becomes necessary. We prove several analytical results that allow the problem size to be greatly reduced. These analytical results are used to develop an effective heuristic for solving this problem. The heuristic has given solutions to a set of test problems that are very close to optimal.
Degree
Ph.D.
Advisors
Ward, Purdue University.
Subject Area
Management|Operations research
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