Single machine scheduling with dynamic arrivals
Abstract
This thesis considers the single-machine scheduling (SMS) problem where jobs are subject to release dates and the objective is to minimize the sum of job completion times. The SMS problem can be used to model many manufacturing environments. The SMS problem is known to be NP-hard in the number of jobs. This implies that the existence of a polynomial time algorithm for its solution is unlikely. In this thesis, a number of procedures are developed for solving SMS. The first is an optimal solution procedure which relies on decomposing the SMS problem into a series of sub-problems which are identified through the use of forecast horizons. The optimal solution for the original problem can then be constructed from the optimal sub-problem solutions. Based on computational results, this approach appears to be more efficient than any previously published method. This computational improvement occurs since it is more efficient to solve several small problems than to solve a single large problem. This decomposition method is implemented as a forward procedure and is applicable to a variety of implicit enumeration methods and scheduling problems. While this decomposition approach is relatively efficient, problems can still become so large that it is impractical to solve them optimally. Thus, a heuristic procedure which identifies good solutions in a reasonable amount of time is developed using insights from the optimal decomposition approach. This heuristic utilizes a rolling horizon framework which allows the size of the sub-problem at each iteration to be controlled. This helps to control the computational effort required to obtain a solution. By increasing the size of the sub-problem, the heuristic can identify improved solutions but at a higher computational cost. Finally, we develop an improvement heuristic. This heuristic considers an existing schedule for SMS and identifies potential areas of improvement. The problem data is then altered in a systematic way so that feasible schedules which may be improvements over the previous schedule can be identified. Computational results indicate that this improvement heuristic is quite effective under a variety of conditions.
Degree
Ph.D.
Advisors
Uzsoy, Purdue University.
Subject Area
Management
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