Lot sizing in general assembly systems with setup costs, setup times, and multiple constrained resources

Article Abstract:

A heuristic algorithm called the Coefficient Modification Heuristic with Cost Balancing and Setup Reduction (CMHBR) for finding good, feasible solutions for multiproduct lot sizing in general assembly systems with setup costs, setup times and multiple constrained resources was presented. CMHBR utilizes the special structure of the underlying mathematical programming model, the one-to-one correlation between a subset of the continuous variables and the set of binary variables. A comparison of the CMHBR's solutions to time-truncated Optimization Subroutine Library (OSL) solutions of medium-sized randomly generated problems and to optimal solutions of small randomly generated problems showed that the algorithm is a practical, fast and efficient approach for solving lot sizing problems with general assembly structures and multiple constrained resources.

Production Management, Heuristic programming

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Lot sizing in serial assembly systems with multiple constrained resources

Article Abstract:

The Coefficient Modification Heuristic (CMH) is presented. It is a new heuristic for lot sizing in assembly systems with multiple stages and multiple constrained resources. It iteratively solves a small linear programming restriction of the original problem while implicitly dealing with the setups. CMH generates solutions by exploiting the resulting model structure instead of solving the underlying lot sizing model. It can therefore be applied to a bigger class of problems having such a structure. A comparison between the performance of CMH and that of the commercial code, Optimization System Library (OSL), is made by applying both to three sets of test problems. Results show that the solutions generated by CMH are, on average, 18% more effective than those obtained in the time constrained OSL runs.

Analysis, Heuristic, Heuristics (Psychology)

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An algorithm for single-item capacitated economic lot sizing with piecewise linear production costs and general holding costs

Article Abstract:

A pseudo-polynomial dynamic programming algorithm for solving the single-item capacitated economic lot sizing problem with piecewise linear production costs and general holding costs was proposed. Computational experiments showed that the running time of the proposed algorithm is only linearly dependent on the magnitude of the data as demonstrated by its capability to solve quite large problem instances within a reasonable length of time. The average running time of the algorithm grows more or less quadratically when the number of periods are increased while keeping all other characteristics constant. These results proved that the dynamic programming algorithm is a computationally feasible technique with a simple and elegant structure.

Research and Development in the Physical, Engineering, and Life Sciences, Mathematics, Polynomials, Dynamic programming, Costs, Industrial, Industrial costs

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