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Optimal level schedules for mixed-model, multi-level just-in-time assembly systems

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Abstract

Solving the level (or balanced) schedule problem is the most important scheduling goal for just-in-time production assembly systems. No previous methods have been presented for determining optimal balanced schedules in multi-level facilities. In this paper, it is shown that the multi-level, min-max problem is NP-hard in the strong sense. A dynamic programming algorithm (DP) is developed for both the min-max and min-sum problems which, for the first time, permits optimal schedules to be determined for large, multi-level problems. The time and space requirements of the DP are analyzed and several techniques for reducing the DP's computational requirements are described. A filtering scheme is proposed to eliminate dominated solutions from a problem's potentially vast state space. Extensive computational testing of the min-max algorithm is reported and the conclusions from this testing are presented.

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Authors
  1. Wieslaw Kubiak
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  2. George Steiner
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  3. Julian Scott Yeomans
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Kubiak, W., Steiner, G. & Scott Yeomans, J. Optimal level schedules for mixed-model, multi-level just-in-time assembly systems. Annals of Operations Research 69, 241–259 (1997). https://doi.org/10.1023/A:1018985029260

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