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Precedence theorems and dynamic programming for the single-machine weighted tardiness problem

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  • Rostami, Salim
  • Creemers, Stefan
  • Leus, Roel

Abstract

We tackle precedence-constrained sequencing on a single machine in order to minimize total weighted tardiness. Classic dynamic programming (DP) methods for this problem are limited in performance due to excessive memory requirements, particularly when the precedence network is not sufficiently dense. Over the last decades, a number of precedence theorems have been proposed, which distinguish dominant precedence constraints for a job pool that is initially without precedence relation. In this paper, we connect and extend the findings of the foregoing two strands of literature. We develop a framework for applying the precedence theorems to the precedence-constrained problem to tighten the search space, and we propose an exact DP algorithm that utilizes a new efficient memory management technique. Our procedure outperforms the state-of-the-art algorithm for instances with medium to high network density. We also empirically verify the computational gain of using different sets of precedence theorems.

Suggested Citation

  • Rostami, Salim & Creemers, Stefan & Leus, Roel, 2019. "Precedence theorems and dynamic programming for the single-machine weighted tardiness problem," European Journal of Operational Research, Elsevier, vol. 272(1), pages 43-49.
    • Handle: RePEc:eee:ejores:v:272:y:2019:i:1:p:43-49
    DOI: 10.1016/j.ejor.2018.06.004
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    References listed on IDEAS

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    2. Rostami, Salim & Creemers, Stefan & Wei, Wenchao & Leus, Roel, 2019. "Sequential testing of n-out-of-n systems: Precedence theorems and exact methods," European Journal of Operational Research, Elsevier, vol. 274(3), pages 876-885.

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