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An Exact Algorithm for the Single-Machine Earliness–Tardiness Scheduling Problem

In: Just-in-Time Systems

Author

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  • Shunji Tanaka

    (Kyoto University)

Abstract

This paper introduces our exact algorithm for the single-machine total weighted earliness–tardiness scheduling problem, which is based on the Successive Sublimation Dynamic Programming (SSDP) method. This algorithm starts from a Lagrangian relaxation of the original problem and then constraints are successively added to it until the gap between lower and upper bounds becomes zero. The relaxations are solved by dynamic programming, and unnecessary dynamic programming states are eliminated in the course of the algorithm to suppress the increase of states caused by the addition of constraints. This paper explains the methods employed in our algorithm to construct the Lagrangian relaxations, to eliminate states and to compute an upper bound together with some other improvements. Then, numerical results for known benchmark instances are given to show the effectiveness of our algorithm.

Suggested Citation

  • Shunji Tanaka, 2012. "An Exact Algorithm for the Single-Machine Earliness–Tardiness Scheduling Problem," Springer Optimization and Its Applications, in: Roger Z. Ríos-Mercado & Yasmín A. Ríos-Solís (ed.), Just-in-Time Systems, chapter 0, pages 21-40, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-1123-9_2
    DOI: 10.1007/978-1-4614-1123-9_2
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    Cited by:

    1. Clautiaux, F. & Detienne, B. & Guillot, G., 2021. "An iterative dynamic programming approach for the temporal knapsack problem," European Journal of Operational Research, Elsevier, vol. 293(2), pages 442-456.

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