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A time-indexed LP-based approach for min-sum job-shop problems

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  • Giuseppe Lancia
  • Franca Rinaldi
  • Paolo Serafini

Abstract

In this paper we propose two time-indexed IP formulations for job-shop scheduling problems with a min-sum objective. The first model has variables associated to job scheduling patterns. The exponential number of variables calls for a column generation scheme which is carried out by a dynamic programming procedure. The second model is of network flow type with side constraints. This model can be strengthened by adding cutting inequalities of clique type. It turns out that the two models are equivalent, since the dual of the second formulation is equivalent to the compact dual of the first model. However, they require significantly different solution approaches and may behave differently in terms of computing time and memory usage. Good upper bounds are found by a heuristic procedure that randomly generates schedules from fractional solutions. These features allow for an effective pruning of the branch-and-bound tree and narrowing the gap between lower and upper bounds. However, the size of both models is critically affected by the time-indexed formulation which may heavily slow down the computation. Copyright Springer Science+Business Media, LLC 2011

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  • Giuseppe Lancia & Franca Rinaldi & Paolo Serafini, 2011. "A time-indexed LP-based approach for min-sum job-shop problems," Annals of Operations Research, Springer, vol. 186(1), pages 175-198, June.
    • Handle: RePEc:spr:annopr:v:186:y:2011:i:1:p:175-198:10.1007/s10479-010-0832-9
    DOI: 10.1007/s10479-010-0832-9
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    Cited by:

    1. Clautiaux, François & Hanafi, Saïd & Macedo, Rita & Voge, Marie-Émilie & Alves, Cláudio, 2017. "Iterative aggregation and disaggregation algorithm for pseudo-polynomial network flow models with side constraints," European Journal of Operational Research, Elsevier, vol. 258(2), pages 467-477.
    2. Giuseppe Lancia & Paolo Serafini, 2016. "Deriving compact extended formulations via LP-based separation techniques," Annals of Operations Research, Springer, vol. 240(1), pages 321-350, May.
    3. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
    4. Kartak, Vadim M. & Ripatti, Artem V., 2018. "The minimum raster set problem and its application to the d-dimensional orthogonal packing problem," European Journal of Operational Research, Elsevier, vol. 271(1), pages 33-39.
    5. T. C. E. Cheng & Bo Peng & Zhipeng Lü, 2016. "A hybrid evolutionary algorithm to solve the job shop scheduling problem," Annals of Operations Research, Springer, vol. 242(2), pages 223-237, July.

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