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Branch and bound algorithms for single-machinescheduling with batch set-up times to minimizetotal weighted completion time

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Abstract

This paper presents several branch and bound algorithms for a single-machine scheduling problem with batching. Jobs are partitioned into families, and a set-up time is necessary when there is a switch from processing jobs of one family to jobs of another family. The objective is to minimize the total weighted completion time. A lower bound based on Lagrangian relaxation of the machine capacity constraint is derived. Also, a multiplier adjustment method to find values of the multipliers is proposed. Computational experience with instances having up to 50 jobs shows that the lower bounds are effective in restricting the search.

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Authors
  1. H.A.J. Crauwels
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  2. A.M.A. Hariri
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  3. C.N. Potts
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  4. L.N. Van Wassenhove
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Crauwels, H., Hariri, A., Potts, C. et al. Branch and bound algorithms for single-machinescheduling with batch set-up times to minimizetotal weighted completion time. Annals of Operations Research 83, 59–76 (1998). https://doi.org/10.1023/A:1018920416308

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  • DOI: https://doi.org/10.1023/A:1018920416308

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