A Branch-and-Price Algorithm for Parallel Machine Scheduling Using ZDDs and Generic Branching

Daniel Kowalczyk () and Roel Leus ()
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Daniel Kowalczyk: ORSTAT, Faculty of Economics and Business, KU Leuven, 3000 Leuven, Belgium
Roel Leus: ORSTAT, Faculty of Economics and Business, KU Leuven, 3000 Leuven, Belgium

INFORMS Journal on Computing, 2018, vol. 30, issue 4, 768-782

Abstract: We study the parallel machine scheduling problem to minimize the sum of the weighted completion times of the jobs to be scheduled (problem Pm ∥∑ w j C j in the standard three-field notation). We use the set covering formulation that was introduced by van den Akker et al. [van den Akker J, Hoogeveen J, van de Velde S (1999) Parallel machine scheduling by column generation. Oper. Res. 47(6):862–872.] for this problem, and we improve the computational performance of their branch-and-price (B&P) algorithm by a number of techniques, including a different generic branching scheme, zero-suppressed binary decision diagrams (ZDDs) to solve the pricing problem, dual-price smoothing as a stabilization method, and Farkas pricing to handle infeasibilities. We report computational results that show the effectiveness of the algorithmic enhancements, which depends on the characteristics of the instances. To the best of our knowledge, we are also the first to use ZDDs to solve the pricing problem in a B&P algorithm for a scheduling problem. The online supplement is available at https://doi.org/10.1287/ijoc.2018.0809 .

Keywords: parallel machine scheduling; weighted completion times; branch-and-price • ZDD; stabilization (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (8)

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