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A Flow-Based Formulation for Parallel Machine Scheduling Using Decision Diagrams

Author

Listed:
  • Daniel Kowalczyk

    (Research Centre for Operations Research and Statistics, Faculty of Economics and Business, KU Leuven, 3000 Leuven, Belgium)

  • Roel Leus

    (Research Centre for Operations Research and Statistics, Faculty of Economics and Business, KU Leuven, 3000 Leuven, Belgium)

  • Christopher Hojny

    (Combinatorial Optimization Group, Department of Mathematics and Computer Science, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands)

  • Stefan Røpke

    (Department of Technology, Management, and Economics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark)

Abstract

We present a new flow-based formulation for identical parallel machine scheduling with a regular objective function and without idle time. The formulation is constructed with the help of a decision diagram that represents all job sequences that respect specific ordering rules. These rules rely on a partition of the planning horizon into, generally nonuniform, periods and do not exclude all optimal solutions, but they constrain solutions to adhere to a canonical form. The new formulation has numerous variables and constraints, and hence we apply a Dantzig-Wolfe decomposition to compute the linear programming relaxation in reasonable time; the resulting lower bound is stronger than the bound from the classical time-indexed formulation. We develop a branch-and-price framework that solves three instances from the literature for the first time. We compare the new formulation with the time-indexed and arc time–indexed formulation by means of a series of computational experiments.

Suggested Citation

  • Daniel Kowalczyk & Roel Leus & Christopher Hojny & Stefan Røpke, 2024. "A Flow-Based Formulation for Parallel Machine Scheduling Using Decision Diagrams," INFORMS Journal on Computing, INFORMS, vol. 36(6), pages 1696-1714, December.
    • Handle: RePEc:inm:orijoc:v:36:y:2024:i:6:p:1696-1714
    DOI: 10.1287/ijoc.2022.0301
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