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A* Search for Prize-Collecting Job Sequencing with One Common and Multiple Secondary Resources

Author

Listed:
  • Matthias Horn

    (TU Wien)

  • Günther R. Raidl

    (TU Wien)

  • Elina Rönnberg

    (Linköping University)

Abstract

We consider a sequencing problem with time windows, in which a subset of a given set of jobs shall be scheduled. A scheduled job has to execute without preemption and during this time, the job needs both a common resource for a part of the execution as well as a secondary resource for the whole execution time. The common resource is shared by all jobs while a secondary resource is shared only by a subset of the jobs. Each job has one or more time windows and due to these, it is not possible to schedule all jobs. Instead, each job is associated with a prize and the task is to select a subset of jobs which yields a feasible schedule with a maximum sum of prizes. First, we argue that the problem is NP-hard. Then, we present an exact A* algorithm and derive different upper bounds for the total prize; these bounds are based on constraint and Lagrangian relaxations of a linear programming relaxation of a multidimensional knapsack problem. For comparison, a compact mixed integer programming (MIP) model and a constraint programming model are also presented. An extensive experimental evaluation on three types of problem instances shows that the A* algorithm outperforms the other approaches and is able to solve small to medium size instances with up to about 40 jobs to proven optimality. In cases where A* does not prove that an optimal solution is found, the obtained upper bounds are stronger than those of the MIP model.

Suggested Citation

  • Matthias Horn & Günther R. Raidl & Elina Rönnberg, 2021. "A* Search for Prize-Collecting Job Sequencing with One Common and Multiple Secondary Resources," Annals of Operations Research, Springer, vol. 302(2), pages 477-505, July.
    • Handle: RePEc:spr:annopr:v:302:y:2021:i:2:d:10.1007_s10479-020-03550-7
    DOI: 10.1007/s10479-020-03550-7
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    References listed on IDEAS

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    1. Allahverdi, Ali, 2016. "A survey of scheduling problems with no-wait in process," European Journal of Operational Research, Elsevier, vol. 255(3), pages 665-686.
    2. Hartmann, Sönke & Briskorn, Dirk, 2010. "A survey of variants and extensions of the resource-constrained project scheduling problem," European Journal of Operational Research, Elsevier, vol. 207(1), pages 1-14, November.
    3. Gunawan, Aldy & Lau, Hoong Chuin & Vansteenwegen, Pieter, 2016. "Orienteering Problem: A survey of recent variants, solution approaches and applications," European Journal of Operational Research, Elsevier, vol. 255(2), pages 315-332.
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    Cited by:

    1. Froger, Aurélien & Sadykov, Ruslan, 2023. "New exact and heuristic algorithms to solve the prize-collecting job sequencing problem with one common and multiple secondary resources," European Journal of Operational Research, Elsevier, vol. 306(1), pages 65-82.

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