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

Matthias Horn (), Günther R. Raidl () and Elina Rönnberg ()
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Matthias Horn: TU Wien
Günther R. Raidl: TU Wien
Elina Rönnberg: Linköping University

Annals of Operations Research, 2021, vol. 302, issue 2, No 8, 477-505

Abstract: 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.

Keywords: Sequencing; A* algorithm; Particle therapy patient scheduling (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10479-020-03550-7

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