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Job sequencing with one common and multiple secondary resources: A problem motivated from particle therapy for cancer treatment

AuthorsHorn, Matthias; Raidl, Gunther; Blum, Christian CSIC ORCID
Learning systems
Integer programming
Patient treatment
Issue Date15-Sep-2017
CitationMachine Learning, Optimization, and Big Data, Third International Conference, MOD 2017, Volterra, Italy, September 14–17, 2017, Revised Selected Papers. LNCS 10710: 506-518 (2018)
AbstractWe consider in this work the problem of scheduling a set of jobs without preemption, where each job requires two resources: (1) a common resource, shared by all jobs, is required during a part of the job¿s processing period, while (2) a secondary resource, which is shared with only a subset of the other jobs, is required during the job¿s whole processing period. This problem models, for example, the scheduling of patients during one day in a particle therapy facility for cancer treatment. First, we show that the tackled problem is NP-hard. We then present a construction heuristic and a novel A* algorithm, both on the basis of an effective lower bound calculation. For comparison, we also model the problem as a mixed-integer linear program (MILP). An extensive experimental evaluation on three types of problem instances shows that A* typically works extremely well, even in the context of large instances with up to 1000 jobs. When our A* does not terminate with proven optimality, which might happen due to excessive memory requirements, it still returns an approximate solution with a usually small optimality gap. In contrast, solving the MILP model with the MILP solver CPLEX is not competitive except for very small problem instances. © Springer International Publishing AG 2018.
Identifiersdoi: 10.1007/978-3-319-72926-8_42
issn: 03029743
isbn: 978-331972925-1
Appears in Collections:(IIIA) Comunicaciones congresos

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