Abstract
We 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.
We gratefully acknowledge the financial support of the Doctoral Program “Vienna Graduate School on Computational Optimization” funded by Austrian Science Foundation under Project No W1260-N35.
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Allahverdi, A.: A survey of scheduling problems with no-wait in process. Eur. J. Oper. Res. 255(3), 665–686 (2016)
Conforti, D., Guerriero, F., Guido, R.: Optimization models for radiotherapy patient scheduling. 4OR 6(3), 263–278 (2008)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Co., New York (1979)
Gilmore, P.C., Gomory, R.E.: Sequencing a one-state variable machine: a solvable case of the traveling salesman problem. Oper. Res. 12(5), 655–679 (1964)
Hart, P., Nilsson, N., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. Syst. Sci. Cybern. 4(2), 100–107 (1968)
Hartmann, S., Briskorn, D.: A survey of variants and extensions of the resource-constrained project scheduling problem. Eur. J. Oper. Res. 207(1), 1–14 (2010)
Kapamara, T., Sheibani, K., Haas, O., Petrovic, D., Reeves, C.: A review of scheduling problems in radiotherapy. In: Proceedings of the International Control Systems Engineering Conference, pp. 207–211. Coventry University Publishing, Coventry (2006)
Maschler, J., Riedler, M., Stock, M., Raidl, G.R.: Particle therapy patient scheduling: first heuristic approaches. In: PATAT 2016: Proceedings of the 11th International Conference of the Practice and Theory of Automated Timetabling, Udine, Italy, pp. 223–244 (2016)
Röck, H.: The three-machine no-wait flow shop is NP-complete. J. ACM 31(2), 336–345 (1984)
Van der Veen, J.A.A., Wöginger, G.J., Zhang, S.: Sequencing jobs that require common resources on a single machine: a solvable case of the TSP. Math. Program. 82(1–2), 235–254 (1998)
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Horn, M., Raidl, G., Blum, C. (2018). Job Sequencing with One Common and Multiple Secondary Resources: A Problem Motivated from Particle Therapy for Cancer Treatment. In: Nicosia, G., Pardalos, P., Giuffrida, G., Umeton, R. (eds) Machine Learning, Optimization, and Big Data. MOD 2017. Lecture Notes in Computer Science(), vol 10710. Springer, Cham. https://doi.org/10.1007/978-3-319-72926-8_42
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DOI: https://doi.org/10.1007/978-3-319-72926-8_42
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