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Simheuristic algorithm for a stochastic parallel machine scheduling problem with periodic re-planning assessment

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Abstract

This paper addresses a parallel machine scheduling problem with non-anticipatory family setup times and batching, considering the task’s stochastic processing times and release dates. The problem arises from a real-life ship scheduling problem in the oil and gas industry. We developed an Iterated Greedy simheuristic with built-in Monte Carlo Simulation to sample the stochastic parameters. We conducted experiments on a set of instances from the literature, considering two simheuristic variants and three uncertainty levels for the stochastic parameters. To highlight the advantages of using simulation to tackle the stochastic problem, the simheuristics are compared against a regular Iterated Greedy metaheuristic, yielding an improvement of up to 16.5% on the objective function’s expected values, with a reduced impact on computational times. During a risk analysis, the Pareto set of solutions is generated to illustrate the trade-off between the expected objective value of the solutions and the conditional value at risk, providing decision-makers with a useful tool to select the schedules that better fit their risk profiles. We use an iterative mechanism to build confidence intervals within a certain confidence level during the method’s simulation step, interrupting the procedure when it reaches the desired error. This strategy’s advantage is highlighted in the computational experiments, which indicates that the number of replications of the simulation is instance and uncertainty level dependent. A periodic re-planning strategy is also used to evaluate the performance of the simheuristic, highlighting the advantages of using the proposed algorithm in a real-life usage situation.

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Notes

  1. http://www.boost.org, last accessed 2021-01-29.

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Funding

This study was financed in part by PUC-Rio, by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001, by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under Grant Numbers 315361/2020-4 and 10940/2019-2, by the Fundação de Amparo á Pesquisa do Estado do Rio de Janeiro (FAPERJ) under Grant number E-26/010.002232/2019, and by the Norwegian Agency for International Cooperation and Quality Enhancement in Higher Education (Diku)—Project number UTF-2017-four-year/10075.

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Authors and Affiliations

  1. Industrial Engineering Department – Pontifical Catholic University of Rio de Janeiro (PUC-Rio), Marquês de São Vicente, 225 - Gávea, Rio de Janeiro, RJ, 22451-900, Brazil

    Victor Abu-Marrul, Rafael Martinelli & Silvio Hamacher

  2. Molde University College - Specialized University in Logistics (HiMolde), Britvegen 2, 6410, Molde, Norway

    Irina Gribkovskaia

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  1. Victor Abu-Marrul
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  4. Irina Gribkovskaia
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Correspondence to Victor Abu-Marrul.

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Abu-Marrul, V., Martinelli, R., Hamacher, S. et al. Simheuristic algorithm for a stochastic parallel machine scheduling problem with periodic re-planning assessment. Ann Oper Res 320, 547–572 (2023). https://doi.org/10.1007/s10479-022-04534-5

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