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Modeling the Parallel Machine Scheduling Problem with Worker- and Position-Dependent Processing Times

Author

Listed:
  • Jairo Montoya-Torres

    (University of La Sabana = Universitad de la Sabana)

  • Valérie Botta-Genoulaz

    (INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées, DISP - Décision et Information pour les Systèmes de Production - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées)

  • Nick Materzok

    (INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées, DISP - Décision et Information pour les Systèmes de Production - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées)

  • Þorgeir Páll Gíslason

    (INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées, DISP - Décision et Information pour les Systèmes de Production - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées)

  • Sélène Mendiela

    (INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées, DISP - Décision et Information pour les Systèmes de Production - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées)

Abstract

Traditional deterministic scheduling problems consider that processing times of jobs are fixed and constant over time. However, this assumption is not realistic in practice in hand-intensive manufacturing contexts. To deal with this, the current paper studies the deterioration effect of processing times on a parallel machine scheduling problem. In such a case, job processing times depend on the position of jobs in the execution sequence. The objective function is the minimization of the maximum delay of the set of jobs, that is the makespan. A mixed-integer linear programming model is provided for the basic case in which the processing time of jobs deteriorate only as a function of their position in the schedule. Then, two original extensions are proposed. The first one considers that both the position and the worker do impact the processing time, while in the second situation workers can have a break after a given period of time. Preliminary experiments are carried out to illustrate the impact of such situations on the objective function. Results are promising.

Suggested Citation

  • Jairo Montoya-Torres & Valérie Botta-Genoulaz & Nick Materzok & Þorgeir Páll Gíslason & Sélène Mendiela, 2021. "Modeling the Parallel Machine Scheduling Problem with Worker- and Position-Dependent Processing Times," Post-Print hal-03523949, HAL.
    • Handle: RePEc:hal:journl:hal-03523949
    DOI: 10.1007/978-3-030-85906-0_39
    Note: View the original document on HAL open archive server: https://hal.science/hal-03523949
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