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Exact and heuristic methods for a workload allocation problem with chain precedence constraints

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  • Pereira, Jordi
  • Ritt, Marcus

Abstract

Industrial manufacturing is often organized in assembly lines where a product is assembled on a sequence of stations, each of which executes some of the assembly tasks. A line is balanced if the maximum total execution time of any station is minimal. Commonly, the task execution order is constrained by precedences, and task execution times are independent of the station performing the task. Here, we consider a recent variation, called the “(Calzedonia) Workload Allocation Problem” (WAP), where the precedences form a chain, and the execution time of a task depends on the worker executing it. This problem was recently proposed by Battarra et al. (2020) and it is a special case of the Assembly Line Worker Assignment and Balancing Problem Miralles et al. (2007) where precedence relations are arbitrary. In this paper we consider the computational complexity of the problem and prove its NP-hardness. To solve the problem, we provide different lower bounds and exact and heuristic procedures. The performance of the proposed methods is tested on previously proposed instances and on new, larger instances with the same characteristics. The results show that the proposed methods can solve instances with up to about 4000 tasks and 29 workers, doubling the size of the instances that previously could be solved to optimality.

Suggested Citation

  • Pereira, Jordi & Ritt, Marcus, 2023. "Exact and heuristic methods for a workload allocation problem with chain precedence constraints," European Journal of Operational Research, Elsevier, vol. 309(1), pages 387-398.
    • Handle: RePEc:eee:ejores:v:309:y:2023:i:1:p:387-398
    DOI: 10.1016/j.ejor.2022.12.035
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    References listed on IDEAS

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