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Benders’ decomposition based exact solution method for multi-manned assembly line balancing problem with walking workers

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Abstract

This article considers multi-manned assembly line balancing problems with walking workers. The objective of the problem is the minimization of number of workers and workstations simultaneously. Several exact-solution algorithms based on Benders’ decomposition are proposed to solve the problem optimally. In one of the algorithms a constructive heuristic that generates effective task-worker assignments and some problem-specific symmetry breaking constraints are used. Moreover, the solutions obtained by meta-heuristic in the literature are used as starting points to increase the performance of proposed decomposition methods. A benchmark set of 99 instances are used to analyze the performance of the proposed exact methods, contribution of the developed heuristic and the ability of Benders’ decomposition on improving the starting solutions. Our results indicate a significiant improvement in the optimal solvability of the problem for larger-sized instances. Suggested methods also improve the results of the meta-heuristic method for significant number of instances. Consequntly, proposed methods solved most of instances optimally and they are able to find the optimal solutions of 17 instances that cannot be solved optimally with previous methods.

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Availability of data and material

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Code availability

The C# programming code generated during the current study are available from the corresponding author on reasonable request.

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Authors and Affiliations

  1. Department of Industrial Engineering, Celal Bayar University, Manisa, Turkey

    Murat Şahin

  2. Graduate School of Natural and Applied Sciences, Gazi University, Ankara, Turkey

    Murat Şahin

  3. Department of Industrial Engineering, Gazi University, Ankara, Turkey

    Talip Kellegöz

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  1. Murat Şahin
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  2. Talip Kellegöz
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Correspondence to Murat Şahin.

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The manuscript has not been submitted to another journal for simultaneous consideration. This work is original and has not been published elsewhere in any form or language. This study is unique and has not been split up into several parts to increase the quantity of submissions. Results have been presented clearly, honestly, and without fabrication, falsification or inappropriate data manipulation. The authors adhered to the discipline required by ethical rules in data collection, selection and processing. Required citations and statements taken from other studies are stated in accordance with ethical rules. Authors are sure they have permissions for the software used in the study. All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. The authors guarantee the accuracy of the above-mentioned statements and accept any liability and deprivation of rights that may arise.

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Şahin, M., Kellegöz, T. Benders’ decomposition based exact solution method for multi-manned assembly line balancing problem with walking workers. Ann Oper Res 321, 507–540 (2023). https://doi.org/10.1007/s10479-022-05118-z

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