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Economic lot-sizing with remanufacturing: complexity and efficient formulations

Author

Listed:
  • Mathijn Retel Helmrich
  • Raf Jans
  • Wilco van den Heuvel
  • Albert Wagelmans

Abstract

Within the framework of reverse logistics, the classic economic lot-sizing problem has been extended with a remanufacturing option. In this extended problem, known quantities of used products are returned from customers in each period. These returned products can be remanufactured so that they are as good as new. Customer demand can then be fulfilled from both newly produced and remanufactured items. In each period, one can choose to set up a process to remanufacture returned products or produce new items. These processes can have separate or joint setup costs. In this article, it is shown that both variants are NP-hard. Furthermore, several alternative mixed-integer programming (MIP) formulations of both problems are proposed and compared. Because “natural” lot-sizing formulations provide weak lower bounds, tighter formulations are proposed, namely, shortest path formulations, a partial shortest path formulation, and an adaptation of the (l, S, WW) inequalities used in the classic problem with Wagner–Whitin costs. Their efficiency is tested on a large number of test data sets and it is found that, for both problem variants, a (partial) shortest path–type formulation performs better than the natural formulation, in terms of both the linear programming relaxation and MIP computation times. Moreover, this improvement can be substantial.

Suggested Citation

  • Mathijn Retel Helmrich & Raf Jans & Wilco van den Heuvel & Albert Wagelmans, 2014. "Economic lot-sizing with remanufacturing: complexity and efficient formulations," IISE Transactions, Taylor & Francis Journals, vol. 46(1), pages 67-86.
    • Handle: RePEc:taf:uiiexx:v:46:y:2014:i:1:p:67-86
    DOI: 10.1080/0740817X.2013.802842
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    1. Kilic, Onur A. & Tunc, Huseyin, 2019. "Heuristics for the stochastic economic lot sizing problem with remanufacturing under backordering costs," European Journal of Operational Research, Elsevier, vol. 276(3), pages 880-892.
    2. Timo Hilger & Florian Sahling & Horst Tempelmeier, 2016. "Capacitated dynamic production and remanufacturing planning under demand and return uncertainty," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 849-876, October.
    3. Kilic, Onur A. & Tunc, Huseyin & Tarim, S. Armagan, 2018. "Heuristic policies for the stochastic economic lot sizing problem with remanufacturing under service level constraints," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1102-1109.
    4. Attila, Öykü Naz & Agra, Agostinho & Akartunalı, Kerem & Arulselvan, Ashwin, 2021. "Robust formulations for economic lot-sizing problem with remanufacturing," European Journal of Operational Research, Elsevier, vol. 288(2), pages 496-510.
    5. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    6. Ahmed Senoussi & Youcef Boutarfa & Nadjib Brahimi & Tarik Aouam, 2024. "Sustainable Hybrid Manufacturing and Refurbishing Systems with Substitution," Sustainability, MDPI, vol. 16(17), pages 1-33, August.
    7. Ahmed Senoussi & Youcef Boutarfa & Nadjib Brahimi & Tarik Aouam, 2024. "Sustainable Hybrid Manufacturing and Refurbishing Systems with Substitution," Post-Print hal-05030212, HAL.
    8. Rowshannahad, Mehdi & Absi, Nabil & Dauzère-Pérès, Stéphane & Cassini, Bernard, 2018. "Multi-item bi-level supply chain planning with multiple remanufacturing of reusable by-products," International Journal of Production Economics, Elsevier, vol. 198(C), pages 25-37.
    9. Boutarfa, Y. & Senoussi, A. & Brahimi, N. & Aouam, T., 2024. "Integration and substitution in hybrid manufacturing and refurbishing systems," International Journal of Production Economics, Elsevier, vol. 274(C).
    10. Suzanne, Elodie & Absi, Nabil & Borodin, Valeria, 2020. "Towards circular economy in production planning: Challenges and opportunities," European Journal of Operational Research, Elsevier, vol. 287(1), pages 168-190.
    11. Syed Ali, Sharifah Aishah & Doostmohammadi, Mahdi & Akartunalı, Kerem & van der Meer, Robert, 2018. "A theoretical and computational analysis of lot-sizing in remanufacturing with separate setups," International Journal of Production Economics, Elsevier, vol. 203(C), pages 276-285.
    12. Merghem, Mohammed & Haoues, Mohammed & Senoussi, Ahmed & Dahane, Mohammed & Mouss, Nadia Kinza, 2026. "Integrated production and maintenance planning in imperfect hybrid manufacturing–remanufacturing systems with outsourcing and carbon emissions," International Journal of Production Economics, Elsevier, vol. 291(C).
    13. M. Turkensteen (Marcel) & van den Heuvel, W., 2019. "The trade-off between costs and carbon emissions from lot-sizing decisions," Econometric Institute Research Papers EI2019-19, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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