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The impact of service level constraints in deterministic lot sizing with backlogging

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  • Gruson, Matthieu
  • Cordeau, Jean-François
  • Jans, Raf

Abstract

This paper studies the impact of service level constraints in the context of the capacitated and uncapacitated lot sizing problems with deterministic demand and backlogging over a discrete and finite time horizon. Because the standard formulation of these problems cannot distinguish between a backlog and a backorder, we use a reformulation to explicitly make this distinction. We then formulate several service level constraints adapted from the stochastic inventory control literature and introduce new ones. We analyze the impact of these constraints on the structure of the optimal solutions in terms of the number of backorders and total backlog, and on the performance of these solutions in terms of various service level indicators (proportion of periods with no backlog, proportion of backorders over total demand, maximum delay, average unit waiting time for an item). We also consider the introduction of various types of backordering costs (both fixed and duration dependent) and study their impact. We find that they tend to stabilize the structure of solutions, regardless of the service level constraints imposed. Finally, we analyze the impact of a first-in first-out order management policy and show that it helps improving most solutions.

Suggested Citation

  • Gruson, Matthieu & Cordeau, Jean-François & Jans, Raf, 2018. "The impact of service level constraints in deterministic lot sizing with backlogging," Omega, Elsevier, vol. 79(C), pages 91-103.
    • Handle: RePEc:eee:jomega:v:79:y:2018:i:c:p:91-103
    DOI: 10.1016/j.omega.2017.08.003
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    5. Soumya Kanti Hota & Biswajit Sarkar & Santanu Kumar Ghosh, 2020. "Effects of Unequal Lot Size and Variable Transportation in Unreliable Supply Chain Management," Mathematics, MDPI, vol. 8(3), pages 1-24, March.
    6. Raj Kumar Bachar & Shaktipada Bhuniya & Santanu Kumar Ghosh & Biswajit Sarkar, 2022. "Controllable Energy Consumption in a Sustainable Smart Manufacturing Model Considering Superior Service, Flexible Demand, and Partial Outsourcing," Mathematics, MDPI, vol. 10(23), pages 1-29, November.
    7. Sereshti, Narges & Adulyasak, Yossiri & Jans, Raf, 2021. "The value of aggregate service levels in stochastic lot sizing problems," Omega, Elsevier, vol. 102(C).
    8. Gruson, Matthieu & Cordeau, Jean-François & Jans, Raf, 2021. "Benders decomposition for a stochastic three-level lot sizing and replenishment problem with a distribution structure," European Journal of Operational Research, Elsevier, vol. 291(1), pages 206-217.
    9. Wang, Qingwei & Zheng, Meimei & Lee, Ka-Man & Shi, Xiaoqian & Shen, Yichi & Pan, Ershun, 2024. "Optimal product and after-sales service decisions considering risk attitudes under price-dependent uncertain demand," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 182(C).

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