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Approximation Algorithms for the Supplier's Supply Chain Scheduling Problem to Minimize Delivery and Inventory Holding Costs

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  • Esaignani Selvarajah

    (Odette School of Business, University of Windsor, Windsor, Ontario, Canada N9B 3P4)

  • George Steiner

    (Operations Management Area, DeGroote School of Business, McMaster University, Hamilton, Ontario, Canada L8S 4M4)

Abstract

We study the upstream supplier's batch scheduling problem in a supply chain, which was defined by Hall and Potts [Hall, N. G., C. N. Potts. 2003. Supply chain scheduling: Batching and delivery. Oper. Res. 51 (4) 566--584]. The supplier has to manufacture multiple products and deliver them to customers in batches. There is an associated delivery cost with each batch. The objective of the supplier is to minimize the total inventory holding and delivery costs. We present simple approximation algorithms for this strongly NP-hard problem, which find a solution that is guaranteed to have a cost at most 3/2 times the minimum. We also prove that the approximation algorithms have worst-case bounds that vary parametrically with the data and that for realistic parameter values are much better than 3/2. The theoretical results are also supported by the findings of a computational study.

Suggested Citation

  • Esaignani Selvarajah & George Steiner, 2009. "Approximation Algorithms for the Supplier's Supply Chain Scheduling Problem to Minimize Delivery and Inventory Holding Costs," Operations Research, INFORMS, vol. 57(2), pages 426-438, April.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:2:p:426-438
    DOI: 10.1287/opre.1080.0622
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    References listed on IDEAS

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    Cited by:

    1. Esaignani Selvarajah & Rui Zhang, 2014. "Supply chain scheduling to minimize holding costs with outsourcing," Annals of Operations Research, Springer, vol. 217(1), pages 479-490, June.
    2. Xiao-Ying Bao & Lei Zhang, 2018. "Green Procurement Relationships Development under Carbon Emissions Regulations: A Bi-Level Programming Approach," IJERPH, MDPI, vol. 15(10), pages 1-14, October.
    3. B.‐Y. Cheng & J.Y.‐T. Leung & K. Li & S.‐L. Yang, 2015. "Single batch machine scheduling with deliveries," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(6), pages 470-482, September.
    4. Long Zhang & Yuzhong Zhang & Qingguo Bai, 0. "An approximation algorithm for a supply-chain scheduling problem with an assignable common due window and holding time," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-13.
    5. Ullrich, Christian A., 2013. "Integrated machine scheduling and vehicle routing with time windows," European Journal of Operational Research, Elsevier, vol. 227(1), pages 152-165.
    6. Selvarajah, Esaignani & Zhang, Rui, 2014. "Supply chain scheduling at the manufacturer to minimize inventory holding and delivery costs," International Journal of Production Economics, Elsevier, vol. 147(PA), pages 117-124.
    7. Agnetis, Alessandro & Aloulou, Mohamed Ali & Fu, Liang-Liang, 2016. "Production and interplant batch delivery scheduling: Dominance and cooperation," International Journal of Production Economics, Elsevier, vol. 182(C), pages 38-49.
    8. Cheng, Ba-Yi & Leung, Joseph Y-T. & Li, Kai, 2017. "Integrated scheduling on a batch machine to minimize production, inventory and distribution costs," European Journal of Operational Research, Elsevier, vol. 258(1), pages 104-112.
    9. Weihua Liu & Yi Yang & Shuqing Wang & Enze Bai, 2017. "A scheduling model of logistics service supply chain based on the time windows of the FLSP’s operation and customer requirement," Annals of Operations Research, Springer, vol. 257(1), pages 183-206, October.
    10. Long Zhang & Yuzhong Zhang & Qingguo Bai, 2022. "An approximation algorithm for a supply-chain scheduling problem with an assignable common due window and holding time," Journal of Combinatorial Optimization, Springer, vol. 44(4), pages 2167-2179, November.

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