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The Multi-Item Joint Replenishment Problem with Transportation and Container Effects

Author

Listed:
  • Nejib Ben-Khedher

    (American Airlines Decision Technologies, Paris, France)

  • Candace A. Yano

    (Department of Industrial Engineering & Operations Research, University of California, Berkeley, California)

Abstract

We address the problem of scheduling the delivery of multiple items from a single supplier to a manufacturer. The items are packaged into containers, and the containers are shipped by truck. There is a fixed charge per truck shipment, and inventory holding costs are charged on end-of-period inventory. We seek to minimize the sum of transportation and inventory costs. The problem is a combination of a bin-packing problem (due to the presence of containers and finite-capacity trucks) and a multi-item joint replenishment problem. We present a heuristic solution procedure which starts with the optimal solution of the problem in which the integrality of the containers is relaxed. (A solution procedure for this relaxed problem appears in N. Ben-Kheder and C. A. Yano, “The Multi-Item Joint Replenishment Problem with Volume-Sensitive Transportation Costs,” Technical Report 89-19, Department of Industrial & Operations Engineering, The University of Michigan, Ann Arbor, MI (1989a). We develop a method to modify this solution to account for the integrality of containers. This modification scheme involves sequentially considering each item and optimally scheduling the fractional containers in the relaxed solution. To solve this single-item problem, we devise a procedure that accounts for the availability of “free” remaining capacity of trucks that have been partially filled with other items. In a computational study, our heuristic is compared with a lower bound, with variations of our heuristic, and with simple rule-of-thumb policies. The results suggest that our heuristic performs very well, especially in problems where considering tradeoffs between inventory and transportation costs is important.

Suggested Citation

  • Nejib Ben-Khedher & Candace A. Yano, 1994. "The Multi-Item Joint Replenishment Problem with Transportation and Container Effects," Transportation Science, INFORMS, vol. 28(1), pages 37-54, February.
    • Handle: RePEc:inm:ortrsc:v:28:y:1994:i:1:p:37-54
    DOI: 10.1287/trsc.28.1.37
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    Citations

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    Cited by:

    1. Kim, Kap Hwan & Kim, Jae-Boum, 2002. "Determining load patterns for the delivery of assembly components under JIT systems," International Journal of Production Economics, Elsevier, vol. 77(1), pages 25-38, May.
    2. Juman, Z.A.M.S. & Hoque, M.A., 2014. "A heuristic solution technique to attain the minimal total cost bounds of transporting a homogeneous product with varying demands and supplies," European Journal of Operational Research, Elsevier, vol. 239(1), pages 146-156.
    3. Tsao, Yu-Chung & Sheen, Gwo-Ji, 2012. "A multi-item supply chain with credit periods and weight freight cost discounts," International Journal of Production Economics, Elsevier, vol. 135(1), pages 106-115.
    4. Engebrethsen, Erna & Dauzère-Pérès, Stéphane, 2019. "Transportation mode selection in inventory models: A literature review," European Journal of Operational Research, Elsevier, vol. 279(1), pages 1-25.
    5. J-M Chen & T-H Chen, 2005. "Effects of joint replenishment and channel coordination for managing multiple deteriorating products in a supply chain," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(10), pages 1224-1234, October.
    6. Jans, R.F. & Degraeve, Z., 2005. "Modeling Industrial Lot Sizing Problems: A Review," ERIM Report Series Research in Management ERS-2005-049-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    7. Martin Grunewald & Thomas Volling & Christoph Müller & Thomas S. Spengler, 2018. "Multi-item single-source ordering with detailed consideration of transportation capacities," Journal of Business Economics, Springer, vol. 88(7), pages 971-1007, September.
    8. Chung-Lun Li & Vernon Ning Hsu & Wen-Qiang Xiao, 2004. "Dynamic Lot Sizing with Batch Ordering and Truckload Discounts," Operations Research, INFORMS, vol. 52(4), pages 639-654, August.
    9. Yang, Liu & Liu, Kanglin & Zhang, Juan & Zelbst, Pamela J., 2024. "Inventory management with actual palletized transportation costs and lost sales," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 184(C).
    10. Monalisha Pattnaik & Padmabati Gahan, 2021. "Preservation effort effects on retailers and manufacturers in integrated multi-deteriorating item discrete supply chain model," OPSEARCH, Springer;Operational Research Society of India, vol. 58(2), pages 276-329, June.
    11. Sancak, Emre & Salman, F. Sibel, 2011. "Multi-item dynamic lot-sizing with delayed transportation policy," International Journal of Production Economics, Elsevier, vol. 131(2), pages 595-603, June.
    12. Dinçer Konur & Joseph Geunes, 2019. "Integrated districting, fleet composition, and inventory planning for a multi-retailer distribution system," Annals of Operations Research, Springer, vol. 273(1), pages 527-559, February.
    13. Tsao, Yu-Chung, 2010. "Managing multi-echelon multi-item channels with trade allowances under credit period," International Journal of Production Economics, Elsevier, vol. 127(2), pages 226-237, October.

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