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Effective Zero-Inventory-Ordering Policies for the Single-Warehouse Multiretailer Problem with Piecewise Linear Cost Structures

Author

Listed:
  • Lap Mui Ann Chan

    () (School of Management, University of Toronto, Toronto, Ontario, Canada)

  • Ana Muriel

    () (Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, Massachusetts)

  • Zuo-Jun Max Shen

    () (Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida)

  • David Simchi-Levi

    () (The Engineering Systems Division and the Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • Chung-Piaw Teo

    () (Department of Decision Sciences, National University of Singapore, Singapore)

Abstract

We analyze the problem faced by companies that rely on TL (Truckload) and LTL (Less than Truckload) carriers for the distribution of products across their supply chain. Our goal is to design simple inventory policies and transportation strategies to satisfy time varying demands over a finite horizon, while minimizing system wide cost by taking advantage of quantity discounts in the transportation cost structures. For this purpose, we study the cost effectiveness of restricting the inventory policies to the class of zero-inventory-ordering (ZIO) policies in a single-warehouse multiretailer scenario in which the warehouse serves as a cross-dock facility. In particular, we demonstrate that there exists a ZIO inventory policy whose total inventory and transportation cost is no more than 4/3 (5.6/4.6 if transportation costs are stationary) times the optimal cost. However, finding the best ZIO policy is an NP hard problem as well. Thus, we propose two algorithms to find an effective ZIO policy: An exact algorithm whose running time is polynomial for any fixed number of retailers, and a linear-programming-based heuristic whose effectiveness is demonstrated in a series of computational experiments. Finally, we extend the worst-case results developed in this paper to systems in which the warehouse does hold inventory.

Suggested Citation

  • Lap Mui Ann Chan & Ana Muriel & Zuo-Jun Max Shen & David Simchi-Levi & Chung-Piaw Teo, 2002. "Effective Zero-Inventory-Ordering Policies for the Single-Warehouse Multiretailer Problem with Piecewise Linear Cost Structures," Management Science, INFORMS, vol. 48(11), pages 1446-1460, November.
  • Handle: RePEc:inm:ormnsc:v:48:y:2002:i:11:p:1446-1460
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    File URL: http://dx.doi.org/10.1287/mnsc.48.11.1446.267
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    Citations

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    Cited by:

    1. Wu, Ting & Shen, Houcai & Zhu, Cheng, 2015. "A multi-period location model with transportation economies-of-scale and perishable inventory," International Journal of Production Economics, Elsevier, vol. 169(C), pages 343-349.
    2. Toptal, Aysegül, 2009. "Replenishment decisions under an all-units discount schedule and stepwise freight costs," European Journal of Operational Research, Elsevier, vol. 198(2), pages 504-510, October.
    3. Lee, Dong Joo & Jeong, In-Jae, 2010. "A distributed coordination for a single warehouse-multiple retailer problem under private information," International Journal of Production Economics, Elsevier, vol. 125(1), pages 190-199, May.
    4. Hill, James & Galbreth, Michael, 2008. "A heuristic for single-warehouse multiretailer supply chains with all-unit transportation cost discounts," European Journal of Operational Research, Elsevier, vol. 187(2), pages 473-482, June.
    5. Toptal, Aysegul & Cetinkaya, Sila, 2008. "Quantifying the value of buyer-vendor coordination: Analytical and numerical results under different replenishment cost structures," European Journal of Operational Research, Elsevier, vol. 187(3), pages 785-805, June.
    6. Hu, Qian & Lim, Andrew & Zhu, Wenbin, 2015. "The two-dimensional vector packing problem with piecewise linear cost function," Omega, Elsevier, vol. 50(C), pages 43-53.
    7. Mustafa Çagri Gürbüz & Kamran Moinzadeh & Yong-Pin Zhou, 2007. "Coordinated Replenishment Strategies in Inventory/Distribution Systems," Management Science, INFORMS, vol. 53(2), pages 293-307, February.
    8. Zaarour, Nizar & Melachrinoudis, Emanuel & Solomon, Marius M., 2016. "Maximizing revenue of end of life items in retail stores," European Journal of Operational Research, Elsevier, vol. 255(1), pages 133-141.
    9. Akbalik, Ayse & Hadj-Alouane, Atidel B. & Sauer, Nathalie & Ghribi, Houcem, 2017. "NP-hard and polynomial cases for the single-item lot sizing problem with batch ordering under capacity reservation contract," European Journal of Operational Research, Elsevier, vol. 257(2), pages 483-493.
    10. Archetti, Claudia & Bertazzi, Luca & Grazia Speranza, M., 2014. "Polynomial cases of the economic lot sizing problem with cost discounts," European Journal of Operational Research, Elsevier, vol. 237(2), pages 519-527.
    11. Ventura, José A. & Valdebenito, Victor A. & Golany, Boaz, 2013. "A dynamic inventory model with supplier selection in a serial supply chain structure," European Journal of Operational Research, Elsevier, vol. 230(2), pages 258-271.
    12. Toptal, Aysegül & Bingöl, Safa Onur, 2011. "Transportation pricing of a truckload carrier," European Journal of Operational Research, Elsevier, vol. 214(3), pages 559-567, November.
    13. Luminiţa Nicolescu & Cristina Galalae & Alexandru Voicu, 2013. "Solving a Supply Chain Management Problem to Near Optimality Using Ant Colony Optimization, in an International Context," The AMFITEATRU ECONOMIC journal, Academy of Economic Studies - Bucharest, Romania, vol. 15(33), pages 8-26, February.
    14. Mendoza, Abraham & Ventura, José A., 2008. "Incorporating quantity discounts to the EOQ model with transportation costs," International Journal of Production Economics, Elsevier, vol. 113(2), pages 754-765, June.
    15. 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.
    16. Ertogral, Kadir, 2008. "Multi-item single source ordering problem with transportation cost: A Lagrangian decomposition approach," European Journal of Operational Research, Elsevier, vol. 191(1), pages 156-165, November.
    17. Yu, Min-Chun & Goh, Mark & Lin, Hung-Chung, 2012. "Fuzzy multi-objective vendor selection under lean procurement," European Journal of Operational Research, Elsevier, vol. 219(2), pages 305-311.
    18. Luca Bertazzi, 2008. "Analysis of Direct Shipping Policies in an Inventory-Routing Problem with Discrete Shipping Times," Management Science, INFORMS, vol. 54(4), pages 748-762, April.
    19. repec:pal:jorsoc:v:59:y:2008:i:1:d:10.1057_palgrave.jors.2602316 is not listed on IDEAS
    20. repec:spr:annopr:v:258:y:2017:i:2:d:10.1007_s10479-015-1941-2 is not listed on IDEAS

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