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On the Effectiveness of Zero-Inventory-Ordering Policies for the Economic Lot-Sizing Model with a Class of Piecewise Linear Cost Structures

Author

Listed:
  • Lap Mui Ann Chan

    (School of Management, University of Toronto, Toronto, Ontario, Canada M5S 3E6)

  • Ana Muriel

    (Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, Massachusetts 01106)

  • Zuo-Jun Shen

    (Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611)

  • David Simchi-Levi

    (The Engineering Systems Division and the Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142)

Abstract

We consider an economic lot-sizing problem with a special class of piecewise linear ordering costs, which we refer to as the class of modified all-unit discount cost functions. Such an ordering cost function represents transportation costs charged by many less-than truckload carriers. We show that even special cases of the lot-sizing problem are NP-hard and therefore analyze the effectiveness of easily implementable policies. In particular, we demonstrate that there exists a zero-inventory-ordering(ZIO) policy, i.e., a policy in which an order is placed only when the inventory level drops to zero, whose total inventory and ordering cost is no more than 4/3 times the optimal cost. Furthermore, if the ordering cost function does not vary over time, then the cost of the best ZIO policy is no more than 5.6/4.6 times the optimal cost. These results hold for any transportation and holding cost functions that satisfy the following properties: (i) they are non decreasing functions, and (ii) the associated cost per unit is non increasing. Finally, we report on a numerical study that shows the effectiveness of ZIO policies on a set of test problems.

Suggested Citation

  • Lap Mui Ann Chan & Ana Muriel & Zuo-Jun Shen & David Simchi-Levi, 2002. "On the Effectiveness of Zero-Inventory-Ordering Policies for the Economic Lot-Sizing Model with a Class of Piecewise Linear Cost Structures," Operations Research, INFORMS, vol. 50(6), pages 1058-1067, December.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:6:p:1058-1067
    DOI: 10.1287/opre.50.6.1058.350
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    References listed on IDEAS

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    1. Albert Wagelmans & Stan van Hoesel & Antoon Kolen, 1992. "Economic Lot Sizing: An O(n log n) Algorithm That Runs in Linear Time in the Wagner-Whitin Case," Operations Research, INFORMS, vol. 40(1-supplem), pages 145-156, February.
    2. Awi Federgruen & Chung‐Yee Lee, 1990. "The dynamic lot size model with quantity discount," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 707-713, October.
    3. C. P. M. van Hoesel & A. P. M. Wagelmans, 2001. "Fully Polynomial Approximation Schemes for Single-Item Capacitated Economic Lot-Sizing Problems," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 339-357, May.
    4. Dong X. Shaw & Albert P. M. Wagelmans, 1998. "An Algorithm for Single-Item Capacitated Economic Lot Sizing with Piecewise Linear Production Costs and General Holding Costs," Management Science, INFORMS, vol. 44(6), pages 831-838, June.
    5. Jiefeng Xu & Leonard L. Lu, 1998. "The dynamic lot size model with quantity discount: Counterexamples and correction," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(4), pages 419-422, June.
    6. Alok Aggarwal & James K. Park, 1993. "Improved Algorithms for Economic Lot Size Problems," Operations Research, INFORMS, vol. 41(3), pages 549-571, June.
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