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Economic Order Quantities and Multiple Set-Up Costs

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  • Steven A. Lippman

    (University of California, Los Angeles)

Abstract

We consider the problem of scheduling the production of a single product at each instant during a time horizon of length T (\leqq \infty ) so as to minimize the average cost per unit time; backlogging of demand and disposal of stock are not allowed. Two types of costs are incurred; the holding cost per unit time is assumed to be proportional to the inventory level while the ordering cost is that associated with the multiple set-up cost function (see (3) and Figure 1). By studying a special case (K = 0 in (3)) in §2, the analysis of the problem practically becomes that of the standard economic lot size model so that we can rigorously derive some not too widely known results about the lot size model while exploring our model. In particular, we obtain planning horizon theorems and characterize the form of an optimal production schedule for T

Suggested Citation

  • Steven A. Lippman, 1971. "Economic Order Quantities and Multiple Set-Up Costs," Management Science, INFORMS, vol. 18(1), pages 39-47, September.
    • Handle: RePEc:inm:ormnsc:v:18:y:1971:i:1:p:39-47
    DOI: 10.1287/mnsc.18.1.39
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    Cited by:

    1. Adel A. Alamri, 2023. "Carbon Emissions Effect on Vendor-Managed Inventory System Considering Displaced Re-Start-Up Production Time," Logistics, MDPI, vol. 7(4), pages 1-29, September.
    2. Robert W. Grubbström & Brian G. Kingsman, 2004. "Ordering and Inventory Policies for Step Changes in the Unit Item Cost: A Discounted Cash Flow Approach," Management Science, INFORMS, vol. 50(2), pages 253-267, February.
    3. Osman Alp & Woonghee Tim Huh & Tarkan Tan, 2014. "Inventory Control with Multiple Setup Costs," Manufacturing & Service Operations Management, INFORMS, vol. 16(1), pages 89-103, February.
    4. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Continuous‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 154-169, January.
    5. Lee, Y.C.E. & Chan, Chi Kin & Langevin, A. & Lee, H.W.J., 2016. "Integrated inventory-transportation model by synchronizing delivery and production cycles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 91(C), pages 68-89.
    6. 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.
    7. Rieksts, Brian Q. & Ventura, Jose A., 2008. "Optimal inventory policies with two modes of freight transportation," European Journal of Operational Research, Elsevier, vol. 186(2), pages 576-585, April.
    8. Perera, Sandun & Janakiraman, Ganesh & Niu, Shun-Chen, 2017. "Optimality of (s, S) policies in EOQ models with general cost structures," International Journal of Production Economics, Elsevier, vol. 187(C), pages 216-228.

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