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Inventory Control with Generalized Expediting

Author

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  • Eric Logan Huggins

    (School of Business Administration, Fort Lewis College, Durango, Colorado 81301)

  • Tava Lennon Olsen

    (Department of Information Systems and Operations Management, University of Auckland Business School, Auckland 1010, New Zealand)

Abstract

We consider a single-item, periodic-review inventory control problem in which discrete stochastic demand must be satisfied. When shortages occur, the unmet demand must be filled by some form of expediting; we allow a very general form for the cost structure of expediting. We explicitly consider the case where expedited production is allowed to produce up to a positive inventory level. We also consider the case where expedited production beyond the deficit is not permitted; an alternate application for this model is an inventory system with general lost sales costs. For the infinite-horizon discounted problem, we characterize the structure of the optimal stationary expediting policy and show that an ( s , S ) policy is optimal for regular production. For the special cases where the expediting cost function is concave or consists of a fixed and linear per-unit cost, we show that the optimal stationary expediting policy is generalized ( s , S ) or order-up-to, respectively. A numerical study allows us to gain insight into when expediting above and beyond the deficit is cost-effective.

Suggested Citation

  • Eric Logan Huggins & Tava Lennon Olsen, 2010. "Inventory Control with Generalized Expediting," Operations Research, INFORMS, vol. 58(5), pages 1414-1426, October.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:5:p:1414-1426
    DOI: 10.1287/opre.1100.0820
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    References listed on IDEAS

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    3. Lucas Böttcher & Thomas Asikis & Ioannis Fragkos, 2023. "Control of Dual-Sourcing Inventory Systems Using Recurrent Neural Networks," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1308-1328, November.
    4. Qing Li & Peiwen Yu, 2012. "Technical Note---On the Quasiconcavity of Lost-Sales Inventory Models with Fixed Costs," Operations Research, INFORMS, vol. 60(2), pages 286-291, April.
    5. Höller, Simon J. & Özsen, Raik & Thonemann, Ulrich W., 2020. "Determining optimal parameters for expediting policies under service level constraints," European Journal of Operational Research, Elsevier, vol. 281(2), pages 274-285.
    6. Youhua (Frank) Chen & Ye Lu & Minghui Xu, 2012. "Optimal inventory control policy for periodic‐review inventory systems with inventory‐level‐dependent demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(6), pages 430-440, September.
    7. Fu, Ke & Xu, Jiayan & Miao, Zhaowei, 2013. "Newsvendor with multiple options of expediting," European Journal of Operational Research, Elsevier, vol. 226(1), pages 94-99.
    8. David A. Goldberg & Martin I. Reiman & Qiong Wang, 2021. "A Survey of Recent Progress in the Asymptotic Analysis of Inventory Systems," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1718-1750, June.
    9. Schneider, Frank & Klabjan, Diego, 2013. "Inventory control in multi-channel retail," European Journal of Operational Research, Elsevier, vol. 227(1), pages 101-111.
    10. Johansen, Søren Glud, 2019. "Emergency orders in the periodic-review inventory system with fixed ordering costs and stochastic lead times for normal orders," International Journal of Production Economics, Elsevier, vol. 209(C), pages 205-214.
    11. Wang, Huihui & Yu, Yimin & Zhang, Wei & Hua, Zhongsheng, 2019. "Procurement strategies for lost-sales inventory systems with all-units discounts," European Journal of Operational Research, Elsevier, vol. 272(2), pages 539-548.
    12. 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—Discrete‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 131-153, January.
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    15. Johansen, Søren Glud & Thorstenson, Anders, 2014. "Emergency orders in the periodic-review inventory system with fixed ordering costs and compound Poisson demand," International Journal of Production Economics, Elsevier, vol. 157(C), pages 147-157.

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