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A Stochastic Inventory Model for Rented Equipment

Author

Listed:
  • William D. Whisler

    (Standard Oil Company of California, San Francisco and University of California, Berkeley)

Abstract

An inventory of rented equipment is studied. Equipment is withdrawn from the inventory by customers who use it for a length of time and then return it. Decisions about the amount of equipment to rent can be made at certain points in time. This paper describes a policy for making these decisions which minimizes expected costs. The dynamic programming model formulated is different than the usual ones considered in the literature because the inventory level can fluctuate up or down and convexity of the cost function is not important since simple optimal policies can be found when the cost function is nonconvex.

Suggested Citation

  • William D. Whisler, 1967. "A Stochastic Inventory Model for Rented Equipment," Management Science, INFORMS, vol. 13(9), pages 640-647, May.
    • Handle: RePEc:inm:ormnsc:v:13:y:1967:i:9:p:640-647
    DOI: 10.1287/mnsc.13.9.640
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    Citations

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    Cited by:

    1. Bitran, Gabriel R. & Leong, Thin-Yin., 1989. "Hotel sales and reservations planning," Working papers 3108-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    2. Ben A. Chaouch, 2018. "Analysis of the stochastic cash balance problem using a level crossing technique," Annals of Operations Research, Springer, vol. 271(2), pages 429-444, December.
    3. Vincent W. Slaugh & Bahar Biller & Sridhar R. Tayur, 2016. "Managing Rentals with Usage-Based Loss," Manufacturing & Service Operations Management, INFORMS, vol. 18(3), pages 429-444, July.
    4. Awi Federgruen & Zhe Liu & Lijian Lu, 2020. "Synthesis and Generalization of Structural Results in Inventory Management: A Generalized Convexity Property," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 547-575, May.
    5. Inderfurth, Karl & van der Laan, Erwin, 2001. "Leadtime effects and policy improvement for stochastic inventory control with remanufacturing," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 381-390, May.
    6. Eduardo González & Leonardo Epstein & Verónica Godoy, 2012. "Optimal number of bypasses: minimizing cost of calls to wireless phones under Calling Party Pays," Annals of Operations Research, Springer, vol. 199(1), pages 179-191, October.
    7. Belleh Fontem, 2022. "An optimal stopping policy for car rental businesses with purchasing customers," Annals of Operations Research, Springer, vol. 317(1), pages 47-76, October.
    8. Liu Shuren & Tang Pei, 2014. "The Stochastic Cash Balance Problem with Fixed Costs: The Risk-averse Case," Journal of Systems Science and Information, De Gruyter, vol. 2(6), pages 520-531, December.
    9. Eduardo González & Leonardo Epstein, 2015. "Minimum cost in a mix of new and old reusable items: an application to sizing a fleet of delivery trucks," Annals of Operations Research, Springer, vol. 232(1), pages 135-149, September.
    10. Apurva Jain & Kamran Moinzadeh & Aussadavut Dumrongsiri, 2015. "Priority Allocation in a Rental Model with Decreasing Demand," Manufacturing & Service Operations Management, INFORMS, vol. 17(2), pages 236-248, May.
    11. Mohammad Firouz & Linda Li & Burcu B. Keskin, 2022. "Managing equipment rentals: Unreliable fleet, impatient customers, and finite commitment capacity," Production and Operations Management, Production and Operations Management Society, vol. 31(11), pages 3963-3981, November.

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