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Optimal Cash Balance Levels

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  • Nadia Makary Girgis

    (Cairo University, U.A.R.)

Abstract

The problem considered in this paper deals with the optimal policies for keeping cash in anticipation of future net expenses. It is an inventory problem in which the inventory level can either decrease or increase, and the decision maker is allowed to change the inventory level in any direction at the beginning of each period. In addition to the usual holding and shortage costs, the problem involves fixed and proportional costs for deciding to change the inventory level. This paper shows the form of the optimal policy if the expected holding and shortage cost is convex and if deciding either to increase or to decrease the inventory level does not involve a fixed cost.

Suggested Citation

  • Nadia Makary Girgis, 1968. "Optimal Cash Balance Levels," Management Science, INFORMS, vol. 15(3), pages 130-140, November.
    • Handle: RePEc:inm:ormnsc:v:15:y:1968:i:3:p:130-140
    DOI: 10.1287/mnsc.15.3.130
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    Cited by:

    1. Salas-Molina, Francisco & Martin, Francisco J. & Rodríguez-Aguilar, Juan A. & Serrà, Joan & Arcos, Josep Ll., 2017. "Empowering cash managers to achieve cost savings by improving predictive accuracy," International Journal of Forecasting, Elsevier, vol. 33(2), pages 403-415.
    2. Awi Federgruen & Nan Yang, 2014. "Infinite Horizon Strategies for Replenishment Systems with a General Pool of Suppliers," Operations Research, INFORMS, vol. 62(1), pages 141-159, February.
    3. Eugene A. Feinberg & Mark E. Lewis, 2007. "Optimality Inequalities for Average Cost Markov Decision Processes and the Stochastic Cash Balance Problem," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 769-783, November.
    4. 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.
    5. Francisco Salas-Molina & Juan A. Rodríguez-Aguilar & Montserrat Guillen, 2023. "A multidimensional review of the cash management problem," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-35, December.
    6. Marcos Melo & Feruccio Bilich, 2013. "Expectancy balance model for cash flow," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 37(2), pages 240-252, April.
    7. Premachandra, I. M., 2004. "A diffusion approximation model for managing cash in firms: An alternative approach to the Miller-Orr model," European Journal of Operational Research, Elsevier, vol. 157(1), pages 218-226, August.
    8. Neil Geismar & Milind Dawande & Divakar Rajamani & Chelliah Sriskandarajah, 2007. "Managing a Bank's Currency Inventory Under New Federal Reserve Guidelines," Manufacturing & Service Operations Management, INFORMS, vol. 9(2), pages 147-167, March.
    9. Gormley, Fionnuala M. & Meade, Nigel, 2007. "The utility of cash flow forecasts in the management of corporate cash balances," European Journal of Operational Research, Elsevier, vol. 182(2), pages 923-935, October.
    10. Hinderer, K. & Waldmann, K. -H., 2001. "Cash management in a randomly varying environment," European Journal of Operational Research, Elsevier, vol. 130(3), pages 468-485, May.
    11. Wei Luo & Kevin Shang, 2015. "Joint Inventory and Cash Management for Multidivisional Supply Chains," Operations Research, INFORMS, vol. 63(5), pages 1098-1116, October.
    12. Francisco Salas-Molina & David Pla-Santamaria & Juan A. Rodriguez-Aguilar, 2018. "A multi-objective approach to the cash management problem," Annals of Operations Research, Springer, vol. 267(1), pages 515-529, August.
    13. 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.
    14. John A. Buzacott & Rachel Q. Zhang, 2004. "Inventory Management with Asset-Based Financing," Management Science, INFORMS, vol. 50(9), pages 1274-1292, September.
    15. 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.
    16. Yonit Barron, 2022. "A probabilistic approach to the stochastic fluid cash management balance problem," Annals of Operations Research, Springer, vol. 312(2), pages 607-645, May.

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