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The Stochastic Cash Balance Problem with Fixed Costs for Increases and Decreases


  • Edwin H. Neave

    (Northwestern University)


The stochastic cash balance problem is an inventory problem in which the stochastic cash (or inventory) change can either be positive or nonpositive, and in which decisions to increase or decrease the inventory are permitted at the beginning of each time period. The paper studies problems in which both fixed and proportional costs can be incurred whenever the inventory is changed in either direction. An example is used to demonstrate that when these costs are positive and the loss function is convex, a simple policy (analogous to a two-sided (s, S) policy) is not generally optimal. The example is also used to display the relations between the cash balance problem and inventory problems previously studied by Scarf and Veinott. When proportional costs of changing the inventory are zero, the two fixed costs are equal, the loss function is symmetric quasi-convex, and the problem's probability densities are quasi-concave a simple policy is shown to be optimal. For the cases in which simple policies are not optimal, the paper develops a technique which employs convex upper and lower bounds on the (nonconvex) cost functions partially to describe the optimal policy. It is suggested that this convex bounding technique may provide an approach to studying the cost implications of following simple, nonoptimal policies in inventory problems for which the optimal policy is complex.

Suggested Citation

  • Edwin H. Neave, 1970. "The Stochastic Cash Balance Problem with Fixed Costs for Increases and Decreases," Management Science, INFORMS, vol. 16(7), pages 472-490, March.
  • Handle: RePEc:inm:ormnsc:v:16:y:1970:i:7:p:472-490

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    Cited by:

    1. Alvarez, Fernando & Lippi, Francesco, 2013. "The demand of liquid assets with uncertain lumpy expenditures," Journal of Monetary Economics, Elsevier, vol. 60(7), pages 753-770.
    2. 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.
    3. John A. Buzacott & Rachel Q. Zhang, 2004. "Inventory Management with Asset-Based Financing," Management Science, INFORMS, vol. 50(9), pages 1274-1292, September.
    4. Frank Milne & Edwin Neave, 2003. "A General Equilibrium Financial Asset Economy with Transaction Costs and Trading Constraints," Working Papers 1082, Queen's University, Department of Economics.
    5. Frank Milne, 2008. "Credit Crises, Risk Management Systems and Liquidity Modelling," Working Papers 1, John Deutsch Institute for the Study of Economic Policy.
    6. 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.
    7. 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.
    8. repec:spr:annopr:v:262:y:2018:i:1:d:10.1007_s10479-016-2297-y is not listed on IDEAS

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