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A Perfect Planning Horizon Procedure for a Deterministic Cash Balance Problem

Author

Listed:
  • Suresh Chand

    (Purdue University)

  • Thomas E. Morton

    (Carnegie-Mellon University)

Abstract

This paper develops a "perfect planning horizon procedure" for the simple cash balance problem, where the objective of the firm is to schedule the selling and buying of its earning assets so that all the positive demands are met at minimum cost. Demand for cash can be both positive or negative; a positive demand means the cash outflow and a negative demand means the cash inflow. While the planning horizon procedure reported in Mensching, Garstka, and Morton (Mensching, J., S. Garstka, T. Morton. 1978. Protective planning-horizon procedures for a deterministic cash balance problem. Oper. Res. 26 637--652.) obtains optimal initial decisions for the infinite horizon cash balance problem by using forecasts for some finite horizon, the perfect procedure in this paper is guaranteed to obtain these decisions by using the minimum possible number of periods of forecast data. We also present a forward dynamic programming algorithm which is computationally more efficient than the forward algorithm of Blackburn and Eppen (Blackburn, J., G. Eppen. 1973. A two asset deterministic cash balance problem. Research Paper No. 133, Stanford University.). Our computational results show that the perfect procedure in this paper can lead to significant savings in the number of periods of forecast data required to obtain optimal initial decisions and the CPU time compared to the planning horizon procedure in Mensching, Garstka, and Morton (Mensching, J., S. Garstka, T. Morton. 1978. Protective planning-horizon procedures for a deterministic cash balance problem. Oper. Res. 26 637--652.).

Suggested Citation

  • Suresh Chand & Thomas E. Morton, 1982. "A Perfect Planning Horizon Procedure for a Deterministic Cash Balance Problem," Management Science, INFORMS, vol. 28(6), pages 652-669, June.
    • Handle: RePEc:inm:ormnsc:v:28:y:1982:i:6:p:652-669
    DOI: 10.1287/mnsc.28.6.652
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    Citations

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    Cited by:

    1. Milind Dawande & Srinagesh Gavirneni & Sanjeewa Naranpanawe & Suresh Sethi, 2007. "Forecast Horizons for a Class of Dynamic Lot-Size Problems Under Discrete Future Demand," Operations Research, INFORMS, vol. 55(4), pages 688-702, August.
    2. Fuying Jing & Zirui Lan, 2017. "Forecast horizon of multi-item dynamic lot size model with perishable inventory," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-15, November.
    3. Alain Bensoussan & Jean‐Marie Proth & Maurice Queyranne, 1991. "A planning horizon algorithm for deterministic inventory management with piecewise linear concave costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(5), pages 729-742, October.
    4. Awi Federgruen & Michal Tzur, 1996. "Detection of minimal forecast horizons in dynamic programs with multiple indicators of the future," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(2), pages 169-189, March.
    5. Dawande, Milind & Gavirneni, Srinagesh & Naranpanawe, Sanjeewa & Sethi, Suresh P., 2009. "Discrete forecast horizons for two-product variants of the dynamic lot-size problem," International Journal of Production Economics, Elsevier, vol. 120(2), pages 430-436, August.
    6. Suresh Chand & Vernon Ning Hsu & Suresh Sethi, 2002. "Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 25-43, September.

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