A Perfect Planning Horizon Procedure for a Deterministic Cash Balance Problem

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.).