Protective Planning-Horizon Procedures for a Deterministic Cash Balance Problem

Abstract

The simple cash balance problem is to determine the timing, direction, and magnitude of transfers between a firm's earning asset (e.g., bonds) and cash balance. Recently, Blackburn and Eppen developed a forward algorithm and limited planning horizon results for a dynamic, deterministic, discrete-time version of this problem. They were able to obtain planning horizons only if an optimal plan for some subproblem included conversion of bonds to cash in the final period and a certain condition on demand was fulfilled. We derive much more general planning horizon results—the transaction is allowed to be conversion of cash to bonds, it need not be in the final period, and the special condition on demand need not be fulfilled. The methodology used is an extension of that developed by Lundin and Morton for the ordinary dynamic lot-size model. Under mild restrictions the planning-horizon procedures derived here can also be shown to be “protective”; that is, any occurring planning horizon will eventually be detected.