Optimal Cash Balance Levels

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.