A high-low search model of inventories with time delay

In most mathematical inventory models a distribution of demand is assumed to be known with certainty and the objective is to minimize expected stockholding and shortage costs. These models are classified as models under risk. If, however, the probability distribution of demand is not known, a model of inventory control under uncertainty results. One way of coping with this uncertainty is to adopt a worst case approach. Recently, Alpern and Snower analysed such a model. This paper extends the A-S model to situations where a time lag of one period occurs. A decision about the production or order level is taken in the absence of information as to whether the current supply is too low or too high. In practice, this phenomenon occurs when either production or leadtime takes more than one demand period or when information processing is slow (e.g. for a firm with several retailer outlets). In contrast to the A-S model, no allowance is made here for discounting. The analysis of this paper leads to a prescription of an ‘ex ante’ sequence of production decisions which can be computed by a recursive algorithm.