The Single-Period Inventory Problem with Triangular Demand Distribution

Abstract

A simple method is presented for determining ‘closed-form’ solutions for an optimum (s, S) ordering policy for the single-period inventory problem with a set-up cost of ordering and the uncertain total demand over the period represented by a triangular probability density function. The distribution reflecting the decision maker's degree of belief that all values of total demand outside of two (possibly ‘soft’) limits are barely credible and all values within the limits have uniform increasing probability density towards a (possibly ‘soft’) modal value. The importance of the closed form solutions obtained is that they remove the need for enumeration over alternative values of s in determining the optimum (s, S) ordering policy, also they can be encoded in an algorithm simple to implement and they allow easy sensitivity analysis of the results to perturbations in the estimates of the problem parameters. A numerical example is presented to illustrate the essential features of the method.