A recursive computer algorithm for determining joint probability inventory distributions

Most reorder point inventory models have been characterized by either variable demands or variable lead times. Commonly used distributions that have been used to represent both demand and lead-time variation have included the Poisson, normal and negative exponential functions. When both demand and lead time are variable, the complexity of constructing a joint distribution to represent the lead-time demand impedes the use of traditional models by practitioners. Practitioners are more likely to use discrete probability distributions to represent both demand and lead-time variation. This paper presents a computer algorithm to facilitate the construction of joint probability distributions that represent the lead-time demand. Component distributions for both demand and lead-time variations are assumed to be discrete. The PASCAL computer model facilitates the construction of joint distributions for numbers of demand and lead-time alternatives too large to permit distribution construction by traditional, manual methods.