Assembling Components with Probabilistic Lead Times

Abstract

This paper examines a production model in which N different types of components are used to assemble a finished product. The components are acquired from various suppliers in lots received at or before the beginning of the assembly process. The lead time between placing and receiving each of the N orders is assumed to be a random variable having a known probability density function. Based on recent results regarding the probability distribution and the expectation of the maximum of a set of independent random variables, the mathematical model describing this production/inventory situation is developed. The mathematical model is then used to derive a closed form formula for the optimal solution that minimizes the total production/inventory cost function. Moreover, the reorder point is shown to depend on the probability distribution and expected value of the random variable representing the maximum among the N lead times. The case in which each of the N lead times follows a Weibull distribution is investigated, and a numerical example is given to illustrate this case.