Determination of Optimal Shipping Quantity for Perishable Goods under Probabilistic Supply

Abstract

The problems of shipping and transporting perishable goods are commonly considered in the literature as significant topics, but rarely did researchers adopt a probabilistic point of view in their models. It is common in SCM environments that the participating entities' behaviors are random and unpredictable and so can only be modeled in a probabilistic way. In this paper, we consider the shipping problem of determining the optimal quantity of perishable products with a limited time to be stored in the warehouse. The optimal quantity minimizes the overall operational costs including those of inventory and shipping. We develop a mathematical model, from which the probability distribution function, mean, and variance of the length of the build-up period are derived and we establish a cost function for determining the optimal shipping value.