A NOVEL APPROACH TO PROBABILISTIC INVENTORYMODELING WITH MIXED SHORTAGES AND VARIABLEHOLDING COSTS UNDER BIVARIATE UNCERTAINTY

Abstract

This study examines a stochastic continuous review inventory
model for a single item sourced from one supplier. It introduces a novel approach to varying holding costs and mixed shortages, factoring in the randomness of both demand and lead time. We derived the distribution of lead time demand X in two scenarios: first, when the demand D is a discrete random variable with a continuous lead time L; and second, when both demand and lead time are modeled as continuous random variables. Using the proposed model, we determined the optimal order quantity and
reorder point by minimizing the expected annual total cost, leveraging the erived distribution of lead time demand. Finally, a numerical example is presented to demonstrate the applicability and effectiveness of the model.