Inventory optimization for combined stock-dependent and stochastic demand

Abstract

This work develops an optimal inventory policy for stock-dependent demand items taking into account both lead time and lead time demand uncertainties. (Q,R) modeling approach has been implemented to deal with uncertainties of demand and lead time. Unlike previous models this model combines a deterministic approach with a stochastic approach to formulate a combined one. Holding cost per unit per unit time is considered an increasing function of quantity in storage up to reorder point and lead time demand is assumed to be proportional to the span of lead time. Lead time is normally distributed and since demand during lead time is proportional to it, the lead time demand also follows a normal distribution. This is a single objective unconstrained optimization model that aims at minimizing inventory cost where the decision variables are order quantity and reorder point. Fill rate will also be evaluated for different combinations of cost and the decision variables. Fill rate and service level are vital for customer satisfaction but these two cause the inventory cost to augment and bring complexity in inventory modeling. A sensitivity analysis will determine cost sensitivity of the parameters which would allow managers to decide on inventory decision such as increasing average stock to enhance fill rate and demand, reduce the cost of replenishments etc.