Optimal replenishment policy for multi-item probabilistic inventory model with all-units discount

In this paper, we develop a multi item inventory model for the retailer by considering all-units discount offered by the supplier. Demands in this model are assumed to be probabilistic following a Gamma distribution with certain values of shape and scale parameters. The aim of the model is to determine the optimal replenishment policy that minimize the total inventory cost. The total inventory cost was composed from the purchasing, ordering, handling or storing and shortage costs. All shortages are handled by backorder. We compare the individual and joint replenishment policies for the model and develop an algorithm to find the optimal replenishment policy. Numerical examples are given to give a better understanding of the model in comparing the individual and joint replenishment policies. We also perform sensitivity analysis by changing values of shape and scale parameters of the demand distribution to analyse the effects on the optimal solution.