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Optimal ordering policy for a multi item probabilistic inventory model with all-units discount
A mathematical model for a multi item probabilistic inventory problem with all-unit discount is the main focus of this paper. In developing the model, our objective is to determine the optimal ordering policy to minimize the total cost. We will also compare the total cost, which consists of the purchasing cost, ordering cost, handling and shortage costs for individual and joint replenishment policy. In the individual order policy, our model will determine the optimal order quantity and reorder point for each item while in the joint replenishment, the optimal ordering time will become the decision variable. Demand for these items are assumed to follow Gamma distribution with certain parameters and all shortages are back-ordered. Supplier gives all-units discount for items ordered above certain amount. This policy will lower the purchase cost and probably the shortage cost but on the other hand handling cost becomes higher. When joint replenishment policy is applied, the ordering cost is lower compared to the ordering cost for the individual ordering policy. Our numerical experiments shows, for three items with one price break for all-units discount, individual replenishment policy gives lower total cost than the joint replenishment policy. However, in general many factors such as demand parameters, holding cost and the joint ordering cost that will determine which policy is preferable.
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