A mathematical model for multi-item inventory- and price-dependent demands with all-units discount.

Inventory control problem becomes one of the most crucial parts in a company. Basically, the problem is to determine the optimal time and quantity of replenishment. But, there are many factors affected the decision such as demand uncertainty, lifetime of the product, deterioration, unit sales price and discount offered by the supplier. In this paper, we consider a mathematical model for inventory control problem. We consider a multi-item problem with inventory and price-dependent demand and all-units discount offered by the supplier. In dealing with multi-item problem, there are two replenishment policies to consider, individual order and joint order policy. Numerical examples are given with different inventory and price-dependent demand functions for each item and compare the individual and joint order policy. We found that in our numerical example, joint replenishment policy gives lower total inventory cost compared to the individual order policy. [ABSTRACT FROM AUTHOR]