Multiproduct purchase scheduling with limited budget and/or group discounts (Q1086123)

In major ongoing purchase decisions, involving several products from a single supplier with a limited purchase budget, purchase scheduling becomes very important. Pooling several products in a single order enables the buyer to exploit group discount opportunities provided by the total dollar value of the order. This, however, increases the cost of capital invested in inventory and strains the purchase budget. The order placing cost, on the other hand, is reduced since there are fewer orders placed. The decisions as to how the products are grouped, the number of distinct groups created, the frequency and size of the orders and the impact of the budget limit must therefore be quantitatively analyzed to obtain the best trade-off between the various savings and costs involved. A grouping scheme is employed whereby the products are ranked by the ratio of the inventory carrying cost per period and the order placing cost, and are assigned to the groups so that the products belonging to a group are consecutive in their rank-order. The product to group assignment is achieved using a ''shortest-path'' approach. We show that the above grouping scheme minimizes the total cost composed of the order placing cost, inventory carrying cost and purchase cost with group discounts. We also establish a powerful and somewhat surprising result that the composition of the optimal groups is not affected even if a limit is placed on the purchase budget.