Optimal ordering policy for substitutable and complementary products under quadratic demand

Abstract

In this article, two mutually substitutable products are considered in the inventory. Out of which one of the product is assumed to be a bundle of two complementary components. The inventory of both products are depleted by its demand, which is assumed to be quadratic. In case of stock out, partial substitution is carried out by the other product to fulfil the demand of the customers with a rate of substitution.  The unmet demand is assumed to be lost. The proposed model is formulated and a solution procedure is suggested to obtain the optimal ordering quantity. Sensitivity analysis has been carried out extensively for all the parameters in the model in order to analyse the behaviour of the model. We observe that, there is a substantial improvement in the total cost with substitution compared to that of total cost without substitution.