Impact of substitution cost on optimal order quantity for substitutable and complementary products with quantity discount under quadratic demand

Abstract

In this article, impact of substitution cost on obtaining optimal ordering quantities for substitutable and complementary products has been studied. Product 1 and 2 are mutually substitutable and each product comprises of two complementary components. The phenomenon of quantity discount is considered in this model. When a product becomes out of stock, partial substitution has been carried out to fulfil the demand of the other product. The demand of both products is assumed to be quadratic. Mathematical model is formulated and a solution a procedure is suggested to obtain the optimal ordering quantities. Optimal total cost for all possible cases has been discussed in this paper. Numerical example is presented and sensitivity analysis is carried out extensively to prove the viability of the proposed inventory model. Substantial improvement in the optimal total cost with substitution over without substitution is observed.