Simultaneous pricing and inventory decisions for substitute and complementary items with nonlinear holding cost

In practice, the holding cost in inventory models can be considered as linear or nonlinear functions. Nevertheless, nonlinear holding cost rarely attracted the attention of the researchers, and to our knowledge, it is novel in the presence of complementary or substitute items. It can also be interpreted as a way to include the perishability of products. Except for the perishability, nonlinear holding cost can be employed for other purposes like cold supply chain. In this paper, a new pricing method based on a multi-product inventory model is presented for complementary and substitute items. This paper aims to find the optimum value of the replenishment cycle and prices for the products supplied together (complementary) or interchangeable (substitute), such that the total cost of the inventory system is minimized. Demand is assumed as a price sensitive function while the proposed model is trying to obtain the optimal values of prices and the replenishment cycle simultaneously.