The application of the logit demand function in a joint pricing and inventory replenishment model with multiple suppliers

We investigate a joint pricing, supplier selection, and inventory replenishment problem for a single item in a two-stage system, where multiple suppliers and one retailer are considered. Each supplier features certain capacity and quality level. Multiple orders may be placed to potential suppliers within a repeating order cycle. The demand is deterministic and sensitive to the selling price set by the retailer, which can be modeled using the logit function. In this context, we develop a mathematical model to find optimal solutions for the selling price and inventory replenishment policy, including the set of selected suppliers, order frequency, and order quantity. We further adopt a piecewise linear approximation technique to simplify the model. A numerical example is then presented to illustrate the results of the proposed model and algorithm.