Dynamic pricing and lot sizing for a newsvendor problem with supplier selection, quantity discounts, and limited supply capacity

This study considers the joint pricing and sourcing decision problem for a buyer purchasing a product from a set of suppliers who offer quantity discounts. The suppliers' supply and/or the buyer's warehouse capacities are bounded, causing the buyer to split its order over multiple suppliers and periods. This study assumes that demand is random over the planning horizon, divided into several periods, and dependent on price and time. The buyer, in each period, has to determine its retail price and the order quantities from the suppliers that maximize its expected profit. The problem is, therefore, formulated as mixed-integer nonlinear programming one, and an algorithm is developed to solve it. Numerical results show that the buyer may not buy up to the maximum capacity of a supplier with the lowest price when its order quantity exceeds the supply capacity of that supplier. In this case, the buyer needs to assign the remaining quantity to a more expensive supplier given that it exceeds that supplier's minimum order quantity. The buyer could consider, as another option, convincing the low-priced supplier to increase its supply capacity in return for accepting a higher wholesale price, which only applies to the portion of an order exceeding the original supply capacity. For this to work, it should be economical for both players. Many numerical examples are provided with their results discussed to draw some insights and concluding remarks.