Application of the logit demand function to determine the retail price and inventory policy in a serial supply chain

We consider a serial supply chain with multiple stages in a centralized control scenario. Within this supply chain, the first stage faces a supplier selection decision for a particular product that experiences a price-sensitive demand. The demand is represented as a logit function, which parameters account for the range and price sensitivity factors. Suppliers are capacitated and offer their individual fixed unit price with a corresponding quality level for the product. The buying stage needs to decide which suppliers to choose and how to allocate orders, determining the optimal inventory policy for all stages and the retail price to offer to end customers, while maximizing the total profit of the supply chain. The problem is formulated as a mixed integer nonlinear programming model and a heuristic approach is proposed to generate an approximate solution. Then, we analyze a special case that considers only one uncapacitated supplier and a buyer with price-sensitive demand in a serial supply chain. An efficient heuristic is developed for this case to obtain a near optimal solution in a timely manner. Finally, we provide a series of numerical examples to illustrate our results and analyze the impact of the parameters within a sensitivity analysis.