Joint optimization of pricing and ordering for two substitute products with a budget constraint

This paper focuses on the revenue management by jointly optimizing pricing and ordering for two substitute products when the retailer has a budget constraint, which is different from most previous literatures where each feature has been addressed separately. We use the Lagrangian method of solving nonlinear programming with inequality constraint to get the optimal close-form solutions and provide numerical examples. Results show that higher substitutability leads to higher price and total revenue, and the change tendency of order quantity depends on the price. Extension to stochastic demand scenario is also discussed.