One-Way Substitution Newsboy Problem under Retailer's Budget Constraint

One-way substitution means that when low-end brand goods are sold out, high-end brand goods can be offered to consumers as substitute goods, but not the opposite. In realistic economic activity, "shortage of funds" is a common practical problem for the retailer in making order decision. This paper proposes a nonlinear optimization model with the retailer's budget to study the optimal order quantities and substitution discount for two one-way substitution products under a stochastic demand scenario, and the objective is to maximize the retailer's revenue. We solve the model mainly according to the Karush-Kuhn-Tucker (KKT) theorem and present the conditions of optimal decisions. Finally, through the numerical study, we analyze the influence of the budget constraint and other parameters on the optimal solutions.