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