A single-period assortment optimization model

This paper studies a single-period assortment optimization problem with unequal cost parameters. The consumer choice process is characterized by a Multinomial Logit (MNL) model. When the store traffic is a continuous random variable, we explicitly derive the structure of the optimal assortment. Our approach is to use a comprehensive measure-profit rate to evaluate the profitability of each variant and then determine which product should be offered. We demonstrate that the optimal assortment contains the few items that have the highest profit rate. When the store traffic is discrete, the optimal solution is difficult to obtain. We propose a "profit rate" heuristic, which is inspired by the result for the case of continuous store traffic. In a special case with equal cost parameters and normal demand distribution, the profit rate heuristic is indeed optimal. Using randomly generated data, we test the effectiveness of the heuristic and find that the average percentage error is less than 0.1% and that the hit rate is above 90%. Our research provides managerial insights on assortment planning and accentuates the importance of measuring the profitability of each product when the demand is random and cannibalization among different products exists.