Bi-objective capacitated assortment planning under the MNL model: Trade-offs between revenue and market share

Assortment planning is a challenge for retailers because most current solutions only consider revenue maximization and ignore the trade-offs between revenue and market share. To address this challenge, we develop a bi-objective capacitated assortment planning (B-CAP) problem based on the multinomial logit (MNL) choice model and reveal managerial insights into the bi-objective function of the B-CAP problem. To solve this problem, we first examine the performance guarantees of the revenue-ordered assortment. Then, we provide parametric linear programming to generate candidate assortments and analyze the unimodality of the bi-objective function to simplify the computational complexity. Hence, the two-stage approach consisting of the geometric algorithm and Fibonacci search is designed to obtain the optimal solution. Finally, we present numerical experiments on both simulated and real data. The results indicate that the two-stage approach performs well in solving the B-CAP problem. Besides, an interesting finding is that market share may be significantly increased without a huge loss in total revenue when the trade-off parameter is small.