Capacitated assortment and price optimization for customers with disjoint consideration sets

We study the capacitated assortment and price optimization problem for customers with disjoint consideration sets. The objective is to find the revenue maximizing set of products and their prices subject to a capacity constraint on the total display space of the offered products. We formulate the problem as a mathematical program and demonstrate its NP-hardness. We propose a fully polynomial-time approximation solution scheme and show that when the weights of the products are identical, our approach yields the optimal solution.