  In this paper, we investigate the capacitated assortment optimization problem
with pricing under the paired combinatorial logit model, whose goal is to
identify the revenue-maximizing subset of products as well as their selling
prices subject to a known capacity limit. We model customers' purchase behavior
using the paired combinatorial logit model, which allows for covariance among
any pair of products. We formulate this problem as a non-linear mixed integer
program. Then, we propose a two-step approach to obtain the optimal solution
based on solving a mixed integer program and Lambert-W function. To further
improve its performance, we design a greedy heuristic algorithm and a greedy
randomized adaptive search procedure to obtain high-quality solutions so as to
balance the tradeoff between accuracy and computational efficiency. A series of
numerical experiments are conducted to gauge the efficiency and quality of our
proposed approaches.
