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In this paper, we investigate the capacitated assortment optimization problemwith pricing under the paired combinatorial logit model, whose goal is toidentify the revenue-maximizing subset of products as well as their sellingprices subject to a known capacity limit. We model customers' purchase behaviorusing the paired combinatorial logit model, which allows for covariance amongany pair of products. We formulate this problem as a non-linear mixed integerprogram. Then, we propose a two-step approach to obtain the optimal solutionbased on solving a mixed integer program and Lambert-W function. To furtherimprove its performance, we design a greedy heuristic algorithm and a greedyrandomized adaptive search procedure to obtain high-quality solutions so as tobalance the tradeoff between accuracy and computational efficiency. A series ofnumerical experiments are conducted to gauge the efficiency and quality of ourproposed approaches.

Capacitated Assortment Optimization with Pricing under the Paired Combinatorial Logit Model