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We develop a variant of the multinomial logit model with impatient customers and study assortment optimization and pricing problems under this choice model. In our choice model, a customer incrementally views the assortment of available products in multiple stages. The patience level of a customer determines the maximum number of stages in which the customer is willing to view the assortments of products. In each stage, if the product with the largest utility provides larger utility than a minimum acceptable utility, which we refer to as the utility of the outside option, then the customer purchases that product right away. Otherwise, the customer views the assortment of products in the next stage as long as the customer’s patience level allows the customer to do so. Under the assumption that the utilities have the Gumbel distribution and are independent, we give a closed-form expression for the choice probabilities. For the assortment-optimization problem, we develop a polynomial-time algorithm to find the revenue-maximizing sequence of assortments to offer. For the pricing problem, we show that, if the sequence of offered assortments is fixed, then we can solve a convex program to find the revenue-maximizing prices, with which the decision variables are the probabilities that a customer reaches different stages. We build on this result to give a 0.878-approximation algorithm when both the sequence of assortments and the prices are decision variables. We consider the assortment-optimization problem when each product occupies some space and there is a constraint on the total space consumption of the offered products. We give a fully polynomial-time approximation scheme for this constrained problem. We use a data set from Expedia to demonstrate that incorporating patience levels, as in our model, can improve purchase predictions. We also check the practical performance of our approximation schemes in terms of both the quality of solutions and the computation times. 

We provide an approximation algorithm for network revenue management problems. In our approximation algorithm, we construct an approximate policy using value function approximations that are expressed as linear combinations of basis functions. We use a backward recursion to compute the coefficients of the basis functions in the linear combinations. If each product uses at most L resources, then the total expected revenue obtained by our approximate policy is at least [Formula: see text] of the optimal total expected revenue. In many network revenue management settings, although the number of resources and products can become large, the number of resources used by a product remains bounded. In this case, our approximate policy provides a constant-factor performance guarantee. Our approximate policy can handle nonstationarities in the customer arrival process. To our knowledge, our approximate policy is the first approximation algorithm for network revenue management problems under nonstationary arrivals. Our approach can incorporate the customer choice behavior among the products, and allows the products to use multiple units of a resource, while still maintaining the performance guarantee. In our computational experiments, we demonstrate that our approximate policy performs quite well, providing total expected revenues that are substantially better than its theoretical performance guarantee.