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Augmenting the Modeling Power of the Multinomial Logit Model Using choice models to capture customer choice behavior has steadily become the common practice in revenue management. Discrete choice models allow one to capture the fact that customers substitute among the offered products, so if a particular product is not offered, then a portion of the customers interested in this product will substitute into a suitable available alternative. The multinomial logit model is one of the most commonly used choice models to capture customer choice in practice. This choice model is based on the utility maximization framework. A customer associates random utilities with the products, as well as the no-purchase option, in which case, the customer purchases the product with the largest utility, as long as its utility exceeds that of the no-purchase option. In "Assortment Optimization under the Multinomial Logit Model with Utility-Based Rank Cutoffs," Bai, Feldman, Topaloglu, and Wagner augment the modeling flexibility of the multinomial logit model, where a customer also leaves without a purchase if she cannot find one of her top few choices. They develop algorithms to find revenue-maximizing assortments. We study assortment optimization problems under a natural variant of the multinomial logit model where the customers are willing to focus only on a certain number of products that provide the largest utilities. In particular, each customer has a rank cutoff, characterizing the number of products that she will focus on during the course of her choice process. Given that we offer a certain assortment of products, the choice process of a customer with rank cutoff k proceeds as follows. The customer associates random utilities with all of the products as well as the no-purchase option. The customer ignores all alternatives whose utilities are not within the k largest utilities. Among the remaining alternatives, the customer chooses the available alternative that provides the largest utility. Under the assumption that the utilities follow Gumbel distributions with the same scale parameter, we provide a recursion to compute the choice probabilities. Considering the assortment optimization problem to find the revenue-maximizing assortment of products to offer, we show that the problem is NP-hard and give a polynomial time approximation scheme. Because the customers ignore the products below their rank cutoffs in our variant of the multinomial logit model, intuitively speaking, our variant captures choosier choice behavior than the standard multinomial logit model. Accordingly, we show that the revenue-maximizing assortment under our variant includes the revenue-maximizing assortment under the standard multinomial logit model, so choosier behavior leads to larger assortments offered to maximize the expected revenue. We conduct computational experiments on both synthetic and real data sets to demonstrate that incorporating rank cutoffs can yield better predictions of customer choices and yield more profitable assortment recommendations. Funding: The work of Y. Bai and H. Topaloglu was partially supported by the National Science Foundation [Grant No. CMMI-1825406]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2021.0060. [ABSTRACT FROM AUTHOR]

Abstract. In this paper, we study a revenue management model over a single flight leg, where the customers are allowed to lock an available fare. Each customer arrives into the [...]

Problem definition: We consider network revenue management problems with flexible products. We have a network of resources with limited capacities. To each customer arriving into the system, we offer an assortment of products. The customer chooses a product within the offered assortment or decides to leave without a purchase. The products are flexible in the sense that there are multiple possible combinations of resources that we can use to serve a customer with a purchase for a particular product. We refer to each such combination of resources as a route. The service provider chooses the route to serve a customer with a purchase for a particular product. Such flexible products occur, for example, when customers book at-home cleaning services but leave the timing of service to the company that provides the service. Our goal is to find a policy to decide which assortment of products to offer to each customer to maximize the total expected revenue, making sure that there are always feasible route assignments for the customers with purchased products. Methodology/results: We start by considering the case in which we make the route assignments at the end of the selling horizon. The dynamic programming formulation of the problem is significantly different from its analogue without flexible products as the state variable keeps track of the number of purchases for each product rather than the remaining capacity of each resource. Letting L be the maximum number of resources in a route, we give a policy that obtains at least 1/(1+L) fraction of the optimal total expected revenue. We extend our policy to the case in which we make the route assignments periodically over the selling horizon. Managerial implications: To our knowledge, the policy that we develop is the first with a performance guarantee under flexible products. Thus, our work constructs policies that can be implemented in practice under flexible products, also providing performance guarantees. Funding: The work of H. Topaloglu was partly funded by the National Science Foundation [Grant CMMI-1825406]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0583. [ABSTRACT FROM AUTHOR]

There are a variety of revenue management systems that require making pricing or availability decisions for unique resources. For example, lodging marketplaces, boutique hotels, and bed-and-breakfasts offer unique rooms, apartments, or houses. Matching platforms for freelancers recommend differentiated workers with unique characteristics. When managing unique resources, one has to keep track of the availability of each resource at each time point in the future. Moreover, if the customers substitute between different resources, then the pricing and availability decisions for all resources become interdependent. Thus, it can be challenging to find good policies to make pricing or availability decisions. In "Revenue Management with Heterogeneous Resources: Unit Resource Capacities, Advance Bookings, and Itineraries over Time Intervals," Rusmevichientong, Sumida, Topaloglu, and Bai consider revenue management problems when unique resources are requested for use over intervals of time under advance reservations. Using the interval structure of resource requests, they give policies with performance guarantees. We study revenue management problems with heterogeneous resources, each with unit capacity. An arriving customer makes a booking request for a particular interval of days in the future. We offer an assortment of resources in response to each booking request. The customer makes a choice within the assortment to use the chosen resource for her desired interval of days. The goal is to find a policy that determines an assortment of resources to offer to each customer to maximize the total expected revenue over a finite selling horizon. The problem has two useful features. First, each resource is unique with unit capacity. Second, each customer uses the chosen resource for a number of consecutive days. We consider static policies that offer each assortment of resources with a fixed probability. We show that we can efficiently perform rollout on any static policy, allowing us to build on any static policy and construct an even better policy. Next, we develop two static policies, each of which is derived from linear and polynomial approximations of the value functions. We give performance guarantees for both policies, so the rollout policies based on these static policies inherit the same guarantee. Last, we develop an approach for computing an upper bound on the optimal total expected revenue. Our results for efficient rollout, static policies, and upper bounds all exploit the aforementioned two useful features of our problem. We use our model to manage hotel bookings based on a data set from a real-world boutique hotel, demonstrating that our rollout approach can provide remarkably good policies and our upper bounds can significantly improve those provided by existing techniques. Funding: This work was supported by the National Science Foundation [Grants CMMI-1824860 and CMMI-1825406]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/opre.2022.2427. [ABSTRACT FROM AUTHOR]

Abstract. Many airline reservation systems offer the commitment option to their potential passengers. This option allows passengers to reserve a seat for a fixed duration before making a final purchase [...]

We consider pricing problems when customers choose among the products according to the nested logit model and there is a quality consistency constraint on the prices charged for the products. [...]

We consider a joint assortment optimization and customization problem under a mixture of multinomial logit models. In this problem, a firm faces customers of different types, each making a choice within an offered assortment according to the multinomial logit model with different parameters. The problem takes place in two stages. In the first stage, the firm picks an assortment of products to carry the subject to a cardinality constraint. In the second stage, a customer of a certain type arrives into the system. Observing the type of the customer, the firm customizes the assortment that it carries by, possibly, dropping products from the assortment. The goal of the firm is to find an assortment of products to carry and a customized assortment to offer to each customer type that can arrive in the second stage to maximize the expected revenue from a customer visit. The problem arises, for example, in online platforms, where retailers commit to a selection of products before the start of the selling season; but they can potentially customize the displayed assortment for each customer type. We refer to this problem as the Customized Assortment Problem (CAP). Letting m be the number of customer types, we show that the optimal expected revenue of (CAP) can beO(m) times greater than the optimal expected revenue of the corresponding model without customization and this bound is tight. We establish that (CAP) is NP-hard to approximatewithin a factor better than 1- 1=e, so we focus on providing an approximation framework for (CAP). As our main technical contribution, we design a novel algorithm, which we refer to as Augmented Greedy; building on it, we give a O(1=logm)-approximation algorithm to (CAP). Also, we present a fully polynomial-time approximation scheme for (CAP) when the number of customer types is constant. Considering the case where we have a cardinally constraint on the assortment offered to each customer type in the second stage of (CAP), we give a O(1= ... m log m)-approximation algorithm. In our computational experiments, we demonstrate the value of customization by using a data set from Expedia and check the practical performance of our approximation algorithm. [ABSTRACT FROM AUTHOR]

We consider two variants of a pricing problem under the nested logit model. In the first variant, the set of products offered to customers is fixed, and we want to [...]

Discrete choice models have recently attracted significant attention to model demand in revenue-management applications, as they can capture the fact that if a product is unavailable, then some customers substitute for this product, whereas others leave the system without a purchase. Although a more sophisticated choice model may capture the choice process of the customers more faithfully, a simpler choice model may result in tractable optimization problems when finding the optimal assortment of products to offer or prices to charge. One approach for coming up with sophisticated choice models is to mix existing ones, where the different segments of customers choose under the different choice models in the mixture. In "Revenue Management Under a Mixture of Independent Demand and Multinomial Logit Models," Cao, Rusmevichientong, and Topaloglu demonstrate that mixing the independent demand and multinomial logit models can significantly increase the modeling flexibility of each of these choice models, while keeping the corresponding operational assortment optimization problems tractable. We consider assortment optimization problems when customers choose under a mixture of independent demand and multinomial logit models. In the assortment optimization setting, each product has a fixed revenue associated with it. The customers choose among the products according to our mixture choice model. The goal is to find an assortment that maximizes the expected revenue from a customer. We show that we can find the optimal assortment by solving a linear program. We establish that the optimal assortment becomes larger as the relative size of the customer segment with the independent demand model increases. Moreover, we show that the Pareto-efficient assortments that maximize a weighted average of the expected revenue and the total purchase probability are nested, in the sense that the Pareto-efficient assortments become larger as the weight on the total purchase probability increases. Considering the assortment optimization problem with a capacity constraint on the offered assortment, we show that the problem is NP-hard, even when each product consumes unit capacity, so that we have a constraint on the number of offered products. We give a fully polynomial-time approximation scheme. In the assortment-based network revenue-management problem, we have resources with limited capacities, and each product consumes a combination of resources. The goal is to find a policy for deciding which assortment of products to offer to each arriving customer to maximize the total expected revenue over a finite selling horizon. A standard linear-programming approximation for this problem includes one decision variable for each subset of products. We show that this linear program can be reduced to an equivalent one of substantially smaller size. We give an expectation-maximization algorithm to estimate the parameters of our mixture model. Our computational experiments indicate that our mixture model can provide improvements in predicting customer purchases and identifying profitable assortments. Funding: The work of Y. Cao was partly supported by the National Natural Science Foundation of China [Grant 72131010]. The work of H. Topaloglu was partly supported by the National Science Foundation [Grant CMMI-1825406]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.2333. [ABSTRACT FROM AUTHOR]