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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.
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Online Matching Frameworks Under Stochastic Rewards, Product Ranking, and Unknown Patience
In e-commerce, customers have an unknown patience in terms of how far down the page they are willing to scroll. In light of this, how should products be ranked? The e-commerce retailer’s problem is further complicated by the fact that the supply of each product may be limited, and that multiple customers who are interested in these products will arrive over time. In “Online Matching Frameworks Under Stochastic Rewards, Product Ranking, and Unknown Patience,” Brubach, Grammel, Ma, and Srinivasan provide a general framework for studying this complicated problem that decouples the product ranking problem for a single customer from the online matching of products to multiple customers over time. They also develop a better algorithm for the single-customer product ranking problem under well-studied cascade-click models. Finally, they introduce a model where the products are also arriving over time and cannot be included in the search rankings until they arrive.
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- Award ID(s):
- 1918749
- PAR ID:
- 10497767
- Publisher / Repository:
- Institute for Operations Research and the Management Sciences (INFORMS)
- Date Published:
- Journal Name:
- Operations Research
- ISSN:
- 0030-364X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1287/opre.2021.0371
