arXiv subjects

Hongzhang Shao

Publications and source records attributed to Hongzhang Shao.

4 recordsLinked to original sources

arXiv2022

Revenue Management Under the Markov Chain Choice Model with Joint Price and Assortment Decisions

Finding the optimal product prices and product assortment are two fundamental problems in revenue management. Usually, a seller needs to jointly determine the prices and assortment while managing a network of resources with limited capacity. However, there is not yet a tractable method to efficiently solve such a problem. Existing papers studying static joint optimization of price and assortment cannot incorporate resource constraints. Then we study the revenue management problem with resource constraints and price bounds, where the prices and the product assortments need to be jointly determined over time. We showed that under the Markov chain (MC) choice model (which subsumes the multinomial logit (MNL) model), we could reformulate the choice-based joint optimization problem as a tractable convex conic optimization problem. We also proved that an optimal solution with a constant price vector exists even with constraints on resources. In addition, a solution with both constant assortment and price vector can be optimal when there is no resource constraint.

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arXiv2021

Tractable Profit Maximization over Multiple Attributes under Discrete Choice Models

A fundamental problem in revenue management is to optimally choose the attributes of products, such that the total profit or revenue or market share is maximized. Usually, these attributes can affect both a product's market share (probability to be chosen) and its profit margin. For example, if a smart phone has a better battery, then it is more costly to be produced, but is more likely to be purchased by a customer. The decision maker then needs to choose an optimal vector of attributes for each product that balances this trade-off. In spite of the importance of such problems, there is not yet a method to solve it efficiently in general. Past literature in revenue management and discrete choice models focus on pricing problems, where price is the only attribute to be chosen for each product. Existing approaches to solve pricing problems tractably cannot be generalized to the optimization problem with multiple product attributes as decision variables. On the other hand, papers studying product line design with multiple attributes all result in intractable optimization problems. Then we found a way to reformulate the static multi-attribute optimization problem, as well as the multi-stage fluid optimization problem with both resource constraints and upper and lower bounds of attributes, as a tractable convex conic optimization problem. Our result applies to optimization problems under the multinomial logit (MNL) model, the Markov chain (MC) choice model, and with certain conditions, the nested logit (NL) model.

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arXiv2021

Optimizing Pricing, Repositioning, En-Route Time, and Idle Time in Ride-Hailing Systems

In ride-hailing systems, en-route time refers to the time that elapses from the moment a car is dispatched to pick up a rider until the rider is picked up. A fundamental phenomenon in ride-hailing systems is that there is a trade-off between en-route time and the time that a car waits for a dispatch. In short, if cars spend little time idle waiting for a dispatch, then few cars are available when a rider makes a request, and thus the mean distance between a rider and the closest available car is long, which means that en-route time is long. This phenomenon is of great importance in ride-hailing, because en-route time increases rapidly as the number of idle cars decreases, and every minute that a car spends en-route is one minute less that the car can transport riders. In spite of this, the existing literature on price optimization for ride-hailing, and on repositioning optimization for ride-hailing, ignores en-route time. Initial attempts to take this trade-off for the mean en-route time into account when considering price optimization or repositioning optimization all resulted in intractable optimization problems. Then we found a way to reformulate a simultaneous price and repositioning optimization problem, that takes this trade-off for the distribution of en-route time into account, as a tractable convex optimization problem. We show how the optimal solution can be used to construct policies that perform much better in simulations than the policies proposed in previous papers.

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arXiv2020

Joint Estimation of Discrete Choice Model and Arrival Rate with Unobserved Stock-out Events

This paper studies the joint estimation problem of a discrete choice model and the arrival rate of potential customers when unobserved stock-out events occur. In this paper, we generalize [Anupindi et al., 1998] and [Conlon and Mortimer, 2013] in the sense that (1) we work with generic choice models, (2) we allow arbitrary numbers of products and stock-out events, and (3) we consider the existence of the null alternative, and estimates the overall arrival rate of potential customers. In addition, we point out that the modeling in [Conlon and Mortimer, 2013] is problematic, and present the correct formulation.

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