Title:
Conic Reformulation Methods in Revenue Management
Conic Reformulation Methods in Revenue Management
Author(s)
Shao, Hongzhang
Advisor(s)
Kleywegt, Anton J.
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Abstract
This thesis presents a comprehensive study on optimization problems in revenue management, with a particular focus on the development and application of conic programming reformulation techniques.
The work is grounded in three distinct but interrelated papers, each addressing a unique aspect of revenue management.
The first paper investigates the trade-off between pickup time and idle time in ride-hailing systems.
Pickup time refers to the duration from when a car is dispatched to pick up a rider until the rider is picked up.
The study reveals that if cars spend less idle time waiting for a dispatch, the mean distance between a rider and the closest available car increases, resulting in longer pickup times.
This phenomenon is crucial in ride-hailing as every minute spent on pickup reduces the time available for transporting riders.
Despite its importance, existing literature on price optimization and repositioning in ride-hailing systems often overlooks pickup time.
This paper presents a novel approach to reformulate a simultaneous price and repositioning optimization problem, considering the distribution of pickup time, into a tractable convex optimization problem.
The optimal solution derived from this approach significantly outperforms policies proposed in previous studies, as demonstrated in simulations.
The second paper delves into the complexities of identifying the ideal product pricing and assortment, a critical aspect of revenue management.
The challenge lies in concurrently establishing prices and assortments while navigating a resource network with finite capacity.
Existing research on the static joint optimization of price and assortment often overlooks resource constraints.
Our study, however, addresses the revenue management problem with resource constraints and price boundaries, where prices and product assortments must be collaboratively determined over time.
We demonstrate that under the Markov chain (MC) choice model (which subsumes the multinomial logit (MNL) model), the choice-based joint optimization problem can be transformed into a tractable convex conic optimization problem.
For static joint optimization without resource constraints, we reveal that the optimal price for a product remains consistent across all optimal solutions with positive sales.
With the same price vector, an assortment can be optimal if it both contains and is contained by optimal assortments.
Interestingly, optimal assortments in such problems are closed under union but may not be closed under intersection.
In the context of revenue management problems, we prove that an optimal solution with a constant price vector is possible, even in the presence of resource constraints.
This finding suggests that there is no need to continuously adjust prices throughout the planning period.
The third paper addresses a fundamental problem in revenue management: finding the optimal choice of product attributes.
These attributes significantly influence both the market share and profit margin of a product.
The decision-maker is tasked with choosing the optimal vector of attributes for each product to maximize total profit, revenue, or market share.
However, existing literature on product line design with multiple attributes often results in intractable optimization problems.
In contrast, studies on pricing problems under discrete choice models typically assume that price is the only attribute to be chosen for each product, and the methods used in such literature cannot be generalized to solve optimization problems with multiple product attributes.
In this paper, we introduce a method to reformulate static multi-attribute optimization problems and multi-stage fluid optimization problems with resource constraints and upper and lower bounds on attributes as tractable convex conic optimization problems.
Our results apply to optimization problems under the multinomial logit (MNL) model, the Markov chain (MC) choice model, and with certain conditions, the nested logit (NL) model.
This method also provides a unified approach to solve pricing problems under discrete choice models and can reproduce many existing results established under different methods.
Overall, this thesis underscores the potential of conic programming reformulation techniques in solving complex optimization problems in revenue management, providing a unified approach that can be applied across various models and scenarios.
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Date Issued
2023-11-29
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Text
Resource Subtype
Dissertation