Student Seminar by Mr. Yuzhen Feng on Mar 26, 2026, 3:30PM

Title: Resource-Constrained User Equilibrium

Speaker: Mr. Yuzhen Feng (The Hong Kong Polytechnic University)

Date: Mar 26, 2026 (Thursday)

Time: 3:30 pm - 4:30 pm

Venue: Room 8-28, Haking Wong Building, The University of Hong Kong

Registration Link: https://forms.cloud.microsoft/r/552KT3frUg

ITS Student Committee will provide a beverage for registered participants.

Abstract: We study user equilibrium with resource constraints (UERC) where users face strict budget on energy, time, risk, etc., motivated by applications in urban mobility, perishable logistics, and itinerary planning. UERC unifies user equilibrium and the resource‑constrained shortest path problem by allowing both travel costs and resource consumption to depend on congestion, making path feasibility endogenous. We formulate UERC as a quasi‑variational inequality and prove that a UERC exists when every user has at least one feasible path regardless of congestion; otherwise, deciding existence is NP-hard. We establish uniqueness in networks with parallel links between a single origin-destination pair, even with heterogeneous budgets among users, and show counterexamples where minimal generalizations destroy uniqueness. When cost equals resource consumption on every link, UERC coincides with classical user equilibrium and thus inherits its uniqueness of link flows. When cost and resource consumption differ but their ratio is uniformly bounded above and below, both the price of anarchy and unfairness (the max-to-min ratio of equilibrium costs experienced by the same user type) are bounded; without such comparability, both can be unbounded. We also reveal a paradoxical comparative statics: increasing users' budgets can raise total system cost by allowing more users to already congested routes. Computationally, we develop a penalty‑based algorithm with column generation that repeatedly solves a resource‑constrained shortest path subproblem, and prove convergence under the same sufficient condition for existence. Experiments on benchmark road networks demonstrate the computational scalability of our algorithm and quantify the impact of endogenous feasibility on equilibrium outcomes.

Bios: Mr. Yuzhen Feng is currently a third-year Ph.D. student in Transportation at The Hong Kong Polytechnic University, supervised by Dr. Wei Liu. His recent work is mainly related to transportation network modeling, optimization, and equilibrium. He received his B.Mgt. degree in Information Management and Information System from the School of Economics and Management at Tongji University in 2023. During his undergraduate studies, he also worked with Prof. Xiaolei Wang on dynamic en-route ride-pooling. He is a recipient of the Hong Kong Ph.D. Fellowship.