Reliability-constrained dynamic assignment and slot pricing for urban construction logistics: a game-theoretic bilevel model

Abstract

Urban construction logistics injects time-critical deliveries into congested corridors precisely when work-zones suppress capacity and raise travel-time variability. We formulate a logistics-oriented, game-theoretic bilevel framework that coordinates work-zone capacity, delivery time windows, and fleet sizing under explicit service-level reliability. The lower level is a variable-demand dynamic traffic assignment with chance constraints on path times Pr [ T ≤ τ ] ≥ ρ ; we prove an equivalence that embeds reliability as a risk-adjusted generalized cost, preserving the structure needed for large-scale Frank–Wolfe–type solvers within a best-response dynamic. The upper level co-optimizes work-zone staging and priced delivery slots to minimize total logistics cost (project NPV, fleet costs, penalties) plus system travel delay, aligning incentives between the construction operator and general traffic. On a 1,240-link metropolitan testbed of a six-week paving program with perishable service windows (ready-mix ≤ 90 min, hot-mix ≤ 75 min), the reliability-aware equilibrium raises on-time delivery from 78% to 90% and cuts late-arrival penalties by 31%. Adding slot pricing and staged closures further lifts on-time performance to 93%, reduces required ready-mix trucks by 14% at constant pour rates, shortens project duration by 8%, and lowers project NPV by 11%, while holding peak-period background delays to +2.3%. The framework redefines work zone planning as a problem of logistics capacity control, explicitly defining service levels, and provides transferable lessons for other time-sensitive urban freight applications where reliability and scheduling, as well as the interactions between the logistics and the network, all play a role in shaping performance.