Certified-Gap Dual-Price Policies for Real-Time Truckload Bid Acceptance with Relocating, Clock-Constrained Resources
Machine LearningArtificial Intelligence
Summary
The authors study how a trucking company can quickly decide to accept or reject delivery loads based on the trucks’ location, work hours, and timing constraints. They create a mathematical model and solve it using a method called Lagrangian relaxation, which offers both a decision policy and a way to measure how close that policy is to the best possible solution. Their approach works very fast and nearly as well as slower, more complex methods, and it provides reliable guarantees on its performance. They also prove some theoretical properties about the method’s optimality and limitations.
Authors
Aswin Chandrasekaran
Abstract
A truckload carrier must accept or reject each load tender within seconds. The decision depends on fleet state, hours-of-service (HOS) clocks, and appointment windows. We model this as a weakly coupled dynamic program in which the resources relocate and carry clocks: serving a request moves the truck to a new market and depletes its clocks, and whether a truck can serve a request depends on its state. Occupancy-based reusable-resource models do not cover this setting. We build a real-time dual-price policy from the same Lagrangian relaxation that gives the problem's upper bound. Policy and bound come from one object, so every run reports a certified optimality gap. We prove three things. First, the certificate is valid for any duals, any discretization, and any surrogate quality. Second, the policy's same-time spatial-gradient rule is exactly fluid complementary slackness, and the policy is asymptotically optimal in the subcritical fluid regime; the fitted prices are also portable across sample paths, by linear-programming basis stability. Third, certificates have limits: per-resource Lagrangian slack can stay bounded away from zero at every fleet size. We exhibit a three-truck kernel with an exact rational certificate and a replication lemma. On a public closed-loop benchmark with thirty paired seeds, the policy -- which needs no rollout labels, only one offline dual solve -- beats a rollout-trained surrogate on two of three scenarios (tight: +2.0 pp, 95% CI [+0.5, +3.6], Wilcoxon p = 0.023; mild: +3.5 pp, CI [+2.4, +4.5]) and ties the third. It decides in 0.04-0.09 ms, three orders of magnitude faster than the Monte Carlo rollout teacher. Its certificates are stable across ten bounded instances per scenario, at 57-64% of optimal, within 3-6 points of what the 1000x-slower teacher certifies.