Latency-Aware Bid Acceptance under Operational Feasibility: A Public Benchmark with Hindsight Ceilings

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.

Sequential contextual stochastic programs model real-time decision systems in which each time epoch commits to an action under uncertainty whose consequences propagate into future decisions. In many practical contexts, these programs require obtaining solutions rapidly as new information becomes available. These problems can be represented through scenario approximations to be solved by off-the-shelf optimization solvers, which achieve high decision quality offline but typically run in seconds to minutes per instance, falling short of the sub-second responses that peak periods of planning require. This paper develops a learning-based optimization proxy: a scenario-embedded neural network trained offline on solver-generated labels, paired online with a decoder that enforces feasibility, replacing the per-epoch solve with a single forward pass. The framework is specialized to omnichannel order fulfillment, where each arriving order requires a sub-second assignment of products to distribution centers and carrier services under stochastic delivery times and future demand. A two-stage contextual stochastic program is introduced to formulate this problem, and its contextual sample average approximation (C-SAA) supplies the offline labels, while a composite training loss combines label imitation, a constraint-violation penalty, and self-supervised cost alignment. In a calibrated simulator built from JD.com transactional records, a detailed computational study is provided. The proxy reduces decision latency by roughly 2800x relative to the online finite-sample C-SAA reference and improves over it by 3.3% in realized fulfillment cost. Relative to established fulfillment policies, the proxy lowers total realized cost by at least 10.7% and roughly halves the late-delivery rate.

Freight brokerages negotiate thousands of carrier rates daily under dynamic pricing conditions where models frequently revise targets mid-conversation. Classical time-dependent concession frameworks use a fixed shape parameter $β$ that cannot adapt to these updates. Deriving $β$ from the live spread enables adaptation but introduces a new problem: a pricing shift can cause the formula to retract a previous offer, violating monotonicity. LLM-powered brokers offer flexibility but require expensive reasoning models, produce non-deterministic pricing, and remain vulnerable to prompt injection. We propose a two-index anchor-and-resume framework that addresses both limitations. A spread-derived $β$ maps each load's margin structure to the correct concession posture, while the anchor-and-resume mechanism guarantees monotonically non-decreasing offers under arbitrary pricing shifts. All pricing decisions remain in a deterministic formula; the LLM, when used, serves only as a natural-language translation layer. Empirical evaluation across 115,125 negotiations shows that the adaptive $β$ tailors behavior by regime: in narrow spreads, it concedes quickly to prioritize deal closure and load coverage; in medium and wide spreads, it matches or exceeds the best fixed-$β$ baselines in broker savings. Against an unconstrained 20-billion-parameter LLM broker, it achieves similar agreement rates and savings. Against LLM-powered carriers as more realistic stochastic counterparties, it maintains comparable savings and higher agreement rates than against rule-based opponents. By decoupling the LLM from pricing logic, the framework scales horizontally to thousands of concurrent negotiations with negligible inference cost and transparent decision-making.