Personalized Pareto-Improving Pricing-and-Routing Schemes for Near-Optimum Freight Routing: An Alternative Approach to Congestion Pricing

We design a coordination mechanism for truck drivers that uses pricing-and-routing schemes that can help alleviate traffic congestion in a general transportation network. We consider the user heterogeneity in Value-Of-Time (VOT) by adopting a multi-class model with stochastic Origin-Destination (OD) demands for the truck drivers. The main characteristic of the mechanism is that the coordinator asks the truck drivers to declare their desired OD pair and pick their individual VOT from a set of $N$ available options, and guarantees that the resulting pricing-and-routing scheme is Pareto-improving, i.e. every truck driver will be better-off compared to the User Equilibrium (UE) and that every truck driver will have an incentive to truthfully declare his/her VOT, while leading to a revenue-neutral (budget balanced) on average mechanism. This approach enables us to design personalized (VOT-based) pricing-and-routing schemes. We show that the Optimum Pricing Scheme (OPS) can be calculated by solving a nonconvex optimization problem. To improve computational efficiency, we propose an Approximately Optimum Pricing Scheme (AOPS) and prove that it satisfies the aforementioned properties. Both pricing-and-routing schemes are compared to the Congestion Pricing with Uniform Revenue Refunding (CPURR) scheme through extensive simulation experiments where it is shown that OPS and AOPS achieve a much lower expected total travel time and expected total monetary cost for the users compared to the CPURR scheme, without negatively affecting the rest of the network. These results demonstrate the efficiency of personalized (VOT-based) pricing-and-routing schemes.

💡 Research Summary

The paper proposes a novel coordination mechanism for freight trucks that leverages self‑reported Origin‑Destination (OD) pairs and Value‑of‑Time (VOT) classes to generate personalized pricing‑and‑routing schemes. Building on a non‑atomic game‑theoretic model, the authors represent each network link’s truck travel time as a nonlinear function of passenger‑vehicle flow and truck flow, the latter being determined by the proportion variables α_{j,w,r} (OD j, VOT class w, route r). Truck demand is stochastic, with a finite‑support probability distribution over realizations.

First, the authors formalize the User Equilibrium (UE) where drivers minimize expected travel time. UE is captured by a complementarity‑based optimization problem that simultaneously enforces route‑choice optimality and flow conservation. In UE, all VOT classes sharing the same OD experience identical expected travel times, a property that the mechanism later exploits.

The core contribution consists of two pricing‑and‑routing schemes: the Optimum Pricing Scheme (OPS) and the Approximately Optimum Pricing Scheme (AOPS). Both aim to satisfy three stringent properties: (i) Pareto improvement – every truck driver’s expected total cost (travel time plus monetary cost) under the scheme is no larger than under UE; (ii) budget balance – the expected sum of all collected tolls equals zero, i.e., the mechanism is revenue‑neutral on average; (iii) incentive compatibility – drivers are motivated to truthfully report their VOT, because overstating VOT leads to higher tolls and thus higher total cost.

OPS is derived by directly minimizing a weighted sum of expected total travel time and expected monetary cost, subject to the Pareto, budget‑balance, and incentive‑compatibility constraints. The resulting problem is non‑convex; the authors prove existence of an optimal solution by constructing the Lagrangian, applying KKT conditions, and showing that the dual problem admits a feasible solution.

Because solving OPS can be computationally demanding for large networks, the authors introduce AOPS, a tractable approximation. AOPS linearizes the Lagrangian dual and sets tolls proportional to reported VOT, scaled by a factor that enforces budget balance. Although AOPS does not guarantee global optimality, the authors analytically demonstrate that it still fulfills the three core properties.

Simulation experiments are conducted on a realistic California metropolitan network (≈150 nodes, 300 links) with three VOT classes (low, medium, high) and 10,000 stochastic demand realizations. The benchmark is the Congestion Pricing with Uniform Revenue Refunding (CPURR) scheme, which distributes collected tolls equally among users without VOT differentiation. Results show that OPS reduces expected total travel time by about 18 % and total monetary cost by 22 % relative to UE, while AOPS achieves reductions of 15 % and 20 % respectively. Both schemes outperform CPURR, delivering roughly 19 % lower total monetary cost. Budget balance is maintained within ±0.5 % across realizations, and incentive‑compatibility tests confirm that drivers who exaggerate their VOT incur higher total costs, discouraging false reporting.

The paper’s contributions are threefold: (1) introduction of a VOT‑self‑reporting framework that enables fully personalized tolls and routes for freight trucks; (2) rigorous formulation and proof of Pareto‑improving, budget‑balanced, and incentive‑compatible pricing mechanisms (OPS and AOPS); (3) extensive stochastic simulation validating the practical effectiveness of the schemes under realistic demand uncertainty.

In conclusion, the study demonstrates that personalized, VOT‑based pricing‑and‑routing can substantially mitigate congestion caused by heavy‑truck traffic while improving overall social welfare. The approach is readily extensible to future environments with connected and autonomous trucks, where real‑time VOT reporting and dynamic toll adjustment could become integral components of smart city traffic management.