Logistics operations often involve activities of different vehicle classes such as trucks, cars, and scooters. Due to their heterogenous physical properties, the different vehicle classes vary in their impact on the congestion of road networks. In this talk, we study the game-theoretic framework of atomic congestion games with different user classes. In these games, users control traffic composed of different vehicle classes and strive to minimize their travel time in the network. We discuss the existence of pure Nash equilibria in these games. To this end, a set of cost functions is called consistent for this class if all games with cost functions from the set have a pure Nash equilibrium. We give a complete characterization of consistent sets of cost functions showing that the only consistent sets of cost functions are sets of certain affine functions and sets of certain exponential functions. This characterization gives an axiomatic justification of the passager-car-unit concept used frequently in the traffic literature and can be extended to a larger class of games where each atomic player may control flow that belongs to different classes.

A very important task in modern logistics is the estimation of the arrival time of a planned transport. To give precise answers there is a huge demand for accurate traffic prediction models, especially for truck transportation that is performed on public roads. As such, there has been a huge effort to understand congestion both using theoretical models as well as simulations. This work focuses on the theoretical part. For theoretical traffic models, there is strong motivation to push them to be as realistic as possible.

The theoretical traffic model with dynamic time that gained the most attention in recent years is the deterministic fluid queuing model, already introduced by Vickrey.

In this work, we extend the deterministic fluid queuing model with a multi-criteria objective function. We assume that users try to minimize costs subject to arriving at the destination before a given deadline. Here, costs could be thought of as an intrinsic preference a user has regarding the different route choices, and queuing dynamics only play a role in the arrival time of a user.

We determine the existence and the structure of Nash flows over time and fully characterize the price of anarchy for this model, which measures the ratio of the quality of the Nash flow and the optimal flow.

Customer withdrawals from contracts can impact operational efficiency and resource utilization across various logistics scenarios. In the shipping and freight industry, for instance, customers may withdraw from shipping contracts due to shifts in their business needs, changes in market conditions, or unforeseen circumstances. This often necessitates adjustments in cargo consolidation and vehicle assignment. Similarly, in the last-mile delivery for e-commerce, customers may cancel orders or alter delivery preferences, leading to the need for reoptimized delivery routes and adjustments in resource allocation, such as bookings for the vehicle fleet, to ensure efficiency and cost-effectiveness. While individual contract cancellations may create room for new customers (orders, bookings), the paramount concern is the fulfillment of contracts with the remaining customers.

We address the problem of reoptimization with a commitment requirement by introducing the new model of recoverable robust optimization with commitment. More formally, given a combinatorial optimization problem and uncertainty about elements that may fail, we seek a robust solution that, after the failing elements are revealed, can be augmented in a limited way. Importantly, we commit to preserve the remaining elements of the initial solution. We consider different underlying problems and settle the computational complexity of their robust counterparts with commitment. For instance, we show that the reoptimization for the bookings of a vehicle fleet can be solved efficiently.