Sequential Service Region Design with Capacity-Constrained Investment and Spillover Effect

This paper addresses the Service Network Design (SND) problem for a logistics service provider (LSP) operating in a multimodal freight transport network, considering uncertain travel times and limited truck fleet availability. A two-stage optimization approach is proposed, which combines metaheuristics, simulation and machine learning components. This solution framework integrates tactical decisions, such as transport request acceptance and capacity booking for scheduled services, with operational decisions, including dynamic truck allocation, routing, and re-planning in response to disruptions. A simulated annealing (SA) metaheuristic is employed to solve the tactical problem, supported by an adaptive surrogate model trained using a discrete-event simulation model that captures operational complexities and cascading effects of uncertain travel times. The performance of the proposed method is evaluated using benchmark instances. First, the SA is tested on a deterministic version of the problem and compared to state-of-the-art results, demonstrating it can improve the solution quality and significantly reduce the computational time. Then, the proposed SA is applied to the more complex stochastic problem. Compared to a benchmark algorithm that executes a full simulation for each solution evaluation, the learning-based SA generates high quality solutions while significantly reducing computational effort, achieving only a 5% difference in objective function value while cutting computation time by up to 20 times. These results demonstrate the strong performance of the proposed algorithm in solving complex versions of the SND. Moreover, they highlight the effectiveness of integrating diverse modeling and optimization techniques, and the potential of such approaches to efficiently address freight transport planning challenges.

Constraint Programming (CP) offers an intuitive, declarative framework for modeling Vehicle Routing Problems (VRP). While classical successor-based CP models can be adapted to handle optional visits or insertion-based heuristics, sequence variables provide a significantly more natural and elegant formulation for these requirements. Building upon our prior work that introduced the initial concept, the main contribution of this article is the complete semantic and operational formalization of sequence variables as a computational domain. Specifically, we formally define the sequence domain and its update operations, and detail the implementation and data structures required to integrate sequence variables into trail-based CP solvers. Furthermore, we introduce consistency levels for associated constraints on this domain alongside specialized global constraints tailored for routing problems. Finally, we demonstrate that sequence variables simplify problem modeling while achieving competitive computational performance on Pickup and Delivery Problems with and without Time Windows, the Dial-a-Ride Problem, and a Prize-Collecting Scheduling Problem.

Existing LLM routing frameworks treat queries as independent events, neglecting the sequential nature of real-world user sessions constrained by global computational budgets. This mismatch inevitably leads to budget bankruptcy: myopic routing policies exhaust resources on early interactions, forcing subsequent and often more complex queries onto inadequate models. We introduce SeqRoute, a framework that formulates multi-turn routing as a finite-horizon Markov Decision Process and solves it via offline reinforcement learning. By incorporating the remaining budget into the state space and training with Conservative Q-Learning (CQL), SeqRoute learns delayed gratification to strategically preserve resources for high-stakes turns later in the session. To overcome data starvation, we propose Hindsight Budget Relabeling (HBR). This technique retrospectively simulates historical trajectories under diverse hypothetical budgets, expanding 10,000 raw sessions into 2.38 million transitions enriched with critical bankruptcy signals. At deployment, a dynamic $λ$-sweep mechanism enables zero-shot navigation of the cost-quality Pareto frontier without retraining. Extensive evaluations demonstrate that SeqRoute reduces operational costs by 6.0-73.5% while maintaining or improving quality, and suppresses bankruptcy rates to under 1%, strictly dominating behavior cloning, budget-aware heuristics, and static baselines across the entire Pareto frontier.