The multi-agent pathfinding problem is the problem of finding a set of collision-free paths for multiple agents traversing a graph. In MAPF, the underlying graph is given, and agents move along adjacent vertex at each timestep. However, this assumption oversimplifies the actual movement of physical agents. Also, in real-world applications such as controlling AGVs or drones, each agent often has computational capabilities to plan and follow its own trajectory. This talk presents a novel integer optimization approach to plan collision-free paths for agents traversing the Euclidean space considering kinematic characteristics of agents. To avoid the computational burden of modelling the movements of agents in detail, we discretize a given space into areas and plan the occupancy of the areas by agents over time. Our approach reduces the computational burden in the planning phase and allows some autonomy to the agents in the execution phase. We present a condition on the discretization under which planned paths are conflict-free, with examples that satisfy the condition. The planning problem is represented as a pattern-based integer optimization model, where each agent's area occupancy over time corresponds to a pattern. We use a robotics simulator to evaluate our approach.

Multimodal transport is a new transportation approach aimed at reducing the role of roadways in freight transportation, and moving toward eco-friendly solutions. This strategy has emerged as a promising method to address environmental concerns and challenges associated with global warming by utilizing multiple transportation modes for freight transshipment. Containerized intermodal transport is a specific type of this strategy, in which the loading unit of container is preserved throughout the journey. In this paper, we introduce a two-stage stochastic optimization model designed to enhance the sustainability and resilience of containerized transport, particularly in the face of unexpected disruptions. The proposed model integrates various environmental and social sustainability metrics, including greenhouse gas emissions, noise pollution, traffic congestion, and accidents. To tackle the complexities inherent in the model, we develop an efficient solution methodology based on Lagrangian relaxation. Validation of the effectiveness of the proposed approach is conducted using real-world transportation system data. Through analysis of the case study, the practical application of the model is illustrated in generating valuable managerial insights for those involved in the freight transport industry. Our analysis reveals that allocating a mere 0.4\% of total costs to preparedness and recovery initiatives can result in a substantial reduction of approximately 4.7\% in overall costs.

The emergence of shared autonomous electric vehicle fleets in transportation networks is expected to yield substantial societal and environmental benefits. In this paradigm, automated and electrified fleets are coordinated to serve passenger travel demand. The operations of shared autonomous electric vehicle systems requires the coordination of recharge trips and rebalancing trips in between passenger trips. Thus, the design of the charging infrastructure is key to the efficiency of the system. We address the charging station location problem in the context of shared autonomous electric vehicle systems. Building on a throughput-maximizing dispatch policy for shared autonomous electric vehicle operations, we propose a mixed-integer linear programming formulation to locate and size charging stations in the network. We exploit the structure of the problem to derive several classes of valid inequalities that aim to strengthen the formulation. We develop Benders' decomposition approaches to enhance the tractability of the solution methods. We conduct numerical experiments on three publicly available transportation networks to investigate the computational performance of four algorithmic configurations. We also conduct sensitivity analyses on problem data including demand, vehicle battery range, fleet cost and the maximum number of chargers available. Our findings show that the derived valid inequalities have a significant impact on reducing computational runtime. Furthermore, we observe that embedding on-the-fly valid inequalities in a Benders' decomposition algorithm can help in improving efficiency.

Motivated by applications in e-commerce logistics where orders or items arrive at different times and must be dispatched or processed in batches, we propose the subadditive dispatching problem (SAD), a strongly NP-hard problem defined by a set of orders with release times and a non-decreasing subadditive dispatch time function. A single uncapacitated vehicle must dispatch orders in batches to minimize the makespan, the time at which all orders have been dispatched. We propose a mixed-integer linear formulation for SAD; based on the linear relaxation's optimal solution, we construct a two-dispatch solution with a 3/2 approximation ratio, and a solution with at most three dispatches that has a 4/3 approximation ratio under an additional assumption. The guarantees are respectively best possible for solutions using at most two or three dispatches. Furthermore, we analyze FIFO solutions, discuss cases when they are optimal, and provide a dynamic program to obtain them. Finally, we computationally test our methods on applications in same-day delivery and routing on restricted topologies.