Related papers: Complexity of MLDP
We consider a constrained shortest path problem with two resources. These two resources can be converted into each other in a particular manner. Our practical application is the energy optimal routing of hybrid vehicles. Due to the…
The cost due to delay in services may be intrinsically different for various applications of vehicle routing such as medical emergencies, logistical operations, and ride-sharing. We study a fundamental generalization of the Traveling…
We consider fundamental scheduling problems motivated by energy issues. In this framework, we are given a set of jobs, each with a release time, deadline and required processing length. The jobs need to be scheduled on a machine so that at…
Segment Routing is a recent network technology that helps optimizing network throughput by providing finer control over the routing paths. Instead of routing directly from a source to a target, packets are routed via intermediate waypoints.…
In last-mile routing, the task of finding a route is often framed as a Traveling Salesman Problem to minimize travel time and associated cost. However, solutions stemming from this approach do not match the realized paths as drivers deviate…
This study examines the problem of hopping robot navigation planning to achieve simultaneous goal-directed and environment exploration tasks. We consider a scenario in which the robot has mandatory goal-directed tasks defined using Linear…
Finding a shortest path in a graph is one of the most classic problems in algorithmic and graph theory. While we dispose of quite efficient algorithms for this ordinary problem (like the Dijkstra or Bellman-Ford algorithms), some slight…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
The Vehicle Routing Problem (VRP) is a fundamental challenge in logistics management research, given its substantial influence on transportation efficiency, cost minimization, and service quality. As a combinatorial optimization problem,…
In this paper, we study a variant of the dynamic ridesharing problem with a specific focus on peak hours: Given a set of drivers and rider requests, we aim to match drivers to each rider request by achieving two objectives: maximizing the…
We consider two-machine routing open shop problem on a tree. In this problem a transportation network with a tree-like structure is given, and each node contains some jobs to be processed by two mobile machines. Machines are initially…
Energy consumption is the major contributor associated with large and growing transportation cost in logistics. Optimal vehicle routing approaches can provide solutions to reduce their operating costs and address implications on energy.…
There has been a series of developments in the recent literature (by essentially a same "circle" of authors) with the absolute/unconditioned (implicit or explicit) claim that there exists no abstraction of an NP-Complete combinatorial…
Modular vehicles (MV) possess the ability to physically connect/disconnect with each other and travel in platoon with less energy consumption. A fleet of demand-responsive transit vehicles with such technology can serve passengers door to…
We consider the problem of maximizing the revenue raised from tolls set on the arcs of a transportation network, under the constraint that users are assigned to toll-compatible shortest paths. We first prove that this problem is strongly…
We introduce and study the complexity of Path Packing. Given a graph $G$ and a list of paths, the task is to embed the paths edge-disjoint in $G$. This generalizes the well known Hamiltonian-Path problem. Since Hamiltonian Path is…
In the present article, we study the numerical approximation of a system of Hamilton-Jacobi and transport equations arising in geometrical optics. We consider a semi-Lagrangian scheme. We prove the well posedness of the discrete problem and…
We study a joint routing-assignment optimization problem in which a set of items must be paired one-to-one with a set of placeholders while simultaneously determining a Hamiltonian cycle that visits every node exactly once. Both the…
The multi-vehicle dial-a-ride problem (mDaRP) is a fundamental vehicle routing problem with pickups and deliveries, widely applicable in ride-sharing, economics, and transportation. Given a set of $n$ locations, $h$ vehicles of identical…
We consider the problem of allocating multiple heterogeneous resources geographically and over time to meet demands that require some subset of the available resource types simultaneously at a specified time, location, and duration. The…