A Survey On Multi Trip Vehicle Routing Problem

The vehicle routing problem (VRP) and its variants are well known and greatly explored in the transportation literature. The vehicle routing problem can be considered as the scheduling of vehicles (trucks) to a set of customers under various side constraints. In most studies, a fundamental assumption is that a vehicle dispatched for service finishes its duty in that scheduling period after it returns back to the depot. Clearly, in many cases this assumption may not hold. Thus, in the last decade some studies appeared in the literature where this basic assumption is relaxed, and it is allowed for a vehicle to make multiple trips per period. We consider this new variant of the VRP an important one with direct practical impact. In this survey, we define the vehicle routing problem with multiple trips, define the current state-of-the-art, and report existing results from the current literature

Semi-autonomous Intersection Collision Avoidance through Job-shop Scheduling

In this paper, we design a supervisor to prevent vehicle collisions at intersections. An intersection is modeled as an area containing multiple conflict points where vehicle paths cross in the future. At every time step, the supervisor determines whether there will be more than one vehicle in the vicinity of a conflict point at the same time. If there is, then an impending collision is detected, and the supervisor overrides the drivers to avoid collision. A major challenge in the design of a supervisor as opposed to an autonomous vehicle controller is to verify whether future collisions will occur based on the current drivers choices. This verification problem is particularly hard due to the large number of vehicles often involved in intersection collision, to the multitude of conflict points, and to the vehicles dynamics. In order to solve the verification problem, we translate the problem to a job-shop scheduling problem that yields equivalent answers. The job-shop scheduling problem can, in turn, be transformed into a mixed-integer linear program when the vehicle dynamics are first-order dynamics, and can thus be solved by using a commercial solver.Comment: Submitted to Hybrid Systems: Computation and Control (HSCC) 201

Planning and Scheduling Transportation Vehicle Fleet in a Congested Traffic Environment

Transportation is a main component of supply chain competitiveness since it plays a major role in the inbound, inter-facility, and outbound logistics. In this context, assigning and scheduling vehicle routing is a crucial management problem. Despite numerous publications dealing with efficient scheduling methods for vehicle routing, very few addressed the inherent stochastic nature of travel times in this problem. In this paper, a vehicle routing problem with time windows and stochastic travel times due to potential traffic congestion is considered. The approach developed introduces mainly the traffic congestion component based on queueing theory. This is an innovative modeling scheme to capture the stochastic behavior of travel times. A case study is used both to illustrate the appropriateness of the approach as well as to show that time-independent solutions are often unrealistic within a congested traffic environment which is often the case on the european road networkstransportation; vehicle fleet; planning; scheduling; congested traffic

A dynamic approach to vehicle scheduling

This paper presents a dynamic approach to the vehicle scheduling problem. We discuss the potential benefit of our approach compared to the traditional one, where the vehicle scheduling problem is solved only once for a whole period and the travel times are assumed to be fixed. In our dynamic approach, we solve a sequence of optimization problems, where we take into account different scenarios for future travel times. Because in the multiple-depot case we cannot solve the problem exactly within reasonable computation time, we use a "cluster-reschedule" heuristic where we first assign trips to depots by solving the static problem and then solve dynamic single-depot problems. We use new mathematical formulations of these problems that allow a fast solution by standard optimization software. We report on the results of a computational study with real life data, in which we compare different variants of our approach and perform a sensitivity analysis with respect to deviations of the actual travel times from the estimated ones.vehicle scheduling;dynamic scheduling;public transport;stochastic programming;stochastic traveltimes

On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools