Time-dependent Vehicle Routing Problem Research Articles

An iterated local search algorithm for the time-dependent vehicle routing problem with time windows

We generalize the standard vehicle routing problem with time windows by allowing both traveling times and traveling costs to be time-dependent functions. In our algorithm, we use a local search to determine routes of the vehicles. When we evaluate a neighborhood solution, we must compute an optimal time schedule for each route. We show that this subproblem can be efficiently solved by dynamic programming, which is incorporated in the local search algorithm. The neighborhood of our local search consists of slight modifications of the standard neighborhoods called 2- opt ∗, cross exchange and Or-opt. We propose an algorithm that evaluates solutions in these neighborhoods more efficiently than the ones computing the dynamic programming from scratch by utilizing the information from the past dynamic programming recursion used to evaluate the current solution. We further propose a filtering method that restricts the search space in the neighborhoods to avoid many solutions having no prospect of improvement. We then develop an iterated local search algorithm that incorporates all the above ingredients. Finally we report computational results of our iterated local search algorithm compared against existing methods, and confirm the effectiveness of the restriction of the neighborhoods and the benefits of the proposed generalization.

Ant colony optimization for real-world vehicle routing problems

Ant colony optimization (ACO) is a metaheuristic for combinatorial optimization problems. In this paper we report on its successful application to the vehicle routing problem (VRP). First, we introduce the VRP and some of its variants, such as the VRP with time windows, the time dependent VRP, the VRP with pickup and delivery, and the dynamic VRP. These variants have been formulated in order to bring the VRP closer to the kind of situations encountered in the real-world. Then, we introduce the basic principles of ant colony optimization, and we briefly present its application to the solution of the VRP and of its variants. Last, we discuss the applications of ACO to a number of real-world problems: a VRP with time windows for a major supermarket chain in Switzerland; a VRP with pickup and delivery for a leading distribution company in Italy; a time dependent VRP for freight distribution in the city of Padua, Italy, where the travel times depend on the time of the day; and an on-line VRP in the city of Lugano, Switzerland, where customers’ orders arrive during the delivery process.

A map-based decision-support system for delivery planning

This paper describes a project to develop a map-based decision-support system for delivery planning in Hong Kong. The system consists of several components, including a map-based interface, bilingual database storing the information of maps and deliveries and some decision support tools for planning the routes of the delivery vehicles in a feasible and cost-effective way. In this paper, we describe (1) the features of the system, (2) the underlying network representation used and (3) two decision-support models, a Time-varying Constrained Shortest Path (TCSP) problem and a Time-dependent Vehicle Routing Problem with Time Windows (TVRPTW) and their corresponding algorithms which have been incorporated into the system. We hope this paper will provide some insights on the techniques and challenges of developing such delivery planning systems.

The real-time time-dependent vehicle routing problem

In this article, the real-time time-dependent vehicle routing problem with time windows is formulated as a series of mixed integer programming models that account for real-time and time-dependent travel times, as well as for real-time demands in a unified framework. In addition to vehicles routes, departure times are treated as decision variables, with delayed departure permitted at each node serviced. A heuristic comprising route construction and route improvement is proposed within which critical nodes are defined to delineate the scope of the remaining problem along the time rolling horizon and an efficient technique for choosing optimal departure times is developed. Fifty-six numerical problems and a real application are provided for demonstration.

Genetic Algorithm for the Time-Dependent Vehicle Routing Problem

A mathematical model is formulated for the time-dependent vehicle routing problem (TDVRP) and a genetic algorithm (GA) is proposed for solving it. Formulation of the problem considers multiple vehicles with different capacities, pick-up or delivery demands with soft time windows, real-time service requests, and real-time variations in travel times between demand nodes. The objective is to minimize the total cost, which consists of routing cost, fixed cost for using the vehicles, and customer inconvenience costs. A mixed-integer linear programming formulation of the TDVRP is presented. Like other combinatorial problems, to solve the TDVRP exactly, a significant amount of processing time is required. A GA is proposed to solve the problem. The proposed GA was tested on the test problems, and GA results were compared with the exact solutions for small test problems. GA results were also compared with the lower bounds obtained for the solution of the larger problems. In the case of small problems, only 2 of 33 cases have gaps between the GA solutions and the exact solutions, and the maximum gap is less than 5 percent. For larger problems, the maximum gaps between GA solutions and lower bound solutions are less than 7 percent.

Plus court chemin avec dépendance horaire : résolution et application aux problèmes de tournées

We solve the time dependent shortest path problem. This problem consists in finding a minimum weight path through a network with respect to time windows constraints, and time varying costs and travelling times. Two issues of this problem are studied: without and with a knapsack type constraint. We show an important application of this problem for the design of an optimal column generation based algorithm for a time dependent vehicle routing problem.

Time Dependent Vehicle Routing Problems: Formulations, Properties and Heuristic Algorithms

The time dependent vehicle routing problem (TDVRP) is defined as follows. A vehicle fleet of fixed capacities serves customers of fixed demands from a central depot. Customers are assigned to vehicles and the vehicles routed so that the total time of the routes is minimized. The travel time between two customers or between a customer and the depot depends on the distance between the points and time of day. Time windows for serving the customers may also be present. The time dependent traveling salesman problem (TDTSP) is a special case of the TDVRP in which only one vehicle of infinite capacity is available. Mixed integer linear programming formulations of the TDVRP and the TDTSP are presented that treat the travel time functions as step functions. The characteristics and properties of the TDVRP preclude modification of most of the algorithms that have been developed for the vehicle routing problem. Several simple heuristic algorithms are given for the TDTSP and TDVRP without time windows based on the nearest-neighbor heuristic. A mathematical-programming-based heuristic for the TDTSP without time windows using cutting planes is also briefly discussed. Test results on small, randomly generated problems are reported.