The vehicle routing problem

Since the late 70s, much research activity has taken place on the class of dynamic vehicle routing problems DVRP, with the time period after year 2000 witnessing a real explosion in related papers. Our paper sheds more light into work in this area over more than 3 decades by developing a taxonomy of DVRP papers according to 11 criteria. These are 1 type of problem, 2 logistical context, 3 transportation mode, 4 objective function, 5 fleet size, 6 time constraints, 7 vehicle capacity constraints, 8 the ability to reject customers, 9 the nature of the dynamic element, 10 the nature of the stochasticity if any, and 11 the solution method. We comment on technological vis-i-vis methodological advances for this class of problems and suggest directions for further research. The latter include alternative objective functions, vehicle speed as decision variable, more explicit linkages of methodology to technological advances and analysis of worst case or average case performance of heuristics. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 671, 3-31 2016

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Dynamic vehicle routing problems: Three decades and counting

Ingredients of Locational Analysis (J. Krarup & P. Pruzan). The p-Median Problem and Generalizations (P. Mirchandani). The Uncapacitated Facility Location Problem (G. Cornuejols, et al.). Multiperiod Capacitated Location Models (S. Jacobsen). Decomposition Methods for Facility Location Problems (T. Magnanti & R. Wong). Covering Problems (A. Kolen & A. Tamir). p-Center Problems (G. Handler). Duality: Covering and Constraining p-Center Problems on Trees (B. Tansel, et al.). Locations with Spatial Interactions: The Quadratic Assignment Problem (R. Burkard). Locations with Spatial Interactions: Competitive Locations and Games (S. Hakimi). Equilibrium Analysis for Voting and Competitive Location Problems (P. Hansen, et al.). Location of Mobile Units in a Stochastic Environment (O. Berman, et al.). Index.

https://link.springer.com/content/pdf/10.1057%2Fjors.1991.208.pdf

Discrete location theory

A literature review on the vehicle routing problem with multiple depots

Given rising energy prices and environmental concerns, train energy-efficient operation techniques are paid more attention as one of the effective methods to reduce operation costs and energy consumption. Generally speaking, the energy-efficient operation technique includes two levels, which optimize the timetable and the speed profiles among successive stations, respectively. To achieve better performance, this paper proposes to optimize the integrated timetable, which includes both the timetable and the speed profiles. First, we provide an analytical formulation to calculate the optimal speed profile with fixed trip time for each section. Second, we design a numerical algorithm to distribute the total trip time among different sections and prove the optimality of the distribution algorithm. Furthermore, we extend the algorithm to generate the integrated timetable. Finally, we present some numerical examples based on the operation data from the Beijing Yizhuang subway line. The simulation results show that energy reduction for the entire route is 14.5%. The computation time for finding the optimal solution is 0.15 s, which implies that the algorithm is fast enough to be used in the automatic train operation (ATO) system for real-time control.

A Subway Train Timetable Optimization Approach Based on Energy-Efficient Operation Strategy

This paper develops a multi-objective optimization model for the passenger train-scheduling problem on a railroad network which includes single and multiple tracks, as well as multiple platforms with different train capacities. In this study, lowering the fuel consumption cost is the measure of satisfaction of the railway company and shortening the total passenger-time is being regarded as the passenger satisfaction criterion. The solution of the problem consists of two steps. First the Pareto frontier is determined using the e-constraint method, and second, based on the obtained Pareto frontier detailed multi-objective optimization is performed using the distance-based method with three types of distances. Numerical examples are given to illustrate the model and solution methodology.

A multi-objective train scheduling model and solution

This paper presents a new model and solution for multi-objective vehicle routing problem with time windows (VRPTW) using goal programming and genetic algorithm that in which decision maker specifies optimistic aspiration levels to the objectives and deviations from those aspirations are minimized. VRPTW involves the routing of a set of vehicles with limited capacity from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. This paper uses a direct interpretation of the VRPTW as a multi-objective problem where both the total required fleet size and total traveling distance are minimized while capacity and time windows constraints are secured. The present work aims at using a goal programming approach for the formulation of the problem and an adapted efficient genetic algorithm to solve it. In the genetic algorithm various heuristics incorporate local exploitation in the evolutionary search and the concept of Pareto optimality for the multi-objective optimization. Moreover part of initial population is initialized randomly and part is initialized using Push Forward Insertion Heuristic and @l-interchange mechanism. The algorithm is applied to solve the benchmark Solomon's 56 VRPTW 100-customer instances. Results show that the suggested approach is quiet effective, as it provides solutions that are competitive with the best known in the literature.

Multi-objective vehicle routing problem with time windows using goal programming and genetic algorithm

In this paper, a multi-objective dynamic vehicle routing problem with fuzzy time windows (DVRPFTW) is presented. In this problem, unlike most of the work where all the data are known in advance, a set of real time requests arrives randomly over time and the dispatcher does not have any deterministic or probabilistic information on the location and size of them until they arrive. Moreover, this model involves routing vehicles according to customer-specific time windows, which are highly relevant to the customers' satisfaction level. This preference information of customers can be represented as a convex fuzzy number with respect to the satisfaction for a service time. This paper uses a direct interpretation of the DVRPFTW as a multi-objective problem where the total required fleet size, overall total traveling distance and waiting time imposed on vehicles are minimized and the overall customers' preferences for service is maximized. A solving strategy based on the genetic algorithm (GA) and three basic modules are proposed, in which the state of the system including information of vehicles and customers is checked in a management module each time. The strategy module tries to organize the information reported by the management module and construct an efficient structure for solving in the subsequent module. The performance of the proposed approach is evaluated in different steps on various test problems generalized from a set of static instances in the literature. In the first step, the performance of the proposed approach is checked in static conditions and then the other assumptions and developments are added gradually and changes are examined. The computational experiments on data sets illustrate the efficiency and effectiveness of the proposed approach.

A multi-objective dynamic vehicle routing problem with fuzzy time windows: Model, solution and application

Multi-objective shortest path problem (MOSP) is an extension of a traditional single objective shortest path problem that seeks for the efficient paths satisfying several conflicting objectives between two nodes of a network. MOSP is one of the most important problems in network optimization with wide applications in telecommunication industries, transportation and project management. This research presents an algorithm based on multi-objective ant colony optimization (ACO) to solve the bi-objective shortest path problem. To analyze the efficiency of the algorithm and check for the quality of solutions, experimental analyses are conducted. Two sets of small and large sized problems that generated randomly are solved. Results on the set problems are compared with those of label correcting solutions that is the most known efficient algorithm for solving MOSP. To compare the Pareto optimal frontiers produced by the suggested ACO algorithm and the label correcting algorithm, some performance measures are employed that consider and compare the distance, uniformity distribution and extension of the Pareto frontiers. The results on the set of instance problems show that the suggested algorithm produces good quality non-dominated solutions and time saving in computation of large-scale bi-objective shortest path problems.

Keivan Ghoseiri

Papers

A multi-objective train scheduling model and solution

Multi-objective vehicle routing problem with time windows using goal programming and genetic algorithm

A multi-objective dynamic vehicle routing problem with fuzzy time windows: Model, solution and application

An ant colony optimization algorithm for the bi-objective shortest path problem

A simulated annealing approach for the multi-periodic rail-car fleet sizing problem