Algorithms for the bicriterion vehicle routing problem with time windows

Abstract

Transportation is crucial for delivery of goods and services. The transportation costs constitute a significant part of the final product costs. Moreover, in many parts of the world transportation is the biggest source of greenhouse gases. Therefore, careful planning of transportation is of both economic and ecological advantage. The Vehicle Routing Problem with Time Windows (VRPTW) is a combinatorial optimization problem. It deals with route planning and the distribution of goods from a depot to geographically dispersed customers by a fleet of vehicles with constrained capacities. The customers´ demands are known and each customer has a time window in which it has to be supplied. The problem is to organize the routes of vehicles optimally, i.e. so that all the operational constraints are satisfied and the total costs, consisting of the number of used vehicles and the overall covered distance, are minimized. In the thesis, the VRP with soft time windows was examined. The problem was formulates as a bicriterion minimization problem and targets at the simultaneous minimization of the penalties and the total costs. The methods were implemented with MATLAB and tested on Solomon´s 56 benchmark problems. The results show that improvements mainly depend on the geometry of the customers´ positions.