### Approximative solutions to the bicriterion Vehicle Routing Problem with Time Windows

Abstract

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 time windows are assumed
to be soft, that means, violations of the time windows are allowed, but associated with penalties. The problem is to organize the
vehicle routes optimally, i.e. to minimize the total costs, consisting of the number of used vehicles and the total distance, and
the penalties simultaneously. Thus, the problem is formulated as a bicriterion minimization problem and heuristic methods are used
to calculate approximations of the Pareto optimal solutions. Experimental results show that in certain cases the allowance of
penalties leads to significant savings of the total costs.