Vehicle routing problems with soft time windows: an optimization based approach

The classical vehicle routing problem involves to design a set of routes for a fleet of vehicles based at one central depot that is required to service a number of geographically dispersed customers, while minimizing the total travel distance or the total distribution cost. Each route originates and terminates at the central depot and customers' demand are known. In many practical distribution problems, a time window is associated to each customer, defining a time interval in which the customer should be supplied. This is the vehicle routing problem with time windows. This works investigates the use of Goal Programming to modeling a vehicle routing problem with soft delivery time window constraints. In this problem vehicles are allowed to service customers before and after the earliest and latest time windows bounds. This relaxation comes at the expense of appropriate penalties that reflect the effect that time windows violations have on the customers' satisfaction.