Liberatore, F., Righini, G., and Salani, M. (2011)

A column generation algorithm for the vehicle routing problem with soft time windows, 4OR: A Quarterly Journal of Operations Research 9(1):49-82.

The Vehicle Routing Problem with Time Windows consists of computing a minimum cost set of routes for a fleet of vehicles of limited capacity visiting a given set of customers with known demand, with the additional constraint that each customer must be visited in a specified time window. We consider the case in which time window constraints are relaxed into "soft" constraints, that is penalty terms are added to the solution cost whenever a vehicle serves a customer outside of his time window. We present a branch-and-price algorithm which is the first exact optimization algorithm for this problem

doi:10.1007/s10288-010-0136-6 (click here for the full paper)