An approximate column generation for the vehicle routing problem with hard time windows and stochastic travel and service times

Abstract : The stochastic vehicle routing problem with hard time windows and stochastic travel and service times (SVRPTW) is a routing problem variant where travel and service times are modeled as random variables with known probability functions. In this study we model the problem as a combined stochastic problem with recourse and chance constrained problem, guaranteeing service levels for customers, vehicles return time to depot and for the solution. Since arrival times are also stochastic (with unknown probability functions), a lognormal approximation is used to check for feasibility and estimate the costs. A column generation using the lognormal approach is performed with state-of-the-art algorithms with newfangled dominance rules. The method is tested on modified Solomon instances where travel and service times are Lognormally and Gamma distributed respectively.