Column Generation-based Heuristics for Vehicle Routing Problem with Soft Time Windows

Abstract

This paper presents a column generation-based heuristics for the Vehicle Routing and scheduling Problem with Soft Time Windows (VRPSTW). The subproblem has been solved using a modified stochastic push forward insertion heuristics that incorporates the early and late arrival penalties. The useful dual information (shadow prices) from the column generation master problem guides the heuristic subproblem to provide negative reduced cost columns of sufficient quality. The performance of column generation-based heuristics is evaluated comparing its results with a genetic algorithms heuristics whose initial population is based on the same insertion heuristics as used in the column generation subproblem. The results showed that the column generation-based heuristics produced better quality solutions, both in terms of cost and environment (CO2), in most cases in only quarter of the computation time, on average.