A Column Generation Approach for the Periodic Vehicle Routing Problem with Time Windows1

We present a column generation approach for obtaining strong lower bounds to the periodic vehicle routing problem with time windows (PVRPTW) where customers must be served several times during a planning period. For this a set-covering model is introduced whose linear programming relaxation is solved. The pricing subproblem, responsible for generating new columns, is an elementary shortest path problem with resource constraints. The latter is solved by a label correcting dynamic programming algorithm for which we introduce appropriate label resources, extension functions, and dominance rules. Different settings for this algorithm are suggested and applied in combination to tune its behavior. We further propose a greedy randomized adaptive search procedure (GRASP) to solve the pricing subproblem. Experimental results on test instances differing in size, time windows and period length indicate strong lower bounds for many instances and the advantage of applying the metaheuristic in combination with the dynamic programming algorithm to save computation time on larger instances.