Polynomial-Time Approximation Scheme for the Capacitated Vehicle Routing Problem with Time Windows

The capacitated vehicle routing problem with time windows (CVRPTW) is a well-known NP-hard combinatorial optimization problem. We present a further development of the approach first proposed by M. Haimovich and A. H. G. Rinnooy Kan and propose an algorithm that, for an arbitrary ε > 0, finds a (1 + ε )-approximate solution for the Euclidean CVRPTW in , where q is an upper bound for the capacities of the vehicles, p is the number of time windows, and TIME(TSP, ρ , n ) is the complexity of finding a ρ -approximation solution of an auxiliary instance of the Euclidean TSP. Thus, the algorithm is a polynomial-time approximation scheme for the CVRPTW with p 3 q 4 = O (log n ) and an efficient polynomial-time approximation scheme for arbitrary fixed values of p and q .