Matheuristics with performance guarantee for the unsplit and split delivery capacitated vehicle routing problem

For the classical unsplit and split delivery capacitated vehicle routing problems, we carry out a worst-case analysis for classes of matheuristics and compare their performance on average, on a large set of benchmark instances. The matheuristics are based on the optimal solution of the bin packing problem, the capacitated concentrator location problem, and the unsplit capacitated vehicle routing problem (CVRP). These matheuristics are compared with the classical algorithms having known finite worst-case performance bound. For the unsplit CVRP, we provide a matheuristic having worst-case performance bound equal to the one of the classical algorithms, but with an average percent cost increase with respect to the optimal cost equal to 1.13%. For the split delivery case, we provide a matheuristic having worst-case performance bound 2 and an average percent cost increase with respect to the best-known cost equal to 0.64%. Moreover, this matheuristic is able to find 22 best-known solutions, 20 of which are new.