conclusion
this study introduces a new VRP variant called the multiple trip vehicle routing with backhaul (MT-VRPB).
An ILPMT-VRPB data set is generate.
the formulation is tested using CPLEX, and found optimal solution for small and medium set is data instances.
To solve the larger instances of the problem a two-level VNS algorithm is developed that uses skeletons of the classical VNS and VDN methodolgies.
A number of neigbourhoods and local searches are employed in a way to achieve diversification at the outer level (basic VNS) of the algorithm and intensification