conclusion
this study introduces aa 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 sixe 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