General VNS for asymmetric vehicle routing problem with time and capacity constraints

We consider a real-life transportation problem from a hypermarket company in Serbia that consists of delivering online ordered and possibly perishable goods from a single depot to multiple customers. It can be modeled as an asymmetric vehicle routing problem that requires visiting and serving all customers using a limited number of homogeneous vehicles and taking into account time and capacity constraints. The objective function to be minimized is the total distance traveled. We provide a mixed-integer programming (MIP) formulation of the problem and develop several Local Search based metaheuristic methods exploring combinatorial formulation of the considered problem: Multistart Local Search (MLS), Greedy Randomized Adaptive Search Procedure (GRASP), and several variants of General Variable Neighborhood Search (GVNS) methods. All methods are compared on real-life instances provided by the hypermarket company and benchmark instances from the relevant literature. The obtained results show the superiority of GVNS-based methods with respect to both solution quality and running time, confirming that systematic search procedures have more success when dealing with hard optimization problems.