Multi-echelon distribution systems are one of the mostapplicable systems in traortation planning, logistics, and supply chainmanagement. These systems are used for urban planning, with a specialapplication in traffic planning. A two-echelon distribution system as the mostuseful multi-echelon distribution system, consists of one or more depot wherethe set of customers’ products delivery activity is performed by consolidatingitems in set of satellites . Inthis research, a Two-echelon Vehicle Routing Problem (2E-VRP) is consideredwhere the routing problem in the first echelon is assigned to deliver itemsfrom depot to satellites, and the routing problem in second echelon isconstructed based on delivering items from satellites to set of customers. Inaddition, route planning needs to consider practical assumptions such astraffic constraints to provide on-time services for customers in distributionnetwork. The constraints have noticeable effect on traortation planning. So,neglecting them causes to inappropriate estimation of total costs and totalservice times. Also, in most of the time, customers ask for their demands inset of periods (days) in planning horizon. In other words, each customer hasone or more visit combination which includes one or more periods (days). Once acustomer’s visit combination is selected, the customer must be satisfied inexisiting day(s) in the visit combination. In this approach, routeplanning must be performed in eachperiod which is affected by other periods, integrally. As a result, in thisresearch, we aim to model a Two-Echelon Time-Dependent and Periodic VRP(2E-TDPVRP) that consists of two components: a set of customers whose demandshave to be satisfied during the several periods and traffic constraints whichinfluence on-time product delivery vehicle services for customers. The problemis modeled by a mixed-integer programming approach. Due to NP-hardness of theproblem, we propose a new Hybrid algorithm to solve the problem. We compare theperformance of our algorithm with the results of CPLEX solver in the smallscale problems. For large scale problems, we develop Variable NeighborhoodSearch algorithm as basis of the Hybrid algorithm. Then, we compare ourproposed hybrid algorithm with VNS. Computational results denote theoutperformance of the proposed Hybrid algorithm.
