The Two-Echelon Location Routing Problems: State of the Art, Models and Algorithms

The Two-Echelon Routing Problem constitutes a class of combinatorial optimization problems with applications in many different fields such as city logistic planning, intermodal transportation, postal and parcel delivery distribution systems and so on. This thesis contains: a survey of the main contributions related to the two-echelon routing, focusing on the Two-Echelon Location Routing Problem, on the Two-Echelon Vehicle Problem and on the Truck and Trailer Routing Problem; an analysis of a particular version of the Two-Echelon Location Routing Problem with single source, referred as Single Vehicle Two-Echelon Location Routing Problem, with two mathematical formulations and a heuristic algorithm; some computational experiments aiming at test the effectiveness of the formulations and the heuristic algorithm. The thesis is divided in three parts: • a literature review of the Two-Echelon Location Routing Problem, of the Two-Echelon Vehicle Routing Problem and of the Truck and Trailer Routing Problem. The Two-Echelon Location Routing Problem refers to a class of problem directly derived from the well-known Location Routing Problem in which two sets of facilities must be located and two levels of routing have to be considered. The Two-Echelon Vehicle Routing Problem is derived from the Vehicle Routing Problem. In this class of problems the distribution of freight is managed through a set of satellites, where operation of consolidation, and/or transhipment and/or storage are performed. The Truck and Trailer Routing Problem models a distribution system in which a vehicle fleet, composed by truck units and trailer units, is used to serve the demand of a set of customers, some of which are accessible only by a truck without trailer; • the description of the Single Vehicle Two-Echelon Location Routing Problem with emphasis on its structure and its components, plus the introduction of two integer programming formulations to determine the optimal location and the optimal number of a set of capacitated facilities, the assignment of customers to these facilities and the related routes. Four sets of instances are adapted from the literature and the results of proposed formulation are reported, comparing their performances in terms of solution quality and computation times. • the introduction of a heuristic algorithm to solve the problem. Five variants of the algorithm are developed, differing from each other for the assignment procedures of the customers to the satellites. The results provided by such algorithm are compared with the optimal solutions, or in some cases with the best lower bounds provided by CPLEX solving the two integer models.