Considerations on Set Partitioning and Set Covering Models for Solving the 2E-CVRP in City Logistics

This chapter proposes a position viewpoint, discussion, and analysis of various aspects of solving 2E-CVRP problems via exact methods, more precisely the use of set partitioning formulations (and consequently set covering ones), as well as column generation to produce bounds and feed branch-and-prize approaches. After an overview of the main exact methods used to solve 2E-CVRP approaches, the author defines the main notions and variables to model the problem via set covering and set partitioning models. Then the paper presents two methods to generate bounds via column generation: the first is a decomposition approach in which first-echelon and second-echelon routes are generated separately, without any relation, and the second generate sets of linked first-echelon and second-echelon routes. The main implications and considerations of those methods are addressed. Finally, main issues regarding the suitability of exact methods for vehicle routing in city logistics are presented.