Algebraic structural analysis of a vehicle routing problem of heterogeneous trucks. Identification of the properties allowing an exact approach.

Abstract

Although integer linear programming problems are typically difficult to solve, there exist some easier problems, where the linear programming relaxation is integer. This thesis sheds light on a drayage problem which is supposed to have this nice feature, after extensive computational experiments. This thesis aims to provide a theoretical understanding of these results by the analysis of the algebraic structures of the mathematical formulation. Three reformulations are presented to prove if the constraint matrix is totally unimodular. We will show which experimental conditions are necessary and sufficient (or only sufficient or only necessary) for total unimodularity