Solving Large Distribution Problems in Supply Chain Networks by a Column Generation Approach

Vehicle routing problems (VRP) are receiving a growing attention in process systems engineering due to its close relationship with supply chain issues. Its aim is to discover the best routes/schedules for a vehicles fleet fulfilling a number of transportation requests at “minimum cost”. Pick-up and delivery problems (PDP) are a class of VRP on which each request defines the shipping of a given load from a specified pickup site to a given customer. In order to account for a wider range of logistics problems, the so-called supply-chain management VRP (SCM-VRP) problem has been defined as a three-tier network of interconnected factories, warehouses and customers. In this problem, multiple products are to be delivered from some supply-sites to a number of customers through a routes-network in order to meet a set of given demands. The vehicle routes must satisfy capacity and timing constraints while minimizing an objective function stating the specified transportation cost. Pickup sites for each demand are decision variables rather than problem specifications. The SCM-VRP had been modeled as an MILP problem and the resolution of this formulation via a standard branch-and-cut software can provide optimal solutions to moderate size instances. In order to efficiently address larger problems, a decomposition method based on a column generation procedure is introduced in this work. In contrast to traditional columns generation approaches lying on dynamic-programming-procedures as route generators, an MILP formulation is here proposed to create the set of feasible routes and schedules at the slave level of the method. Furthermore, a branch-and-price method based on node-to-routes assignment decisions is constructed to better exploit the MILP route-generator. Finally, several benchmark examples were presented and satisfactorily solved.