The stratified p-center problem

This work presents an extension of the p-center problem. In this new model, called Stratified p-Center Problem (SpCP), the demand is concentrated in a set of sites and the population of these sites is divided into different strata depending on the kind of service that they require. The aim is to locate p centers to cover the different types of services demanded minimizing the weighted average of the largest distances associated with each of the different strata. In addition, it is considered that more than one stratum can be present at each site. Different formulations, valid inequalities and preprocessings are developed and compared for this problem. An application of this model is presented in order to implement a heuristic approach based on the Sample Average Approximation method (SAA) for solving the probabilistic p-center problem in an efficient way.Comment: 32 pages, 1 pictur

Addressing the Location Problem of a Perishables Redistribution Center in the Middle of Europe

This work aims to contribute to the debate on practical utilization of different location models for consolidation, redistribution, and repackaging centers in a supply chain to optimize shipments, thereby reducing food loss and waste, within the framework of quality of customer service improvement. The scenario in question is the creation of a redistribution center for highly perishable products (fruits and vegetables) from southeast Spain—the leading European supplier—for customers throughout Europe. It is estimated that 10% of exports (more than 530,000 metric tons) from this area are returned by customers due to minor defects. These products cannot be reused and are therefore wasted. Regarding the methodology, comparisons were made between the p-median, gravity p-median, and p-center models. Scenarios of change in demand and randomness in distances were also tested. In addition, the modelling used included the cost and time within a multicriteria optimization framework to assess the possibility of a transport mode change. It was observed, for example, that the gravity p-median model proved useful for perishable products and the logistics strategy chosen. Furthermore, the p-median model displayed strong robustness against long-term changes in demand and random distances. In general, it was demonstrated that this strategy would successfully reduce the response time and distance of shipment from the distribution center to the customers and thereby improve sustainability of the service, reducing the waste related to direct shipments. Furthermore, this research also demonstrated the difficulty of using intermodality in this context, mainly due to transit time, which would undoubtedly increase the waste generate

Formulations and valid inequalities for the capacitated dispersion problem

This work focuses on the capacitated dispersion problem for which we study several mathematical formulations in different spaces using variables associated with nodes, edges, and costs. The relationships among the presented formulations are investigated by comparing the projections of the feasible sets of the LP relaxations onto the subspace of natural variables. These formulations are then strengthened with families of valid inequalities and variable-fixing procedures. The separation problems associated with the valid inequalities that are exponential in number are shown to be polynomially solvable by reducing them to longest path problems in acyclic graphs. The dual bounds obtained from stronger but larger formulations are used to improve the strength of weaker but smaller formulations. Several sets of computational experiments are conducted to illustrate the usefulness of the findings, as well as the aptness of the formulations for different types of instances

The stratified p-center problem

This work presents an extension of the discrete p-center problem. In this new model, called Stratified p-Center Problem (SpCP), the demand is concentrated in a set of sites and the population of these sites is divided into different strata depending on the kind of service that they require. The aim is to locate p centers to cover the different types of services demanded minimizing the weighted average of the largest distances associated with each of the different strata. In addition, it is considered that more than one stratum can be present at each site. Different formulations, valid inequalities and preprocessings are developed and compared for this problem. An application of this model is presented in order to implement a heuristic approach based on the Sample Average Approximation method (SAA) for solving the probabilistic p-center problem in an efficient way.Peer ReviewedPostprint (author's final draft

The stratified p-center problem

This work presents an extension of the discrete p-center problem. In this new model, called Stratified p-Center Problem (SpCP), the demand is concentrated in a set of sites and the population of these sites is divided into different strata depending on the kind of service that they require. The aim is to locate p centers to cover the different types of services demanded minimizing the weighted average of the largest distances associated with each of the different strata. In addition, it is considered that more than one stratum can be present at each site. Different formulations, valid inequalities and preprocessings are developed and compared for this problem. An application of this model is presented in order to implement a heuristic approach based on the Sample Average Approximation method (SAA) for solving the probabilistic p-center problem in an efficient way.Peer Reviewe