Separable cross decomposition to solve the assign-routing problem

Abstract

THE INVENTORY-ROUTING PROBLEM EMERGES ON A LOGISTICAL CON TEXT, THAT IS PRESENTED INTO THE COMPANIES AND THAT IT SEEKS TO SATISFY THE DEMANDS OF A GROUP OF CLIENTS DISTRIBUTED GEOGRAPHICALLY, USING A FLOTILLA OF VEHICLES OF LIMITED CAPACITY, WHICH ARE IN A CENTRAL WARE HOUSE, AT THE SMALLEST POSSIBLE COST. THE IRP IS A NP-HARD PROBLEM THAT IS USUALLY GREAT SIZE IN REAL APPLICATIONS. FOR ITS SOLUTION WAS DE SIGNED AN STRATEGY THAT USES OF COMBINED FORM, THE CROSSED DE COMPOSITION AND THE SEPARABLE LAGRANGE AN RELAXATION IN ORDER TO SOLVE THE AS SIGN DISTRIBUTION PHASE, WITH WHAT IT IS OBTAINED A PING-PONG TYPE SCHEME BETWEEN TWO SUB PROBLEMS, WHICH ARE FROM TRANS PORT TYPE, WITH WHICH IT IS OBTAINED A VERY EFFICIENT ALGORITHM OF ORDER O(N3 ) AND EASY TO IMPLEMENT FOR THE COMPLETE PROBLEM.