Modeling and solving of bi-objective multi-product production routing problem with outsourcing and accident risk in transportation

Organizations with integrated production and routing programs sometimes encounter traffic when they use vehicles for distribution. So there are risks such as an accident that could result in damage, loss of product quality, unavoidable delivery delays, or even irreversible impacts on costs and service time. Therefore, by taking account the risk of accident into the production routing problem, the model becomes closer to reality. In this study, a production routing problem with the purpose of reducing costs and the risk of accident in the transportation with outsourcing, multi-product and multi-period, is considered in which the production routing problem combines with the lot sizing and vehicle routing problem according the supplier's inventory management system. Since this is an NP-hard problem, after modeling the problem, to solve it, a Non-dominated Sorting Genetic Algorithm II (NSGA II) has been used. To examine the efficiency of the algorithm, the solutions of ε-constraint method in GAMS obtained in small-size instances have been compared with NSGA II. Finally, to validate the proposed algorithm and evaluate its performance in large-size instances, the results of NSGA II have been compared with multi-objective genetic algorithm using several indices. The obtained results showed that the NSGA II algorithm had better performance.