Modelling and scheduling integration of distributed production and distribution problems via black widow optimization

Production and distribution are two important sectors in a supply chain and their managements become an essential issue in industrial fields. The integrated operation of production and distribution stages are regarded as an effective approach. This work proposes an integrated production and distribution optimization problem, where jobs are processed in a distributed manufacturing system with multiple flow shops, and then they are delivered to customers locating in geographically-dispersed points. To mathematically describe this problem, a mixed integer programming model is formulated to minimize maximum completion time. In order to optimally solve the proposed problem, an enhanced black widow optimization algorithm is developed to deal with the studied problem. In this proposed approach, the solution representation, population initialization, procreation, cannibalism, and mutation along with a simulated annealing approach are specially designed. Then, a design of experiment approach is employed to analyze the influence of sensitive parameters on the proposed approach. Performance and efficiency of the designed method are validated through conducting extensive experiments on a set of benchmark test problems. Besides, comparisons with some well-known optimizers in the literature have been conducted to show the superiority of the proposed method.