A joint scheduling of production and distribution operations in a ow shop manufacturing system

In traditional scheduling problems and many real-world applications, the production operations are scheduled regardless of distribution decisions. Indeed, the completion time of a job in such problems is dened traditionally as the time when the production sequences of a job are nished. However, in many practical environments, completed orders are delivered to customers immediately after production stages without any further inventory storage. Therefore, in this paper, we investigate an integrated scheduling model of production and distribution problems simultaneously. It is assumed that products proceed through a permutation ow shop scheduling manufacturing system and are delivered to customers via available vehicles. The objective of our integrated model is to minimize the Maximum Returning Time (MRT), which is the time it takes for the last vehicle to deliver the last order to a relevant customer and return to production center. The problem is formulated mathematically, and then an Improved Imperialist Competitive Algorithm (I-ICA) is proposed for solving it. Furthermore, a sucient number of test problems are generated for computational study. Various parameters of the algorithm are analyzed to calibrate the algorithm by means of the Taguchi method. At the end, the eectiveness of the proposed model and suggested algorithm is evaluated through a computational study where the obtained results show the appropriate performance of the integrated model and solving approach in comparison to those of the other algorithms