Scheduling of virtual manufacturing cells with outsourcing allowed

This paper presents a bi-objective mixed integer programming model for operations scheduling in virtual manufacturing cells where outsourcing is allowed, and set-up times are considered to be sequence dependent. Two objective functions of the model are the minimisation of the maximum completion time (or makespan) and the minimisation of the total cost of inter and intra-plant transportation. Two multi-objective solution algorithms are then developed to solve the proposed model. The first algorithm is an epsilon-constraint method which can find the exact set of efficient solutions for small-size problems. Since the investigated problem is non-polynomial (NP) hard, exact algorithms cannot be used for large-scale real-world cases and, therefore, a bi-objective genetic algorithm (GA) is developed as the second algorithm. A numerical example is given to evaluate the effectiveness of the proposed model and solution algorithms. The results reveal the superiority of the proposed model over the base models and demonstrate that in comparison with the epsilon-constraint method, the proposed GA can obtain efficient solutions in much less computational time.