This paper studies the multi-factory production (MFP) network scheduling problem where a number of different individual factories join together to form a MFP network, in which these factories can operate more economically than operating individually. However, in such network which known as virtual production network with self-interested factories with transportation times, each individual factory usually focuses on self-benefits and does not care much about the others within the network. We first described the realistic features which incorporate in problem definition. Then two different variants of the problem are considered. In the first case, we propose approximation algorithms with the best achievable theoretical guarantee in three cases: (i) all factories are interested in the makespan, (ii) all factories are interested in the sum of completion times, and (iii) the case in which among all factories, some factories are interested in the sum of completion times and the others are interested in the makespan. Furthermore, with considering the transpiration, we model the problem as a mixed integer linear programming to minimize the makespan and total completion time and solve it by CPLEX solver to obtain Pareto solutions by applying modified ϵ -constraint approach. Experiments show that this procedure is capable of producing good results to approximate the efficient set.
