This paper will introduce the Monte Carlo-based heuristic with seven local searches (LSs) which are carefully designed for distributed production network scheduling. Distributed production network consists of the number of different individual factories that joins together to form a network, in which these factories can operate more economically than operating individually and each individual factory usually focuses on self-benefits. Some realistic features such as heterogeny of factories and the transportation among factories are incorporated in our problem definition. However, in such network, each individual factory usually focuses on self-benefits and it plans to optimize its own profit. In this problem, among F exit factories in the network, F′ factories are interested in the total earliness costs and the remaining factories (F″= F − F′) are interested in the total tardiness cost. Cost minimization is achieved through the minimization of earliness in F′factories, tardiness in F″ factories and the total costs of operation time of all jobs. This algorithm initializes with best known non-cooperative local scheduling and then the LSs search simultaneously through the same solution space, starting from the same current solution. Upon receiving the solutions from the LSs, the new solution will be accepted based on the Monte Carlo acceptance criterion. This criterion always accepts an improved solution and, in order to escape local minima, accept the worse solutions with a certain probability, which this probability decreases with deteriorating solutions. After solving the mixed integer linear programming by the CPLEX solver in the small-size instances, the results obtained by heuristic are compared with two genetic algorithms in the large-size instances. The results of the scheduling before cooperation in production network were also considered in the experiments. 
Minimizing cost-related objective in synchronous scheduling of parallel factories in the virtual production network