Designing a Mathematical Model of a Collaborative Production System Based on Make to Order under Uncertainty

We present a mathematical model for the problem of collaborative production system based on order with fairness to allocate production loads. The main objectives of the model are to minimize total production costs and maximize the use of resources in order to distribute production loads fairly in conditions of uncertainty. Fuzzy programming was used to control uncertain parameters. The results show that, with increasing the uncertainty rates, production system costs have increased. Since the capacity of factories is constant, with the increase in demand, the amount of production has increased and the maximum use of resources of each factory has also increased. Also, contrary to the trend of system cost changes, with the increase in the number of factories, the maximum use of available resources has decreased. To solve large sample problems, the NSGA II algorithm with a suitable chromosome is used to search the problem space. Numerical results of solving 15 sample problems show the high efficiency of NSGA II algorithm in solving the problem of cooperative production system in a very short time.