7. Conclusion
This paper addresses flexible multi-cells part scheduling (MCPS) problem. It focuses on how to cooperate between different cells with the objective of minimizing the make-span. An INLP mathematical model is proposed to describe the M-CPS problem. An auction-based approach containing an auction based model and an auction-bid approach is designed to solve it. In an auction, it contains call for auction, bid construction, modify bids and winner announcement. A reference matrix is also applied in the auction to guarantee parts to finish as early as possible. To check the efficiency of the proposed auction-based approach, a series of test problem were generated. The solution obtained by the proposed auctionbased approach was compared to the optimal values obtained by Lingo 11.0 based on the INLP mathematical model and solutions obtained by three kinds of soft computing methods on test problems. These tests demonstrated that the proposed auction-based approach is a good method with high effectiveness and stability for solving this type of scheduling problem, especially when the scale of the problem is large and computation time is short. In practical production, the transportation source is time-restricted usually, such as when it is a robot or vehicles. In future study, the transportation source is sufficient can be tightened as limited according to the proposed problem in our paper, which makes the scenario more close to practical production.
