OPTIMIZED FUZZY SCHEDULING OF MANUFACTURING SYSTEMS

Transcription

1 OPTIMIZED FUZZY SCHEDULING OF MANUFACTURING SYSTEMS N.C. Tsourveloudis, L. Doitsidis Intelligent Systems & Robotics Laboratory Department of Production Engineering and Management Technical University of Crete S. Ioannidis Department of Mathematics University of the Aegean

2 OVERVIEW Introduction Fuzzy Scheduling Evolutionary Fuzzy Scheduling Experimental Results Discussion & Conclusions

3 Introduction Production Performance Measures Work In Process (WIP) vs, Backlog (BL) Production Control Policies Classical Approach Intelligent Systems Approach Fuzzy Approach Evolutionary Fuzzy Approach

4 Fuzzy Scheduling A production system can be viewed as a network of machines and buffers. Control Modules

5 Distributed Fuzzy Scheduling The expert knowledge that describes the distributed control objective can be summarized as follows: If the surplus level is satisfactory then try to prevent starving or blocking by increasing or decreasing the production rate accordingly. If the surplus is either too low or too high then produce at maximum or zero rate respectively. The above knowledge is formally represented as a fuzzy logic rule, for the case of the transfer line, as follows: IF b j,i is LB (k) AND b i,l is LB (k) AND s i is LS i (k) AND x i is LX (k) THEN r i is LR i (k)

6 Supervised Fuzzy Scheduling In the supervised fuzzy scheduling approach, the supervisory controller utilizes macroscopic data of higher hierarchies to adjust the overall system's behavior. The expert knowledge that describes the distributed control objective can be summarized as follows: If the upper surplus bound is reduced there is an immediate reduction of WIP. If the upper surplus bound is increased there is an increase of WIP and the total production rate leading to a small reduction of backlog. If the lower surplus bound is increased a substantial reduction of backlog and an increase in WIP is achieved. If there is a reduction of lower surplus bound as a result we have a deterioration of backlog with an improvement of WIP. An example of a fuzzy rule for the case of the Supervisory Controller is the following: IF mx e is LMX (k) AND e x is LE x (k) AND e w is LE w (k) THEN u c is LU c (k) AND l c is LL c (k),

7 Evolutionary Fuzzy Scheduling We consider the application of an evolutionary algorithm for the optimal selection of MFs. The basic idea is to represent the complete set of MFs by an individual (chromosome) and to evolve shape and location of the MFs.

8 Evolutionary Fuzzy Scheduling The objective is to optimize a performance measure which in the EAs context is called fitness function. In the case of the distributed fuzzy control evolution concept, it has the following form: F = N j= 1 ( D( t j ) PR( t j 2 )) 1

9 Evolutionary Fuzzy Scheduling n the case of the supervised fuzzy control evolution concept, the fitness function has e following form: F = 1 c WIP + I c b BL

10 Evolutionary Fuzzy Scheduling The pseudo code that describes the procedure is the following:

11 Experimental Results In order to test both the distributed and the supervised evolutionary fuzzy approach the following systems were used. Production line Production Network.

12 Experimental Results DISTRIBUTED EVOLUTIONARY FUZZY APPROACH HDF EDF Demand W IP BL W IP BL Constant Stochastic Results for the test case of the production line HDF EDF Demand W IP BL W IP BL Constant Stochastic Results for the test case of the production network

13 Experimental Results The production cost consists of inventory and backlog costs. Thus, the mean production cost C is given by: C = ci WIP + c b BL Cost C Demand c I c b HDF EDF Cost analysis for the case of the production line

14 Experimental Results SUPERVISED EVOLUTIONARY FUZZY APPROACH HSF ESF Demand W IP BL C W IP BL C Comparative results for the test case of the production line HSF ESF Demand W IP BL C W IP BL C Comparative results for the production network test case

15 Discussion & Conclusions Simulation results, for a number of taste cases, have shown an important improvement of performance and production related costs, with the use of EA strategies. The evolutionary approaches achieve a substantial reduction of WIP in almost every case. On the contrary there is a small increase of backlog in most cases. With the use of the evolutionary algorithm the system s performance becomes more balanced. In all cases the sum of WIP and BL is reduced. In the future it would be very interesting to consider the case of seasonal demand. Another interesting extension would be the use of EA strategies in more complex production systems such as multiplepart-type and/or reentrant systems.