1. INVENTORY CONTROL AS IDENTIFICATION PROBLEM BASED ON FUZZY LOGIC ALEXANDER ROTSHTEIN Dept. of Industrial Engineering and Management, Jerusalem College of Technology – Machon Lev 21 Havaad Haleumi, 91160, Jerusalem, Israel rot@mail.jct.ac.il 1

2. INTRODUCTION 2 STORAGE COST IS A MAJOR CONCERN OF PRODUCTION CLASSICAL INVENTORY MODELS CONSTRUCTED TO DEEL WITH MINIMIZING STORAGE COST THEIR AIM IS TO MAINTAIN ENOUGH QUANTITIES OF NEEDED PARTS TO PRODUCE A PRODUCT WITHOUT EXESSIVE STORAGE COST THE BASIC INVENTORY MANAGEMENT PROBLEM IS TO DECIDE WHEN NEW PART SHOULD BE ORDERED (ORDER POINT ) AND IN WHAT QUANTITIES TO MINIMIZE THE STORAGE COST THIS IS COMPLICATED OPTIMIZATION PROBLEM ( SEE FOR INSTANCE FOGATRY & HOFFMANN, 1983 ) THE EXISTING CLASSICAL MATHEMATICAL METHODS MAY PROGUSE A SOLUTION QUITE DIFFERENT FROM THE REAL SITUATION

3. 3 FUZZY APPROACH A GOOD ALTERNATIVE TO CLASSICAL METHODS IS FUZZY LOGIC CONTROL (FLC) METHODOLOGY ITS PURPOSE IS NOT TO MINIMIZE COST DIRECTLY BUT TO MAINTAIN A PROPER INVENTORY LEVEL REFLECTING THE DEMAND AT A GIVEN TIME THE BASIC OF FUZZY INVENTORY CONTROL IS EXPERIENCE AND KNOWLEDGE OF MANAGERS  FUZZY INVENTORY MODEL TWO INPUT VARIABLES : 1. DEMAND VALUE FOR A PRODUCT 2. QUANTITY- ON -HAND PARTS ( IN STOCK) NEEDED TO BUILD THE PRODUCT ONE OUPUT VARIABLE : INVENROTY ACTION - REORDERING OF PARTS - REDUCING THE NUMBER OF ALREADY EXISTING - NO ACTIONS AT THAT TIME

4. INVERTED PENDULUM CONTROL SYSTEM 4 IF ANGLE IS NEGATIVE MEDIUM AND VELOCITY IS POSITIVE SMAL THEN FORSE IS NEGATIVE SMALL IF ANGLE IS NEGATIVE MEDIUM AND VELOCITY IS POSITIVE MEDIUM, THEN FORCE IS POSITIVE SMALL THE AIM DESIGN AND TUNING THE FUZZY INVENTORY CONTROL SYSTEM BASED ON IDENTIFICATION TECHNIGUE

5. 5 METHOD OF IDENTIFICATION

6. 6 FUZZY INVENTORY CONTROL MODEL FUZZY INVENTORY CONTROL MODEL

7. OUTPUT DEPENDENCY BETWEEN AND INPUTS OUTPUT DEPENDENCY BETWEEN AND INPUTS 7

8. FUZZY KNOWLEDGE BASE 8

9. 9 FUZZY LOGICAL EQUATIONS

10. 10 MEMBERSHIP FUNCTIONS

11. 11 THE ALGORITHM OF DECISION MAKING TO FIX THE DEMAND AND STOCK QUANTITY-ON-HAND VALUES AT THE TIME MOMENT t=t 0. TO DEFINE THE MEMBERSHIP DEGREES OF AND VALUES TO THE CORRESPONDING TERMS WITH THE HELP OF MEMBERSHIP FUNCTIONS TO CALCULATE THE MEMBERSHIP DEGREE OF THE INVENTORY ACTION AT THE TIME t = t 0 TO EACH OF THE DECISIONS CLASSES WITH THE HELP OF FUZZY LOGICAL EQUATIONS. THE TERM WITH MAXIMAL MEMBERSHIP FUNCTION IS THE INVENTORY ACTION AT THE TIME t=t 0.

12. 12 THE CRISP VALUE OF THE INVENTORY ACTION AT THE TIME t=t 0 :

13. 13 FUZZY MODEL TUNING TRAINING DATA

14. 14 TUNING PROBLEM STATEMENT

15. 15 TRAINING DATA change of the demand for the produce in 2001 stock quantity-on-hand change in 2001 inventory action in 2001

16. 16

17. 17 FUZZY TERMS MEMBERSHIP FUNCTIONS BEFORE TRAINING FUZZY TERMS MEMBERSHIP AFTER TRAINING FUNCTIONS

18. 18 MEMBERSHIP FUNCTIONS PARAMETERS BEFORE (AFTER) TRAINING RULES WEIGHTS BEFORE (AFTER) TRAINING

19. 19 COMPARISON OF MODEL AND REFERENCE CONTROL BEFORE AND AFTER FUZZY MODEL TRAINING Inventory action generated by fuzzy model before training INVENTORY ACTION GENERATED BY FUZZY MODEL AFTER TRAINING

20. 20 COMPARISON OF THE PRODUCE REMAINDER AFTER CONTROL BEFORE AND AFTER FUZZY MODEL TRAINING Produce remainder in store after control before fuzzy model training Produce remainder in store after control after fuzzy model training

21. 21  THE PROPOSED APPROACH USES THE AVAILABLE INFORMATION ABOUT CURRENT DEMAND AND STOCK QUANTITY-ON-HAND  THE APPROACH IS BASED ON THE METHOD OF NONLINEAR DEPENDENCIES IDENTIFICATION BY FUZZY KNOWLEDGE BASES  FUZZY MODEL TUNING BY TRAINING DATA ALLOWS TO APPROXIMATE MODEL CONTROL TO THE EXPERIENCED EXPERT DECISIONS  THE APPROACH PROPOSED DOES NOT REQUIRE THE STATEMENT AND SOLUTION OF THE COMPLEX PROBLEMS OF MATHEMATICAL PROGRAMMING  FURTHER DEVELOPMENT OF THE APPROACH CONSISTS IN THE ADAPTIVE (NEURO-FUZZY) INVENTORY CONTROL MODELS CREATION, WHICH ARE TUNED WITH THE ACQUISITION OF NEW EXPERIMENTAL DATA ABOUT SUCCESSFUL DECISIONS  FACTORS INFLUENCING THE DEMAND AND QUANTITY-ON-HAND CAN BE TAKEN INTO ACCOUNT WITH THE HELP OF SUPPLEMENTARY FUZZY KNOWLEDGE BASES CONCLUSION