inventory control as identification problem based on fuzzy logic alexander rotshtein dept. of...

INVENTORY CONTROL INVENTORY CONTROL AS IDENTIFICATION AS IDENTIFICATION PROBLEMPROBLEMBASED ON FUZZY LOGICBASED ON FUZZY LOGIC

ALEXANDER ROTSHTEIN Dept. of Industrial Engineering and Management ,

Jerusalem College of Technology – Machon Lev

21 Havaad Haleumi, 91160, Jerusalem, Israelrot@mail.jct.ac.il

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INTRODUCTIONINTRODUCTION

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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

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FUZZY APPROACHFUZZY 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

INVERTED PENDULUM CONTROL INVERTED PENDULUM CONTROL SYSTEMSYSTEM

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IF ANGLE IS NEGATIVE MEDIUM AND VELOCITY IS POSITIVE SMALTHEN 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 CONTROLSYSTEM BASED ON IDENTIFICATION TECHNIGUE

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METHOD OF IDENTIFICATIONMETHOD OF IDENTIFICATION

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FUZZY INVENTORY CONTROL MODELFUZZY INVENTORY CONTROL MODEL

OUTPUT DEPENDENCY OUTPUT DEPENDENCY BETWEEN AND INPUTSBETWEEN AND INPUTS

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FUZZY KNOWLEDGE FUZZY KNOWLEDGE BASEBASE

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FUZZY LOGICAL EQUATIONS

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MEMBERSHIP FUNCTIONS

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THE ALGORITHM OF DECISION MAKING

TO FIX THE DEMAND AND STOCK QUANTITY-ON-HAND VALUES AT THE TIME MOMENT t=t0.

 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 = t0 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=t0.

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THE CRISP VALUE OF THE INVENTORY ACTION AT THE TIME t=t0:

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FUZZY MODEL TUNING

TRAINING DATA

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TUNING PROBLEM STATEMENT

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TRAINING DATA

change of the demand for the produce in 2001

stock quantity-on-hand change in 2001

inventory action in 2001

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FUZZY TERMS MEMBERSHIP FUNCTIONS BEFORE TRAINING

FUZZY TERMS MEMBERSHIP AFTER TRAINING FUNCTIONS

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MEMBERSHIP FUNCTIONS PARAMETERS BEFORE (AFTER) TRAINING

RULES WEIGHTS BEFORE (AFTER) TRAINING

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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

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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

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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