a study on fuzzy inventory control system under demand...

A STUDY ON FUZZY INVENTORY CONTROL SYSTEM UNDER DEMAND UNCERTAINTY

Master’s Thesis Presentation 2010.02.15

Author : Achmad RIADISupervisor: Prof. Saburo TSURUTA

Logistics System EngineeringCourse of Maritime Technology and Logistics

Tokyo University of Marine Science and Technology

Contents

1. Introduction

2. Review of Past Studies Related to Fuzzy Application in Inventory Control

3. Data Used for the Dynamic Simulation of Inventory Control

4. Model Design for the Dynamic Simulation of Inventory Control

5. Result of the Simulations

6. Conclusion

7. Future Research Direction 2

Introduction

Background

3

1. Inventory is needed to allow balancing between supply and demand.

2. Careful inventory control is needed to make good economic sense.

3. Considering demand uncertainty is important in inventory control.

4

Introduction (cont.)

Problem

In an ordinary inventory control system, the demand uncertainty is measured by statistical model of a normal distribution, specified by Mean and Standard Deviation.

Prediction of Mean and Standard Deviation of demand used in an ordinary inventory control system is not always precise.

Many methods have been carried out for the precise prediction of future demand:

- Adaptive forecasting, such as Moving Average, etc.

- Fuzzy system.

5

Introduction (cont.)

Objective

To investigate the effectiveness of Fuzzy inventory control system for controlling the inventory, especially with the presence of demand uncertainty.

In what condition Fuzzy inventory control system is effective?

When Fuzzy inventory control system is more effective?

6

Problem Domain:

Solving demand uncertainty by utilizing demand as Fuzzy

variable.

Showing the effectiveness by comparing the inventory control

systems (ordinary, moving average and Fuzzy inventory

control system)

Differences between this study and the other past studies:

Utilizing demand as Fuzzy variable with membership

functions.

Comparing the inventory control systems by dynamic

simulation with the possibility that the value of future

demand will change.

Review of Past Studies Related to Fuzzy Application in Inventory Control

Data Used for the Dynamic Simulation of Inventory Control

Many data have been collected and the following data have been decided which are appropriate with the needs of the study.

Demand Data

Perpetual demand with normal distribution specified by:

Mean : 651 units/day

Sta. Dev. : 200 units/day

Lead Time Data

Constant 2 days.

Relevant Costs Data

Holding Cost : 20% of unit cost per annum.

Ordering Cost : ¥688 / order (0.47% of unit cost)

Stockout Cost : 0% ~ 4% of unit cost per unit.

Unit Cost : ¥150 7

Model Design for the Dynamic Simulation of Inventory Control

There are three dynamic simulation models, which have been designed in this study:

Ordinary Inventory Control System.

Moving Average Inventory Control System.

Fuzzy Inventory Control System.

Basic method for controlling inventory is periodic review inventory control (base stock policy).

8

9

Model Design for the Dynamic Simulation of Inventory Control (cont.)

Periodic Review Inventory Control (Base Stock Policy)

Q∗ = 2CD

H T =

Q

D

∗ M∗ = d T + LT + z(s′

d)

Source: Ballou, R.H (2004)T = Re-orders period M* = Maximum

inventory level

Wrap To Zero

z-i

In

DelayOut

Variable

Integer Delay

150

Unit Cost

simout_dlvry

To Workspace 7

simout_oq

To Workspace 6

simout_oc

To Workspace 5

simout_uc

To Workspace 4

simout_hc

To Workspace 3

simout_so

To Workspace 2

simout_inv

To Workspace 1

Switch 2

Switch 1

Subtract 2

Subtract 1

|u|

Stockout

round

Rounding

Function

Review Period

688

Ordering Cost

Order

Quantity

5820

Maximum

Inventory Level

2

Lead Time

K Ts

z-1

Inventory

0.08

Holding Cost

Demand

0

Constant 2

0

Constant 1 ~= 0

Compare

To Zero

10


Dynamic Simulation Model for Ordinary Inventory Control System

M* = d(T+LT) + z(s’d)5820 units

5 days

T =Q

D

∗

Maximum

Inventory

Level

2.3

safety factor, z

Wrap To Zero

z-i

In

DelayOut

Variable

Integer Delay

150

Unit Cost

simout_dlvry

To Workspace 7

simout_oq

To Workspace 6

simout_oc

To Workspace 5

simout_uc

To Workspace 4

simout_hc

To Workspace 3

simout_so

To Workspace 2

simout_inv

To Workspace 1

Switch 2

Switch 1

Sum 3

Sum 2

Sum 1

Subtract 2

Subtract 1

|u|

Stockout

round

Rounding

Function 3

roundRounding

Function 2

round

Rounding

Function

Review Period

688

Ordering Cost

Order

Quantity

In1

In2

In3

In4

In5

In6

In7

In8

Out

1

Out

2

Out

3

Out

4

Out

5

Out

6

Out

7

Moving

Variance

In1

Out

1

Out

2

Out

3

Out

4

Out

5

Out

6

Out

7

Moving

Average

sqrtMath

Function

2

Lead Time

K Ts

z-1

Inventory

0.08

Holding Cost

Demand

0

Constant 2

0

Constant 1 ~= 0

Compare

To Zero

11


Dynamic Simulation Model for Moving Average Inventory Control System

Maximum

Inventory

Level

Wrap To Zero

z-i

In

DelayOut

Variable

Integer Delay

150

Unit Cost

simout_dlvry

To Workspace 7

simout_oq

To Workspace 6

simout_oc

To Workspace 5

simout_uc

To Workspace 4

simout_hc

To Workspace 3

simout_so

To Workspace 2

simout_inv

To Workspace 1

Switch 2

Switch 1

Subtract 2

Subtract 1

|u|

Stockout

Standard

Deviation

round

Rounding

Function 2

round

Rounding

Function

Review Period

688

Ordering Cost

Order

QuantityMean

2

Lead Time

K Ts

z-1

Inventory

0.08

Holding Cost

Fuzzy Logic

Controller

Demand

0

Constant 2

0

Constant 1 ~= 0

Compare

To Zero

12


Dynamic Simulation Model for Fuzzy Inventory Control System

13


Process inside the Fuzzy Logic Controller Block

Fuzzy Inference

System by ANFIS

Output Max. Inventory Level

Uncertain Inputs (mean, std. dev)

with linguistic variables

Fuzzy Inference System includes membership functions, rules, and output parameters.

ANFIS will construct a Fuzzy inference system with some parameters are tuned (adjusted).

Result of the Simulations

14

Demand mean Demand standard

deviation

Condition 1 (There is no change with the

future demand or the future

demand is same as the

expected demand)

Expected demand

mean

Expected demand

standard deviation

Condition 2-A

(Future demand mean is

uncertain, demand standard

deviation is fixed)

Condition 2-B (Future demand mean is

fixed, demand standard

deviation is uncertain)

Vary from -50% to

+50% of expected

demand mean (step

is 10%)

Expected demand

mean (fixed)

Expected demand

standard deviation

(fixed)

Vary from -50% to

+50% of expected

demand standard

deviation (step is

10%)

Simulation Conditions

15

Result of the Simulations (cont.)

Simulation Results with Condition 1 (there is no change with the future demand)

95

100

105

110

115

120

125

130

135

140

SC is 0% of unit cost





Tota

l rel

evan

t co

sts

(¥)

x103

Total Relevant Costs between Three Inventory Control Systems (Seed Num. 100)

Ordinary inventory control system

MA inventory control system

Fuzzy inventory control system

0.38% < Ordinary Inv. Contr. Syst.

9.43% > Ordinary Inv. Contr. Syst.



16


Simulation Results with Condition 1 (there is no change with the future demand)

Ordinary Moving Average Fuzzy

Service Level (%) 99.41 98.77 99.29

Conclusion of Simulation Results with Condition 1

When the stockout cost is not considered, Fuzzy inventory control system is more effective.

When the stockout cost is considered, ordinary inventory control system is more effective.

17


Simulation Results with Condition 2-A (demand mean is uncertain, demand std. dev is fixed)

0.0

0.5

1.0

1.5

2.0

2.5

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Tota

l Re

leva

nt

Co

sts

Demand Mean

Total Relevant Costs with Uncertain Demand Mean(In Case of Stock out Cost = 0% of Unit Cost)

OrdinaryMoving AverageFuzzy

Expected Demand Mean

Percent Different13.43%

Service Level50.83%

Service Level98.34%

18


Simulation Results with Condition 2-A (demand mean is uncertain, demand std. dev is fixed)

0.0

0.5

1.0

1.5

2.0

2.5

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Tota

l Re

leva

nt

Co

sts

Demand Mean

Total Relevant Costs with Uncertain Demand Mean(In Case of Stock out Cost = 4% of Unit Cost)


Expected Demand Mean

19


Simulation Results with Condition 2-B(demand mean is fixed, demand std. dev is uncertain)

0.8

0.9

1

1.1

1.2

1.3

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Tota

l Re

leva

nt

Co

sts

Demand Std. Dev.

Total Relevant Costs with Uncertain Demand Std. Dev.(In Case of Stock out Cost = 0% of Unit Cost)


Expected DemandStd. Dev.

Service Level98.21%

Service Level98.95%

20


Simulation Results with Condition 2-B(demand mean is fixed, demand std. dev is uncertain)

0.8

0.9

1

1.1

1.2

1.3

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

Tota

l Re

leva

nt

Co

sts

Demand Std. Dev.

Total Relevant Costs with Uncertain Demand Std. Dev.(In Case of Stock out Cost = 4% of Unit Cost)


Expected DemandStd. Dev.

Conclusion

• When there is no change with the future demand:

Fuzzy inventory control system is more effective (stock out cost is not considered)

Ordinary inventory control system is more effective (stock out cost is considered)

• When the future demand mean is uncertain:

Fuzzy inventory control system is more effective.

• When the future demand standard deviation is uncertain:

Stockout cost is not considered:

Fuzzy inventory control system is effective only when the future demand sta. dev. lower than the expected demand sta. dev.

Stockout cost is considered:

Both ordinary and Fuzzy inventory control system is effective. 21

22

Future Research Direction

The other uncertainties such as supply uncertainty, lead time uncertainty and costs uncertainty can be present in inventory control.

Comparing the result of this study with the result of the other studies with different Fuzzy system.

Concerning the multi echelons/stages within the supply chain is also interesting for the future research.

Thank YouFor Your Attention

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a study on fuzzy inventory control system under demand...

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