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Hybrid Simulation with Qualitative and Quantitative Integrated Model under Uncertainty Business Environment

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Title: Hybrid Simulation with Qualitative and Quantitative Integrated Model under Uncertainty Business Environment


1
Hybrid Simulation with Qualitative and
Quantitative Integrated Model under Uncertainty
Business Environment
IFIP/IIASA/GAMM Workshop on Coping with
Uncertainty 10-12 December, 2007
  • Masanori Akiyoshi (Osaka University)
  • Masaki Samejima (Osaka University)

2
Contents
  1. Research Background
  2. Research Purpose
  3. Problems to be tackled
  4. Approach
  5. Proposed Method
  6. Evaluation
  7. Conclusion
  8. Future Work

3
Research background - business scenario design
Business scenario
A sequence of changes in business factors
How many do customers increase?
The number of customers
production lot size
Price of a product
A scenario designer cant evaluate an effect of
a scenario.
  • Many business factors
  • Complex relations between business factors

4
Research background - simulation methods
  • Simulation is used for various fields
  • Physical/Chemical simulation, Business
    simulation, etc.
  • Conventional simulation methods

Model elements Relations Disadvantage
System Dynamics Quantitative factors Equations Unavailable for the model including qualitative information
Qualitative Simulation Qualitative factors Causal Relation The value of originally quantitative factors can not be handled.
No appropriate methods for the model including
both quantitative and qualitative information
based on causal relationships
5
Research purpose - hybrid simulation
Simulation method for hybrid model including
quantitative and qualitative information
Quantitative arc
Qualitative arc
Quantitative node(b)
ba10
(M1)
Quantitative node(a)
Quantitative node(d)
Qualitative node (c)

-(M2)
a10, 0ltalt15
cH
Node Arc
Quantitative Initial value and range Relational expression
Qualitative Five kinds of state values D(x,y) Cause-effect relation Mi Magnitude correlation
  • H(high)
  • (a slightly high)
  • M(normal)
  • (a slightly low)
  • L(low)

In case of increasing x, y increases - In
case of increasing x, y decreases
A number in ascending sequence of joining arcs
by magnitude of effects
6
Research problems
- (M1)
Price
The number of customers
The number of quality manager

(M2)
Quality level
A value of nodes cant be decided.
In simulation models, propagated effects are not
unique.
7
Approach
- (M1)
Price
The number of customers
The number of quality manager

(M2)
Quality level
  • By using Monte Carlo Simulation
  • Decide effects by a random number based on
    qualitative information.
  • Repeat the above simulation process and decide
    the value statistically

8
Propagation in the hybrid model
In order to propagate the effect between nodes,
  • Landmarks(LLH, L , L , LL) are used for
    discriminating states
  • of quantitative nodes.
  • Corresponding pair of states on source node and
    destination node
  • is used for propagation
  • In case that a destination node is quantitative,
    a random number in the
  • corresponding pair of range is generated to
    decide the value.

Quantitative node
Initial value
100

Qualitative node
Range
50, 300
300
H
Corresponding pair
L
H
When qualitative arc is
L
The higher a qualitative value is, the larger a
quantitative value is.
100
M
L
L
L
A value is decided to be a random number in LH,
300
L
50
9
Combination of effects by effect ratios
In order to reflect magnitude correlations in a
value of a destination node, a ratio of an effect
by a qualitative arc i (1 ? i ? n) in a range is
defined as Effect Ratio (ERi).
Effect Ratio (ERi)
Decided by random numbers under the magnitude
correlations (Sum of ERi equals to 1)
Combination of effects
Decide effect ranges
  • Magnitude
  • correlation (Mi)
  • Range of
  • the destination node

Effect ratio
1500
ER1

Decided by propagation method
Effect800
ER1 0.6


Price
500
ER1


Quality
ER2 0.4
-(M1)
1500
ER2

Effect500
level
The number of customers
Price
500
ER2

Sum
Quality
Decided by a random number

level
500,1500
Total Effect 1300
Weighted ranges
(M2)
10
Evaluation experiments I
PurposeTo test validity of applying method
Compared the simulation results on a quantitative
model with results on a hybrid model that is
modified partially
Target model
Quality level
The number of manager
Frequency of test
Nq
Volume of sales
Amount of production
Production time
Tp
Opportunity loss rate
Lead time
11
Evaluation experiments I
Outline of the experiment
1. Required the value of Volume of sales( Q )
by equations of quantitative arcs in the model
2. Applied proposed method to mostly the same
model except that Quality level and
Opportunity loss rate are assumed to be
qualitative(Model B)
3. Compared an unique value Q and a distribution
calculated by Model B
Simulation Conditions
  • Random numbers are uniform random numbers (U.R.)
  • and gaussian random numbers (G.R.) under 0.1
    confidence coefficient
  • Seven kinds of inputs, 10,000 times simulation

Cases A B C D E F G
Nq 15 15 20 20 15 25 25
Tp 5 4 5 4 3 5 3
12
Result of experiments I

Q and average of distribution in each case
Q
G
F
E
D
C
B
A
Cases
567
204
1125
553
720
363
405
Q

576
225
1050
500
732
362
451
Q (U.R.)

576
226
1055
502
734
361
452
Q (G.R.)
U.R.
G.R.

ltCase Agt
ltCase Agt
Q
451
Q
405

Q
405
Q
452
Frequency
Frequency
60
60
60
50
50
50
40
40
40
30
30
30
20
20
20
Volume o of sales
Volume of sales
10
10
10
0
0
0
200
300
400
500
600
700
200
300
400
500
600
700
200
300
400
500
600
700
  • average

  • average

0.183
0.093

Q
Q
-

Q
-
Q
  • variance
  • variance

0.005
0.018
Q
Q
  • standard
  • deviation
  • standard
  • deviation

0.075
0.132

Q and Q are considered to be mostly same
13
Evaluation experiments II
Evaluate scenarios of a practical model that was
used in consulting business
A scenario designer would like to decrease LT
and IC
Target model
Time for order works
Estimated cost
-

Simplification of order process
Estimated time
-
Initial cost(IC)
Lead time(LT)
Simplification of selecting partners
The number of partner companies
-

Unit cost for procurement
-
Scenarios of the model
Scenario A order process is simplified
  • Estimated time and cost are
  • decreased
  • LT and IC are decreased
  • The number of partner companies
  • is increased
  • LT and IC are decreased

Scenario B selecting partner is simplified
14
Result of experiments II
Simulation Conditions
  • Random numbers for Monte Carlo simulation are
    uniform random numbers
  • 10,000 times simulation


Result
Scenario B selecting partner is simplified
Scenario A order process is simplified
Frequency
Frequency
dH
H
dH
LT is decreased to 4
H
LT
LT
4
7
6
7
6.5
6
LT
dH
Frequency
Frequency
IC is decreased to 69000
dH
IC
H
H
IC
IC
84000
69000
84000
82100
A scenario designer can judge that Scenario B is
more effective than Scenario A
Business scenario could be investigated
15
Conclusion
  • In order to support business scenario design, we
    propose a simulation method on qualitative and
    quantitative hybrid model
  • For propagation and combination of effects by
    qualitative causal relations, we introduce a
    statistical approach based on Monte Carlo
    simulation
  • Through applied results to practical models, it
    is confirmed that there are mostly same between
    results derived from quantitative relations and
    results derived from the proposed method.
  • And, it is confirmed that a scenario designer can
    judge which business scenario is better.

16
Future Work
  • Goal-oriented Simulation
  • From decision-making points of views, attended
    nodes are given in advance, then input for
    operational nodes are desired in some situation.
  • Automatic Tuning of Landmark Values
  • Propagation in Cycle of Graph

17
Thank you for your attention
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