hybrid simulation with qualitative and quantitative integrated model under uncertainty business...
TRANSCRIPT
Hybrid Simulation with Qualitative and Quantitative Integrated Model under Uncertainty
Business Environment
Masanori Akiyoshi (Osaka University)Masaki Samejima (Osaka University)
IFIP/IIASA/GAMM Workshop on Coping with Uncertainty10-12 December, 2007
2
Contents
1. Research Background2. Research Purpose3. Problems to be tackled4. Approach5. Proposed Method6. Evaluation7. Conclusion8. Future Work
3
Research background - business scenario design
Business scenarioA sequence of changes in business factors
The numberof customers
production lot size
A scenario designer can’t evaluate an effectof a scenario.
•Many business factors•Complex relations between business factors
In order to evaluate a business scenario clearly
1. Modeling a business structure• Considerable factors and relations• Some factors are qualitative, some are quantitative.• Some relations are qualitative, some are quantitative.
2. Simulating the model• Deciding effects based on factors and relations
How many docustomers increase?Price of
a product
4
Research background - simulation methods
• Simulation is used for various fields– Physical/Chemical simulation, Business simulation, etc.
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
• Conventional simulation methods
5
Research purpose - hybrid simulation
Simulation method for hybrid model including quantitative and qualitative information
Quantitative node(a)
Quantitative node(b)
Qualitative node(c)
Quantitative node(d)
Quantitative arcQualitative arc
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)
H
L
＋ ： 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
b=a*10
a=10, 0<a<15
+(M1)
－ (M2)+c=H
6
Research problems
A value of nodescan’t be decided.
In simulation models, propagated effects are not unique.
Propagationof an effect
•Propagation of an effect
Combinationof effects
•Combination of effects
The numberof customers
The number ofquality manager
Price
Quality level+
－ (M1)
+ (M2)
7
Approach
The num. ofcustomers
frequency
1. Propagation of an effect
2. Combination of effectsDecide a qualitative value or a range for generation of random numbersin accordance with magnitude correlation
Decide a qualitative value or a range for generation of random numbers in accordance with a value of a source node
The numberof customers
The number ofquality manager
Price
Quality level+
－ (M1)
+ (M2)
Propagationof an effect
Combinationof effects
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
• Landmarks （ L=LH, 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.
Propagation in the hybrid model
Initial value:100Range[50, 300]
H
Qualitativenode
＋ Quantitativenode
M
L
300
50
100
LH
L
L
LL
H
L
H
L
H L
In order to propagate the effect between nodes,
Corresponding pair
When qualitative arc is “+”
The higher a qualitative value is,the larger a quantitative value is.
A value is decided to be a random number in [LH, 300]
9
Combination of effects by effect ratiosIn 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)
Price
Qualitylevel
－ (M1)
[500,1500]
1500 ×ER1•Price ER1
=0.6•Qualitylevel ER2
=0.4
Effect ratio
500 × ER1
1500× ER2
500× ER2
•Magnitude correlation (Mi)•Range of the destination node
+(M2)
The numberof customers
Decided bya randomnumber
Weighted ranges
Effect=800
Effect=500
Total Effect 1300
Combination of effects
Sum
…Decide effect ranges
Decided bypropagationmethod
10
Evaluation experiments I
Target model
The numberof manager
Productiontime
Frequencyof test
Quality level
Amount ofproduction
Opportunityloss rate
Volumeof sales
Lead time
Nq
Tp
Purpose ： To test validity of applying method
Compared the simulation results on a quantitative model with results on a hybrid model that is modified partially
Opportunityloss rate
Quality level
(Model B)
11
Evaluation experiments I
Cases A B C D E F G
Nq 15 15 20 20 15 25 25
Tp 5 4 5 4 3 5 3
• 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
Simulation Conditions
3. Compared an unique value Q and a distribution calculated by Model B
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 ）
Outline of the experiment
12
Q and Q are considered to be mostly same
Result of experiments I
GFEDCBACases
5762261055502734361452Q (G.R.)
5762251050500732362451Q (U.R.)
5672041125553720363405Q
Q =405
Volumeof sales
Q =451^
0102030405060
200 300 400 500 600 7000102030405060
200 300 400 500 600 700
Frequency
0102030405060
200 300 400 500 600 700
Frequency
Volume oof sales
Q and average of distribution in each caseQ̂
Q =405 Q =452^U.R. G.R.
^
^
0.1830.018
0.132
|Q－ Q|^
Q
•average 0.093•variance 0.005•standard deviation
0.075
|Q－ Q|^
Q
•average•variance•standard deviation
<Case A> <Case A>
^
13
Evaluation experiments II
Initialcost(IC)
The numberof partnercompanies
Leadtime(LT)
Estimated time
Time for orderworks
Estimated cost
-
-
+Unit cost forprocurement
--
Simplificationof selecting partners
Simplificationof order process
Evaluate scenarios of a practical model that was used in consulting business
Target model
Scenarios of the model
•Estimated time and cost are decreased•LT and IC are decreased
•The number of partner companies is increased•LT and IC are decreased
Scenario A: order process is simplified
Scenario B: selecting partner is simplified
A scenario designerwould like to decrease LT and IC
14
Frequency
Result of experiments II
76.56
dH
H
dH
H
H
8400069000
4 76LT
•Random numbers for Monte Carlo simulation are uniform random numbers•10,000 times simulation
Simulation Conditions
Scenario A: order process is simplified
Result
Frequency
Scenario B: selecting partner is simplified
dH
8400082100
ICH
LT
FrequencyLT is decreased to 4
FrequencydH IC is
decreased to69000
A scenario designer can judge that Scenario B is more effective than Scenario A
IC
LT
IC
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