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 Uncertainty December, 2007

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 The number of customers production lot size A scenario designer can’t evaluate an effect of 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 do customers increase? Price of a product

4 Research background - simulation methods Simulation is used for various fields –Physical/Chemical simulation, Business simulation, etc. Model elements RelationsDisadvantage System DynamicsQuantitative factors EquationsUnavailable for the model including qualitative information Qualitative SimulationQualitative 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 arc Qualitative arc NodeArc QuantitativeInitial value and rangeRelational expression QualitativeFive 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 b=a*10 a=10, 0<a<15 +(M1) － (M2) + c=H

6 Research problems A value of nodes can’t be decided. In simulation models, propagated effects are not unique. Propagation of an effect Propagation of an effect Combination of effects Combination of effects The number of customers The number of quality manager Price Quality level + － (M 1 ) + (M 2 )

7 Approach The num. of customers frequency 1. Propagation of an effect 2. Combination of effects Decide a qualitative value or a range for generation of random numbers in 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 number of customers The number of quality manager Price Quality level + － (M 1 ) + (M 2 ) Propagation of an effect Combination of 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=L H, L, L, L L ） 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 :100 Range [50, 300] H Qualitative node ＋ Quantitative node M L L H L L L 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 [L H, 300]

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 （ ER i ） ”. “Effect Ratio (ER i )” Decided by random numbers under the magnitude correlations (Sum of ER i equals to 1) Price Quality level － (M 1 ) [ 500,1500] 1500 × ER 1 Price ER 1 =0.6 Quality level ER 2 =0.4 Effect ratio 500 × ER × ER × ER 2 Magnitude correlation (M i ) Range of the destination node +(M 2 ) The number of customers Decided by a random number Weighted ranges Effect=800 Effect=500 Total Effect 1300 Combination of effects Sum … Decide effect ranges Decided by propagation method

10 Evaluation experiments I Target model The number of manager Production time Frequency of test Quality level Amount of production Opportunity loss rate Volume of 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 Opportunity loss rate Quality level (Model B)

11 Evaluation experiments I CasesABCDEFG Nq Tp 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 Q (G.R.) Q (U.R.) Q Q=405 Volume of sales Q =451 ^ Frequency Frequency Volume o of sales Q and average of distribution in each case Q ^ Q=405 Q =452 ^ U.R. G.R. ^ ^ |Q － Q| ^ Q average variance standard deviation |Q － Q| ^ Q average variance standard deviation ^

13 Evaluation experiments II Initial cost(IC) The number of partner companies Lead time(LT) Estimated time Time for order works Estimated cost Unit cost for procurement - - Simplification of selecting partners Simplification of 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 designer would like to decrease LT and IC

14 Frequency Result of experiments II dH H H H LT 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 IC H LT Frequency LT is decreased to 4 Frequency dH IC is decreased to 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