Simulation: An overview

Jack P.C. KleijnenProfessor of Simulation & Information Systems

Department of Information Systems & ManagementTilburg University

One-day seminar ‘Simulation in Economics’

SIKS/’Modeling & Simulation’

17 September 2003, Erasmus University, Rotterdam

18 September 2003 2

Summary of Overview

� For whom?� Level: Undergraduate students, graduate students, faculty� Field: Informatics, economics, business, OR, etc.� Domain: Logistics, insurance, management, ports, trains, etc

� About what?Simulation in ‘Economics’, including Business/Management

� Guideline: ’Simulatie’, i-Catcher, October 2000, pp. 12-14 (paper # 163 on http://center.kub.nl/staff/kleijnen/papers.html)

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What is ‘simulation’?

� Simulation: Computer model of a systems’ performance(see examples on next slides)

� Goals:� Sensitivity analysis (‘what if’)� Uncertainty analysis (risk)� Optimisation (with or without constraints)

(see examples on later slides)� Conclusion: Module of DSS, including ERP, MRP, etc.

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How does simulation ‘work’?

Example: Loan of € 10,000 (@ 6%?), to be paid back in 5 yearsAlternatives:

1. Annuity (interest + amortization = constant)2. Fixed amortization amount (interest amount decreasing)

DSS: Spreadsheet (Excel)Characteristic: Dynamic model (including time t)

Loan(t) = Loan (t – 1) - Amortization (t, t – 1)Interest (t) = 0.06 x Loan (t – 1)

Compute Net Present Value (NPV) of alternatives 1 and 2 resp.;select lowest NPV

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Example continued

Problem: Uncertain interest percentage (4% - 11%?)Solution: Sample percentage -- through random numbers rCompute Net Present Value (NPV) of alternatives 1 and 2 respProblem: Outlier sampled? (r = 0.00000000000000000000003)Solution: Repeat (say) 1,000 times ⇒ 1,000 NPVs

⇒ NPV distribution ⇒ average, variance, quantiles (‘risk’)Characteristic: Random model solved through Monte Carlo

method (i.e., random numbers)

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Simulation example 2: Arena’s FMS

ReleaseOrder

Cell 1 Cell 2

SystemExit

Cell 3Cell 4

Order ReleaseCell 1

SS

S

Source: Textbook/manual by Kelton et al. (2000)Discrete-event simulation: Dynamic & random

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Simulation types

� Methodology types:� Discrete-event (DEDS, GSMP) versus continuous

(differential equations)� Random (Monte Carlo) versus deterministic� Dynamic versus static

� Karplus (1977): Application domains � Hard sciences

Examples: CAE (chips; t.v. monitors; cars; airplanes)� Soft sciences

Examples: Economics (microscopic simulation of financial markets)

� Web sites: WSC, SAMO, etc. (addresses: see my web page)

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My own consulting projects� Personnel allocation (ABP, Heerlen): Discrete-event (Arena)� Animal disease control (Wageningen): Continuous, random� Urban warfare (NPS, Monterrey): Agents, random� Milk robots (University, Wageningen): Discrete event (Arena)� Nuclear waste disposal (Sandia, Albuquerque): Combined

discrete-continuous (Fortran)� Production planning DSS (VBF, Oosterhout): Discrete- event

(Simula)� Sonar-hunt for sea-mines (FEL-TNO, Scheveningen):

Combined� Global warming (RIVM, Bilthoven): Continuous, deterministic� And so on

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Design of experiments (DOE)for simulation

� Goals:� Sensitivity analysis: What if simulation’s inputs or

structure are changed?� Risk analysis: What if input parameters are uncertain?

Robust solution (Taguchi’s approach)� Optimalisation: Many methods (RSM, SA, TS, etc.)

� My on-going research on DOE: See next slides

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Recent research: Project 1Fredrik Person: Supply chain at Ericsson in Sweden

� Nearly 100 inputs: Which are really important? Screening (Sequential bifurcation) identifies 10 inputs

� Risk analysis: Sample the environmental inputs Latin Hypercube Sampling (LHS) refines Monte Carlo sampling

� Optimisation: Factorial design for controllable inputs

C i r c u i t B o a r dM a n u f a c t u r i n g

S M D a n dV i s i o n T e s t

W a v eS o l d e r i n g

F r a m eA s s e m b l y

S o l d e r i n g A s s e m b l y

T e s t T e s t T e s t F u n c t i o n T e s t T i m e T e s t F i n a l T e s t( a )

SMD and vision test

Function test

Yield

Circuit board manufacturing

Assembly

75 %

Test Frame assembly Time test Final test

Yield Yield Yield Yield

Flow of materials

Scrap Scrap Scrap Scrap Scrap

Rework Rework Rework Rework Rework

= Tes station

= Buffer

= Operation

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Recent research: Project 2

Ebru Angun: Optimization of simulated systems with constraints on multiple outputs and inputs

Heuristic: RSM & Interior Point & binary search; see figure

Goal output 0

Constrained output 1 Constrained output 2

Local area 1Local area 2

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Recent research: Project 3

Wim Van Beers: Kriging (meta)models of simulation models

Assumption: The closer the inputs, the more correlated the outputs.

Research problems:

1. Adapt Kriging to random (non-deterministic) simulation

2. Design: Sequential design; see final result in next figure(more samples in more difficult area)

012345

6789

1 0

0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0

x

y ( x )

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Recent research: Project 4

Christina Ivanescu: Production scheduling in chemical industrySolution: Regression predictor for ‘make span’,

based on six job characteristicsProblem: Few actual data when estimating regression

parameters (= characteristics’ weights)Solution: Increase data base through bootstrapping

Monte Carlo resampling of actual data

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Summary of Overview

� Many application domains: Hard & soft sciences� Different methodologies:

� Discrete-event/continuous/combined� Deterministic/random (Monte Carlo)� Dynamic/static

� Goals realized via DOE:� Sensitivity analysis (‘what if’)� Uncertainty analysis (risk)� Optimisation

� DOE: 4 Ph.D. projects

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References

� Undergraduate & graduate course on simulation:Law & Kelton (2000, 760 pages): 80,000 copies sold

� Simulation software: Many products:Swain (2003): 6th survey

� Arena software:Kelton et al. (2004, 600 pages), 3d version

� Design & analysis of simulation:See my web site for nearly 200 publications

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