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When should I use simulation?
Prof. Brian Harrington
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Introductions
Brittany Hagedorn, MBA, CSSBB - SIMUL8’s Healthcare Lead
for North America - Experienced Six
Sigma Blackbelt and Healthcare Consultant
- Here to answer your questions at the end
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Introductions
Brian Harrington, CSSBB - 20 years in simulation at
Ford Motor Company - Experienced Six
Sigma Blackbelt and Simul8 Manufacturing Consultant
- Director of MTN-SIM, a simulation specialist consulting firm
- Our presenter for today
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Agenda
• Manufacturing issues • Different types of simulation • Using Math • Using Excel/Monte Carlo simulation • Using Discrete Event Simulation • Simulation for Six Sigma • Q&A
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Manufacturing Dilemma
• Any product development process involves extensive prototyping;
• Yet, costly manufacturing production systems are typically not prototyped
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Simulation in Manufacturing
• System Design • Operational Procedures • Performance Evaluation
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System Design
• Plant Layout • Effects of introducing new equipment • Location and sizing of inventory buffers • Location of inspection stations • Optimal number of carriers, pallets • Resource planning • Protective capacity planning
Biggest Bang for the Dollar! Contains Operational Procedures &
Performance Metrics.
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Operational Procedures
• Production Scheduling - Choice of scheduling and dispatching rules
• Control strategies for material handling equipment
• Shift patterns and planned downtime • Impact of product variety and mix • Inventory Analysis • Preventative maintenance on equipment
availability Continuous Improvement
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Performance Evaluation
• Throughput Analysis (capacity of the system, identification of bottlenecks); Jobs per Hour
• Time-in-System Analysis • Assessment of Work-in-process (WIP)
levels • Setting performance measure standards;
OEE If you can measure it, you can manage it!
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Agenda
• Manufacturing issues • Different types of simulation • Using Math • Using Excel/Monte Carlo simulation • Using Discrete Event Simulation • Simulation for Six Sigma • Q&A
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Why Simulation?
• Competition drives the following: • Leaner production environment • Shorter product development cycles • Narrower profit margins • Flexible Manufacturing (1 Facility, 1
Process, Multiple Models)
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Types of Simulation
• Mathematical Modeling – e.g. Queuing Theory
• Monte Carlo Simulation – e.g. Excel based models
• Discrete Event Simulation – e.g. Using simulation software
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Simulation Overview
System Model
Deterministic Stochastic
Static Dynamic Static Dynamic
Continuous Continuous Discrete Discrete
DES
Monte Carlo
Differential equations
Queuing Theory
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Question Time:
Which of the following Simulation techniques do you use: 1. Math, Queuing Theory 2. Excel Based, Monte Carlo 3. Discrete Event Simulation 4. None
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Agenda
• Manufacturing issues • Different types of simulation • Using Math • Using Excel/Monte Carlo simulation • Using Discrete Event Simulation • Simulation for Six Sigma • Q&A
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A Queuing System
Jockeying
Queue
Queue
Reneging
Service Mechanism
Queue Structure Service Process
Arrival Process
Balking
Serv
ed C
usto
mer
s
Input Source
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Queuing Concepts Relationships for M/M/C
P = o 1
Σ n=0
C-1 (λ/µ) n
n!
c + (λ/µ)
c! ( ) cµ
cµ - λ
L = q (λ/µ)
2
c (λ µ) o P
(c – 1)! (cµ – λ)
λ = mean arrival rate µ= mean service rate C = number of parallel servers ρ = utilization
These are messy to calculate by hand, but are very easy with appropriate software or a table.
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Queuing Concepts A Comparison of Single Server Models
L = q 2(1 - λ/µ)
2 λ σ + (λ/µ) 2 2
L = q 2(1 - λ/µ)
2 (λ/µ)
L = q (1 - λ/µ) (λ/µ) 2
M/G/1 M/D/1 M/M/1
Note that M/D/1 is ½ of M/M/1
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Benefits & Common Uses
Proven mathematical models of queuing behavior; the underlying framework of more comprehensive models. • Computer Networks – data buffering before
loss of data transmission • Healthcare – optimizing staffing levels
according to patient arrivals • Traffic & Parking lots – Traffic lights, toll booths • Service Industry – Number of servers, check-
outs, lanes, ATM machines, etc.
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Limitations on Queuing Models
• What if: – we don’t have one of these basic models? – we have a complex system that has segments
of these basic models and has other segments that do not conform to these basic models?
• Then – simulate!
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Excel Based Simulations
• Uses Data Table functions • Each Row might be one iteration of a simulation • Each Col is a random variable generated in the
simulation • RAND(), VLOOKUP(), COUNTIF(), NORMINV() • Calculation & Iteration • >>> Using VBA to bring in Probability functions
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Monte Carlo Simulation
• Named after the gaming tables of Monte Carlo • Also referred to as a Static Simulation Model in
that it is a representation of a system at a particular point in time
• In contrast, a Dynamic Simulation is a representation of a system as it evolves over time
• Might be accomplished using Excel and the Random()
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Monte Carlo Simulation A Simple Example
Day RN Demand UnitsSold
Units Unsold
Units Short
Sales Rev
Returns Rev
Unit Cost
Good Will
Profit $
1 10 16 16 2 0 4.80 0.16 2.70 0.00 2.26 2 22 16 16 2 0 4.80 0.16 2.70 0.00 2.26 3 24 17 17 1 0 5.10 0.08 2.70 0.00 2.48 4 42 17 17 1 0 5.10 0.08 2.70 0.00 2.48 5 37 17 17 1 0 5.10 0.08 2.70 0.00 2.48 6 77 18 18 0 0 5.40 0.00 2.70 0.00 2.70 7 99 20 18 0 2 5.40 0.00 2.70 0.14 2.56 8 96 20 18 0 2 5.40 0.00 2.70 0.14 2.56 9 89 19 18 0 1 5.40 0.00 2.70 0.07 2.63 10 85 19 18 0 1 5.40 0.00 2.70 0.07 2.63
Avg 2.50 Where do these numbers come from?
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Benefits & Common Uses
Proven technique that captures random behavior (at a specific point in time); can go further than mathematical solutions. • Business risk assessment
– Demand & Profit • Sizing of a market place
– Consumption rate • Project schedules (best case, worst case)
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Limitations & Disadvantages
• Stochastic, but static! Usually the time evolution of a manufacturing system is significant!
• Excel based models, soon start to use VBA, and become very complicated
• Might require 1000’s of iterations; Data Tables become slow
• Difficult to communicate results to management.
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Agenda
• Manufacturing issues • Different types of simulation • Using Math • Using Excel/Monte Carlo simulation • Using Discrete Event Simulation • Simulation for Six Sigma • Q&A
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Benefits of using DES Simulation
• Mathematical & Excel based models only go so far
• Less difficult than mathematical methods • Adds lot of “realism” to the model. Easy to
communicate to end users and decision makers • Time compression • Easy to “scale” the system and study the effects • User involvement results in a sense of
“ownership” and facilitates implementation
Sim Tree
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Manufacturing Models
• The element that the system evolves over time is important
• Contain several complicated queuing systems • Internal process steps are significant to achieve
the desired result • Conditional build signals (Batch, In-Sequence) • Several sources of stochastic
behavior • Contain several shared
resources and conditional decisions
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Manufacturing Plant Example
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Plant Example cont…
How do you simulate an entire plant?
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DES Building Blocks
The 8 Core Building Blocks: Start Point, Queue, Activity, Conveyor, Resource, and End Point. Then the Logical aspect Labels & Conditional Statements.
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8 is all you Need
1. Work Item Types: Can represent parts, carriers, signals, phone calls, just about anything that requires a “Label Profile”.
2. Activities: Work Centers, machines, tasks, process steps, anything that requires a “Cycle Time”.
3. Storage Areas: Buffers, de-couplers, banks, magazines, anything that requires a finite space to occupy over time.
4. Conveyors: Moving parts from pt A to pt B; Number of parts & Speed of conveyor.
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…8 is all you Need…
5. Resources: Manpower, crews, forklifts, tugs; anything that require a certain resource to be present.
6. End Pt: Keep track of statistics and free memory!
7. Labels: The attributes of a Work Item. 8. Visual Logic: The ability to create conditional
statements; variables, loops, commands & functions.
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Question Time…
How do you use 6-Sigma techniques within your current role? 1. I don’t use 6-Sigma 2. I use 6-Sigma on specific types of
projects 3. I use 6-Sigma on all my projects 4. I use an integrated toolset which includes
6-Sigma
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Agenda
• Manufacturing issues • Different types of simulation • Using Math • Using Excel/Monte Carlo simulation • Using Discrete Event Simulation • Simulation for Six Sigma • Q&A
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Less is More using 6-Sigma
DES Steps: • Objective, Assumptions, Data Collection, Build Model,
Verify, Validate, Experimentation, Results
DMAIC or DMADV steps: • Define, Measure, Analyze, Improve, Control • Define, Measure, Analyze, Design, Verify
Very similar steps!
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Y=f(x’s) Transfer Function
Six Sigma focuses on Key Input Factors (x’s) to deliver your Response.
All of the x’s can be measured & controlled to increase accuracy & precision of hitting your Target (Y).
System/Process
Trivial Many (N’s)
Vital Few (X’s)
Inputs (N’s & X’s) Output (Y)
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The P-Diagram
The P-Diagram not only helps engineers to define the Key Parameters for a robust design, but also acts as an excellent communication tool for team reviews.
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Leverage Statistical Distributions!
• Curve fit your data! Instead of using lengthy spreadsheets.
• Black-box; entire segments of the model can be collapsed using distributions.
• If using empirical datasets, drop them into a “Probability Profile Distribution”
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Graph your Data!
One of the most basic steps in 6-Sigma; Exploit your data!
Stat-Fit for SIMUL8
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Use Known Distributions
The data collection phase of modeling can be the lengthiest and most time consuming.
Downtime (MTBF & MTTR); such as Exponential & Erlang respectively. Cycle times often use a Fixed distribution; that is the “Design Cycle Time”.
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Steady State
A common data collection error is to capture all data points, and attempt to force them into one distribution.
– Filter out the outliers; usually catastrophic points are outside the scope of the steady state system.
42
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Concluding Thoughts
• Queuing Theory & Monte Carlo Simulations can meet your specific objectives in certain applications. Yet, can become overwhelming when pulling them beyond their intent.
• Most Manufacturing, Healthcare objectives go much further beyond these capabilities. Where the dynamic aspects of time are critical!
• Discrete Event Simulation is a user friendly tool that is built on the foundations of queuing theory & statistical sampling.
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Q & A