When should I use simulation?

Prof. Brian Harrington

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

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

Agenda

• Manufacturing issues • Different types of simulation • Using Math • Using Excel/Monte Carlo simulation • Using Discrete Event Simulation • Simulation for Six Sigma • Q&A

Manufacturing Dilemma

• Any product development process involves extensive prototyping;

• Yet, costly manufacturing production systems are typically not prototyped

Simulation in Manufacturing

• System Design • Operational Procedures • Performance Evaluation

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.

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

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!

Agenda

• Manufacturing issues • Different types of simulation • Using Math • Using Excel/Monte Carlo simulation • Using Discrete Event Simulation • Simulation for Six Sigma • Q&A

Why Simulation?

• Competition drives the following: • Leaner production environment • Shorter product development cycles • Narrower profit margins • Flexible Manufacturing (1 Facility, 1

Process, Multiple Models)

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

Simulation Overview

System Model

Deterministic Stochastic

Static Dynamic Static Dynamic

Continuous Continuous Discrete Discrete

DES

Monte Carlo

Differential equations

Queuing Theory

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

Agenda

• Manufacturing issues • Different types of simulation • Using Math • Using Excel/Monte Carlo simulation • Using Discrete Event Simulation • Simulation for Six Sigma • Q&A

A Queuing System

Jockeying

Queue

Queue

Reneging

Service Mechanism

Queue Structure Service Process

Arrival Process

Balking

Serv

ed C

usto

mer

s

Input Source

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.

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

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.

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!

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

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()

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?

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)

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.

Agenda

• Manufacturing issues • Different types of simulation • Using Math • Using Excel/Monte Carlo simulation • Using Discrete Event Simulation • Simulation for Six Sigma • Q&A

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

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

Manufacturing Plant Example

Plant Example cont…

How do you simulate an entire plant?

DES Building Blocks

The 8 Core Building Blocks: Start Point, Queue, Activity, Conveyor, Resource, and End Point. Then the Logical aspect Labels & Conditional Statements.

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.

…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.

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

Agenda

• Manufacturing issues • Different types of simulation • Using Math • Using Excel/Monte Carlo simulation • Using Discrete Event Simulation • Simulation for Six Sigma • Q&A

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!

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)

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.

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”

Graph your Data!

One of the most basic steps in 6-Sigma; Exploit your data!

Stat-Fit for SIMUL8

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”.

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

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.

Q & A