when should i use simulation? - institute of industrial ... 11-5-2013.pdf · manufacturing...

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 Manufacturing Consultant

- Teaches Stochastic Systems at Wayne State University

- 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



• Using Math




• 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 ContinuousDiscrete 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



• Using Math




• Q&A

A Queuing System

Jockeying

Queue

Queue

Reneging

ServiceMechanism

Queue Structure Service Process

ArrivalProcess

Balking

Serv

ed

Cu

sto

mers

Input Source

Queuing ConceptsRelationships for M/M/C

P = o

1

ΣΣΣΣn=0

C-1 (λλλλ/µµµµ)n

n!

c+ (λλλλ/µµµµ)

c!( )cµµµµ

cµ µ µ µ - λλλλ

L = q

(λλλλ/µµµµ)

2

c(λ µ)λ µ)λ µ)λ µ) oP

(c – 1)! (cµµµµ – λλλλ)

λ = mean arrival rateµ= mean service rateC = number of parallel serversρ = utilization

These are messy to calculate by hand, but are very easy with appropriate software or a table.

Queuing ConceptsA Comparison of Single Server Models

L = q

2(1 - λλλλ/µµµµ)

2λ λ λ λ σ + (λσ + (λσ + (λσ + (λ/µ)µ)µ)µ)

22

L = q

2(1 - λλλλ/µµµµ)

2(λ(λ(λ(λ/µ)µ)µ)µ)

L = q

(1 - λλλλ/µµµµ)

(λ(λ(λ(λ/µ)µ)µ)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!

Agenda



• Using Math




• Q&A

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 SimulationA 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



• Using Math




• 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



• Using Math




• 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.

43

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 dynamicaspects of time are critical!

• Discrete Event Simulation is a user friendly tool that is built on the foundations of queuing theory & statistical sampling.

when should i use simulation? - institute of industrial ... 11-5-2013.pdf · manufacturing...

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