TKMM01

Manufacturing simulation

…….…......…...Taylor ED

Starting up ED

• Possible to download to your personal computers via the schools computers

• Works together with Windows 7 but without help files (run in compatibility mode with XP)

Modeling in Taylor ED

• Objects queue up and are serviced by other objects

• Processing is modeled as a (stochastic) time step

• A model according to this principle is called a queuing network model

• The object or building block of Taylor ED:

ATOM

Atom Overview

• Everything is an Atom

• Resources and products are atoms

• Atoms can contain other atoms

• Atoms can be moved from atom to atom

• Atoms can be created and destroyed

• Atoms can inherit behavior from atoms

• 4 Dimensional

• x,y,z location

• time

Application Hierarchy

• Taylor ED

• Logistic suite application

• Library < model | create >

• modeling atoms

• functional atoms

• Model < model | edit >

• model atoms

• functional atoms

Contains mother atoms

Do not modify!!!

Building a Model

• <Model | Create> or

• drag atoms from library into the 2D model layout

• double and/or right click to edit atom parameters

• time always in seconds

• sizes always in meters

Moving around in a view

• Pan:

• press and hold left mouse button

• move around your mouse

• Zoom

• press and hold both left and right mouse button

• zoom in: move your mouse vertically up

• zoom out: move your mouse vertically down

• Change view angle (3D only)

• press and hold right mouse button

• move around your mouse: the center of the view window is your pivot point

Running a Model

• <model | run>, <Shift + F4> or to popup run control

• unlimited speed

• (synchro) real time

• slide control

• custom speed

• press reset and then run to start the simulation

Atom Channel Concept

• <View | Channels> to set the channel view Tip! Use Ctrl+R

• 0..n input/output channels

• Input and output channels are used to pass atoms or to reference to other atoms

• 1 central channel

• Central channel is used for referencing only

• Channels connect:

• one output is connected to one input channel

• multiple channels can be connected to the central channel

• connect to own central channel to delete the connection

Atom Channels

• <View | Channels> to

• connect by dragging mouse from dot to dot

• right click on channel dot: show current connections

• double click on channel dot: interactively change a connection

• create/delete channels by pressing the small plus “+” or minus “-” sign

• red: closed

• green: open

• Channels as arch or line

• <view | set | channels as arch>

• <file | preferences | visualization>

Atom Categories

• Baseclass (mother atoms) Do not change a mothers atom!

• “bare” atom, no functionality

• library atoms are created by adding functionality to a baseclass atom

• Daughter

• inherits functionality from it’s mother (original)

• when creating an atom by dragging, you create a daughter

• Duplicate

• direct copy

• there is no inheritance of functionality between the original and the copy

Library Tree <Shift + F2>

The treeview of the library, also the “Model Layout” window will pop up

• View:

• Atom Info: will display atom help

• VEG: will display Visual Editing Guide

• Tree

• refreshes, collapse or expand the treeview

• VEG

• visual editing guide: displays the active tree atom in a simple layout view

• autoscale, zoom in, zoom out

Model Layout Window

• Edit:

• cut, copy, paste and delete atoms

• set the rotation

• View:

• Channels and grid settings

• override display settings

• up <Ctrl+U> and down <Ctrl+D> in hierarchy (highest is the model level)

Library Contents

Part 1 Part 2 Part 3

Model Tree <Shift + F3>

The tree-view of the complete model

Menu is the same as the library tree plus

• Right or double click:

• atom specific: user interface

• general: standard parameters editing

• label: atom specific labels

• VEG is more useful here

Tip! Use Refresh (F5) to update the Model tree

Tip!

Use understandable names on your atoms

2D/3D View

• 2D view

• Left mouse drag: pan through the view

• Both left and right mouse button drag:

• Up/down: zoom in/out

• 3D view Tip! Shift+F9

• Left mouse drag: pan through the view

• Right mouse drag:

• Left/right: rotate

• Up/Down : view angle

• Both left and right mouse button drag:

• Up/down: zoom in/out

4DScript

4DScript Overview

• 4DScript is a functional language:

• example: 1+2 is written +(2,1)

• 4DScript for everything

• model logic

• create atoms

• control Taylor ED from outside applications

• 4DScript is auto compiled during run-time

• In logistic suite mostly used to manipulate labels in triggers and conditional statements

4DScript Syntax

• 4D Script words have 0..25 parameters

• Parameters between ( )

• Parameters separated by a comma: “ , ”

• Parameters can be:

• values

• strings

• expressions

• (4DScript) Strings always between square brackets “ [ .. ] ”

• Comments between { }

4DScript Syntax

Quick example

setlabel(e1,e2,e3)

e1 – Name of the label, a string within [] brackets

e2 – Value, number -> plain text or string -> within [] brackets

e3 – Reference to location (c,i or reference functions e.g. in(1, c))

setlabel([testlabel], 44, i)

4DScript Syntax

• Multiple lines and spaces

• NOT sensitive in 4DScript

• sensitive label or other naming

• Lower and/or upper case

• NOT sensitive in 4DScript

• sensitive label or other naming

• All brackets must match!

Tip!

Use tabs and new line when writing longer functions e.g.

do(

setlabel([blue], 1,i),

setlabel([green], label([blue],i), i),

setlabel([red],0,i)

)

Instead of writing

do(setlabel([blue],1,i),setlabel([green],label([blue],i),i),setlabel([red],0,i))

Atom Labels

• Also called dynamic database fields

• To read and write data on specific atoms:

• strings

• values

• Setting labels:

• setlabel(e1,e2,e3)

• Sets label e1 (string) of atom e3 (reference) to e2 (string or value)

• 4DScript “sddb” does the same

• Labels do not need to be declared

Atom Labels

• Query labels

• label(e1,e2,{e3})

• Returns label e1 of atom e2

• e3 is optional:

• e3=1 then always value is returned

• e3=2 then always string is returned

• 4DScript “ddb” does the same

• Name of the label is case sensitive

Atom Referencing

• About atom referencing

• In Entry and Exit triggers

• Direct referencing

• Relative referencing

About atom referencing

• Referencing in Taylor ED is like using a pointer

• You need to reference other atoms to:

• get information or data from that atom

• send atoms or messages to other atoms

• To refer to an atom is in general always relative

• Relative referencing is used because:

• it is needed in an object oriented environment !!

• everything is an atom (model, product, machine…)

• it is fast

In Entry/Exit Triggers

• Current “c” & Involved “i”

• ‘c’ is current atom or the atom where the statement is written on

• ‘i’ is the involved atom or the atom that triggered an eventhandler

i

c

Entry/Exit Triggers

Example Trigger on Creation in a Source ATOM

Direct Atom Referencing

• Sometimes Atoms can be referenced directly:

• library = library atom

• model = model atom

• treeatom = currently selected atom in treeview

• animatom = currently selected atom in 2D animation window

• atombyname([e1], e2) = atom with name e1 in container e2

• atombyID(e1, e2) = atom with ID-number in container e2 (e.g. model)

• if tables have aliases you can use the table name direct

Relative Atom Referencing

• All other referencing is relative: start from the atom where statement is written (=c):• first(e1) = first atom inside atom e1• last(e1) = last atom inside atom e1• next(e1) = the atom next of atom e1 in same

container• prev(e1) = the atom previous of atom e1 in same

container• up(e1) = container of atom e1• in(e1,e2) = atom connected to input channel e1 of

atom e2• out(e1,e2) = atom connected to output channel e1 of

atom e2• rank(e1,e2) = atom at position e1 in queue of atom

e2

Atom Statistics

Is available for every atom at any time:

• age - time from creation or reset

• content - current number of atoms contained in an atom

• avgcontent - average number of atoms contained in an atom since reset

• avgstay - average time (sec.) atoms have stayed in an atom since reset

• input - the number of atoms which have entered

• output - the number of atoms which have exited

• status - the state of an atom (see table of atom T029-Statuslist)

• entrytime - time (sec.) at which an atom has entered

Empirical Distribution Atom

• Maximum 50 records per distribution

• Use an alias name to assign the distribution direct

Table Atom

• Indirect referencing use:

• setcell(1,1,123,c)

• cell(1,1,c)

• Direct referencing use

• an alias name has been created eg: times

• settimes(1,1,123)

• times(1,1)

• Column and row 0 are the header columns and rows

• Index out of range will not give an error message, but results in the return of 0

Tip!If you need to create or use large

tables (larger then 100 rows or columns)

use local table instead of linking to excel table. This speeds up the

simulation.

Conditional Statements

• if(e1,e2,{e3})

• e1 = condition

• e2 = true logic

• e3 = false logic, not mandatory => 0 is returned

• and/or allowed in condition

Example: if(comparetext(label([ok],i),[yes]),

negexp(10),

negexp(50)

)

Multiple Statements

• “DO” - statement

• do(e1,do(e1..e25),..e25)

• maximum is 25 parameters

Example:do( setlabel([ok],[yes],i), setlabel([time],negexp(60),i))

4DScript Editor Functionality

Tip!

Use check syntax (F10)

Repeat Statements

• loopuntil(e1,e2,e3)

• e1 = condition

• e2 = statements

• e3 = maximum repetitions

• use ‘count’ for the current number of loops made

• omitting e3 might result in endless loop

Repeat Statements

• repeat(e1,e2)

• e1 = number of repetitions

• e2 = statements

• use ‘count’ for the current number of loops made

repeat(

content(c),

stopatom(rank(count,c))

)

Statistical distributions

Use of statistics:

• Before simulation:

- determine the distributions

- goodness of fit

• During simulation:

- random numbers

- samples from a distribution

• After simulation:

- analysis of results

- reliability

Discrete Distributions

A discrete stochastic variable represents a countable number of possible values.

One particular value has a chance (greater than zero) of occurring.

0

5

10

15

20

25

30

35

40

1 2 3 4 5

chan

ce o

f x=

? i

n %

>

Bernoulli distribution

• Parameters in Taylor ED:

- probability in %

- result1

- result2

• A sample having result1 is equal

to probability,

result2 has a chance of

100% - probability.

Choice between two values: bernoulli(40,6,10)

0

10

20

30

40

50

60

70

6 10

Prob

abilit

y in

% >

Empirical distribution

Product mix, Route choices, Test passed,..

P(x) Value

15% 2

25% 7

20% 10

35% 12

5% 30

In Tayor ED you can use an alias name

0

5

10

15

20

25

30

35

40

2 7 10 12 30

chan

ce o

f x=?

in

%

>

a b x>

dens

ity ƒ

(x)

Continuous Distributions

The chance of a sample, according to a certain distribution, results in a value between ‘a’ and ‘b’, is equal to the dark gray area.

The chance the sample will result in precisely ‘a’, is equal to zero.

Uniform Distribution

• Can be used if the information is global

• uniform(e1,e2)

a x > b

dens

ity ƒ

(x)

Normal Distribution

• Fluctuations around an average

• normal(e1,e2)

x >

dens

ity ƒ

(x)

>

Negative Exponential Distribution

• To model irregular (arrival) processes

• negexp(e1)

0 x >

dens

ity ƒ

(x)

Lognormal Distribution

• Asymmetrical “normal” distrubution

• Repair times and process times

• lognormal(e1,e2)

0 x >

dens

ity ƒ

(x) >

More Distributions

• Continuous:

- Beta

- Gamma

- Triangular

- Weibull

• Discrete:

- Poisson

- Binomial

- Geometric

Typical Waiting Times

Waiting is :

• Time consuming

• Boring

• Expensive

Bottle neck process:

WaitingTime 90%

ProcessTime 10%

Influence Factors

• Fluctuations in arrivals

• Fluctuations in process times

• Priority rules

• Blocking

• Failures

• Availability

• Utilization

Theoretic Waiting Times

• Consider arrivals to be negative exponential distributed

• Define variance coefficient of processes:

• CV = standard deviation ÷ mean

• Two extremities:

• CV=0, constant distribution

• CV=1, chaos, negative exponential distribution

Average waiting time (Pollaczek-Kyntchin):

WT CV PT

12

211

( )( )

,

utilization

Waiting Time versus Utilization

0 10 20 30 40 50 60 70 80 90

Utilization in %

Wai

ting

time

>

low CV

high CV

Shortening Waiting Times

• Lower utilization

• More regular processes

• Parallel processes

• Controlled processing

• Less failures

• Smaller batches

Waiting

Waiting problems are actually waiting distributing problems.

Balance between:

- waiting of workstation

- waiting of products

- waiting of customers

Result Analysis• Shit in is Shit out

• Simulating more or longer, results in more reliable results

Analysis of Terminating Systems

• N different simulation runs => n independent values (new random seeds)

• Calculate confidence interval

Ask yourself if you have to simulate a system like a terminating system. It’s sometimes better to simulate a worst case scenario of the system.

Analysis of Steady State Systems

• When has a steady state been reached ?

• How long is the warm up period ?

Two formal methods:

• N different runs

• One long run divided into sub-runs

Warm-up Period

At the beginning of a simulation the system is normally empty.

0

50

100

150

200

250

300

350

400

0 20 40 60 80 100 120 140 160 180 200 220

Time >

Pro

duct

ion

per

hour

>

The production per hour will have the characteristics of this graph.

N Different Runs

• Determine the warm up period.

• Simulate N different runs; every time the data from the warm-up period is disregarded.

The length of a run and the number of runs in total determine the confidence interval.

If the warm-up period is long, the sub-run method is preferred.

Final Tip!

• Shit in is Shit out! - the result of the simulation is not better then the data you base your simulation on

• Test in small scale - When testing out new functions and atoms construct small systems and test the function there instead of import the new function or atom directly in to your “big” simulation system

• Use understandable names on atoms, labels etc.

• Use the help files or the 4DSkript Command list to understand functions and find new functions

• A simulation is a perfect model of the world, the world is not perfect!

That is all!

Contact information: Kristofer Elo kristofer.elo@liu.se