ACEIT Sys by Site

BOEING is a trademark of Boeing Management Company.Copyright © 2007 Boeing. All rights reserved. ACEIT_Sys_by_Site.ppt |

Modeling Manufacturing Costs with System by Site Wizard

in ACEIT

Karen MourikasAMSE ExperimentationIntegrated Defense SystemsJanuary 2008

Copyright © 2007 Boeing. All rights reserved.

1/25/2008ACEIT_Sys_by_Site.ppt | 2

Overview

Description of ProblemProposed SolutionInput AssumptionsMatrix Functions in ACECost ModelSystem By Site WizardResultsSummary



Description of the Problem



Problem Description

Problem Overview– Analyze a “Messy” Manufacturing Problem with “Messy” Data– Develop a Cost Model to Estimate the Production Cost

Multiple Combinations of InputsVarious Product Performance Capabilities

Principal Requirements of Cost Model– Quickly Adapt to Change of Program Direction

Cost, Schedule, Performance, Supplier Data– Rapidly Assess Different Manufacturing Scenarios

Each with their Own Costs and Benefits

Flexibility is Key!!



The Manufacturing Problem

Requirements– Multiple Components

Combinations of up to 29 Components– Numerous Configurations of Varying Capabilities

Currently 18 ConfigurationsSelected Components Determines Configuration Capabilities

– Variations in Procurement Assumptions Frequently Changing Quantity and Schedule Data

– Inputs from Several Different Suppliers in Diverse FormatsCosts

– Average Lot costs based on Specified Procurement Schedules With and without “Learning”

– Average Unit Costs based on Previous (All) Quantities ProducedPrevious Lot Buy

Different Learning Parameters Applied– Learning Rates, Breaks in Learning, Rotation, Displacement, Loss



Previous Efforts

Original Cost Model Created in Excel– Eventually Translated to ACEIT– Still had Excel Look and Feel

Inputs “Hard Coded”– Only Specific Configurations Included in Model

All Others Excluded (Until Needed)– Could Not Easily Alter Configuration Combinations– Buy Quantities/Schedule Fixed– Same Learning Assumptions Applied to all Components

Previous Quantities, CRC, No Breaks

Model Kept Growing – Bigger and Messier– Each Scenario Included Explicitly

Difficult to Organize Data Time Consuming to Update and/or Maintain Model



Proposed Solution



The Solution

Create Cost Model in ACEIT – Using Matrix Formats, Matrix Functions, and System by Site Wizard

Due to the Principal Requirement

Quickly Adapt to Change of Program Direction

– Frequently Changing Combinations of Components ConfigurationsProcurement Assumptions

– The Need for FlexibilityMultiple Reports Rapid Assessments of Costs and Benefits for Different Scenarios

– Ease of Implementation



Modeling Solution – ACEIT Matrix Functions

Benefits – Easier to Organize and Update Data

ACEIT Inputs in Matrix FormatSame Format as Excel Data File

– More Straightforward to Maintain Model– Inputs flexible

Changing ConfigurationsFrequent Updates to Buy Quantities/Schedule Different Learning Techniques Applied Various Cost Formats

– Model GrowthModel Size Reduced by More than 50%Model Included All Scenarios

– Expanded Reporting CapabilityBuilt-in ReportsACE and POST



Modeling Solution – ACEIT Matrix Functions

Disadvantages– Analyst “Training” Needed to Manipulate Model– Need an Understanding of Matrix Functions

In General Within ACEIT

Advantages Outweigh Disadvantages!



Presentation of the Solution

First, Understand the Theory – What’s going on– What we want to do

Next, Learn Algorithms & Techniques to Apply Theory– How to do it “long hand”

Then, Derive Formulas (can think of them as Shortcuts)– To Simplify Application of Theory– To Reduce Chance of Errors

Finally, Appreciate Shortcut!



Input Assumptions



Buy Quantity Data in Matrix Format

Sample Procurement Assumptions in Matrix Format– Configuration Buy Quantities and Schedules– Frequent and/or Last-Minute Changes– (Partial listing)

Data Stored in Excel Spreadsheet

FY10 FY11 FY12 FY13 FY14 FY15 FY16 FY17 FY18 FY19 FY20Config1 138 178 576 576 601 601 589 596 317 320 305Config2 26 27 66 305 410 617 568 576 662 693 801Config3 78 39 39 39 78 39 138 144Config4 Config5 Config6 24 24 59 52 53 131 610 618 Config7 78 39 39 39 78 39 138 144 39 57 69Config8 12 12 30 26 27 66 305 309 Config9 78 39 39 39 78Config10 Config11 468 234 234 234 468Config12 24 24 24 59 52 53 131 317 320 305 310Config13 13 7 7 7 13 7 23 24 7 10 12Config14

Buy Quantities per Configuration per Year



Input Data into ACE Model

Easy to Insert Excel Matrix into ACE’s Yearly Phasing PageDates From Excel Coincide with Fiscal Years (FYs) in ACEUnique ID of Matrix– M_QTY “M” Stands for “Matrix” ☺

FY10 FY11 FY12 FY13 FY14 FY15 FY16 FY17 FY18 FY19 FY20Config1 138 178 576 576 601 601 589 596 317 320 305Config2 26 27 66 305 410 617 568 576 662 693 801Config3 78 39 39 39 78 39 138 144Config4 Config5 Config6 24 24 59 52 53 131 610 618 Config7 78 39 39 39 78 39 138 144 39 57 69Config8 12 12 30 26 27 66 305 309 Config9 78 39 39 39 78Config10 Config11 468 234 234 234 468Config12 24 24 24 59 52 53 131 317 320 305 310Config13 13 7 7 7 13 7 23 24 7 10 12Config14

Buy Quantities per Configuration per Year



Configuration Data in Matrix Format

Sample Component-Configuration Data in Matrix Format– Some Components Used in All Configurations (Comp 8)– Some Components Not Used in Any Configuration (Comp 17)– Could Change Tomorrow

Data Stored in Excel Spreadsheet– Row Contains Number of Units for All Configurations– Column Contains Components That Define Each Configuration

Config1

Config2

Config3

Config4

Config5

Config6

Config7

Config8

Config9

Config10

Config11

Config12

Config13

Config14

COMP 1 2 1 1 1 2 1 1 1 1 1 2COMP 2 1 1 2 2 2 2 2 1 2 2COMP 3 1 1COMP 4 2 2 2 2 2 1 1COMP 5 3 5 4 4 2 2 2 5 1 1COMP 6 1 1 1 3 2 2 2 1 1COMP 7 1 2 1 2 1 1COMP 8 1 4 4 4 4 2 2 2 2 2 1 1 1 1COMP 9 4 2 2 1 1 1 1 4 4 1COMP 10 2 3 2 2 3 2 2 1 3 1COMP 11 1 1 1 1 1 1 4 4 4 4 2COMP 12 1 1 1 4 4 1 4 1 COMP 13 2 1 1 2 2 2 2 1COMP 14 1COMP 15 1 2 2 2 2 1 1 COMP 16 4 4 2 2 2 2 1 1 1 1 1COMP 17 COMP 18 1 1 1 1 2 1 1 2COMP 19 3 2 2 1 3 1 3 3 2 3COMP 20 2 5 1 1 3 5 4 4

Component - Config Quantity Matrix



Config1

Config2

Config3

Config4

Config5

Config6

Config7

Config8

Config9

Config10

Config11

Config12

Config13

Config14

COMP 1 2 1 1 1 2 1 1 1 1 1 2COMP 2 1 1 2 2 2 2 2 1 2 2COMP 3 1 1COMP 4 2 2 2 2 2 1 1COMP 5 3 5 4 4 2 2 2 5 1 1COMP 6 1 1 1 3 2 2 2 1 1COMP 7 1 2 1 2 1 1COMP 8 4 4 4 4 2 2 2 2 1 1 1COMP 9 4 2 2 1 1 1 1 4 4 1COMP 10 2 3 2 2 3 2 2 1 3 1COMP 11 1 1 1 1 1 1 4 4 4 4 2COMP 12 1 1 1 4 4 1 4 1 COMP 13 2 1 1 2 2 2 2 1COMP 14 1COMP 15 1 2 2 2 2 1 1 COMP 16 4 4 2 2 2 2 1 1 1 1 1COMP 17 COMP 18 1 1 1 1 2 1 1 2COMP 19 3 2 2 1 3 1 3 3 2 3COMP 20 2 5 1 1 3 5 4 4


Input Another Matrix into ACE Model

Easily to Incorporate Excel Data as Matrix in Yearly Phasing Page“Ignore” FY Columns in ACE– Data Not Associated with Particular Years– But Notice the Column Headers

Unique ID of Matrix– M_CONF



Combining Input Data

So Far We Have– Configuration Buy Quantity Matrix– Component-Configuration Matrix

We Need to Know The Number of Components in Each Year– In Other Words, the Component Buy Quantities– A Combination of the Above Two Matrices

Formed via Matrix Multiplication

* Year

Com

pone

nts

Cost Element FY 2010 FY 2011 FY 2012 FY 2013 FY 2014 FY 2015 COMP 1 402 516 1347 1791 1991 2127 COMP 2 253 326 721 925 1002 917 COMP 3 24 24 59 52 53 131 COMP 4 313 387 1219 1211 1269 1341 COMP 5 229 223 363 744 602 913 COMP 6 437 361 834 1143 1437 1552 COMP 7 190 232 708 1186 1421 1835 COMP 8 410 375 598 1978 2329 3195 COMP 9 805 928 2616 3386 3948 4196 COMP 10 697 657 1606 2420 3123 3585

Component Buy Quantities

=

Configuration

Com

pone

nts Config

1Config

2Config

3Config

4Config

5Config

6COMP 1 2 1 1 1 2 1COMP 2 1 1 2 COMP 3 1COMP 4 2 2 2COMP 5 3 5 4 4COMP 6 1 1 1COMP 7 1 2 COMP 8 1 4 4 4 4 2COMP 9 4 2 2 1COMP 10 2 3 2 2


Con

figur

atio

n

Year

Buy Quantities per Configuration per YearFY10 FY11 FY12 FY13 FY14 FY15

Config1 138 178 576 576 601 601Config2 26 27 66 305 410 617Config3 78 39 39Config4 Config5 Config6 24 24 59 52 53 131



The Number of Components in Each Year Required – Components Buy Quantities

Calculated within ACE Using Matrix Function MatColRow()– Based on Configuration Procurement Quantities and Component Configuration Matrices– Unique ID

M_SSQ (Sub System Quantities)Sub Systems = Components

Component Buy Quantity Matrix in ACE



Matrix FunctionsIn ACE



Matrix Function – MATCOLROW()

MatColRow() Function– MATrix COLumn ROW– This function performs a type of vector multiplication for column by

row calculation. It returns the dot product of a row in one matrix with the column in another matrix. (from ACE Help)

– Number of Columns in First Matrix Must Equal Number of Rows in Second Matrix

Order of Matrices ImportantBe Careful How to Define Matrices

*

Configuration

Com

pone

nts Config

1Config

2Config

3Config

4Config

5Config



Configuration

Com

pone

nts Config

1Config

2Config

3Config

4Config

5Config



Con

figur

atio

n

Year


Config1 138 178 576 576 601 601Config2 26 27 66 305 410 617Config3 78 39 39Config4 Config5 Config6 24 24 59 52 53 131C

onfig

urat

ion

Year



10 X 6 6 X 6



Matrix Function – MATCOLROW()

MatColRow ( N_Rows, @Quantity, @Config, ColRow )– Multiplies Row in Configuration Matrix by a Column in Quantity Matrix– Recall: Order of Matrices is Important

@Config is the “First” Matrix@Qty is the “Second” Matrix

– N_Rows Represents the Number of Rows in the Quantity matrix Columns in the Configuration matrix

– ColRow Represents the Row of the Configuration Matrix

*

Configuration

Com

pone

nts Config

1Config

2Config

3Config

4Config

5Config



Configuration

Com

pone

nts Config

1Config

2Config

3Config

4Config

5Config



Con

figur

atio

n

Year


Config1 138 178 576 576 601 601Config2 26 27 66 305 410 617Config3 78 39 39Config4 Config5 Config6 24 24 59 52 53 131C

onfig

urat

ion

Year



@Config @Qty



How MATCOLROW() Works (My Interpretation)

MatColRow (18, @M_QTY, @M_CONF,1)– Populates One Row of M_SSQ

FY2010

FY2010FY2011

FY2011



Populate SubSystem Quantities Matrix

For Each Component (29) – Populate M_SSQ using MatColRow()– Code MatColRow() 29 times for each row (component)

But Instead of – MatColRow (18, @M_QTY, @M_CONF,1)– MatColRow (18, @M_QTY, @M_CONF,2)– MatColRow (18, @M_QTY, @M_CONF,3)– Etc

Make it Generic– MatColRow (18, @M_QTY, @M_CONF, IVal)

Include DEC Column with Index IVal– Very Easy to Replicate

No Changes to Equation – Row Repeated 29 times

IVal Represents Row (Component) in Config MatrixIndexed from 1 to 29



MatColRow() and DEC Representation

Each Equation – Exactly the Same

Only Thing Different– The Index

Easy to Modify/Maintain– Replicate Rows

To View Matrix– Run BY Phased Rpt



How M_SSQ Matrix Used in Model

Now That We Have a Matrix of Component Quantities– What Do We DO with it?

M_SSQ Matrix Used To Calculate– Component Costs

Total and Average CostsUsing Learning or Cost Reduction Theory As Buy Quantities

– Configuration CostsTotal and Average CostsWith SiteCost() Function



Cost Model:Learning Assumptions

And M_SSQ



Learning/Cost Reduction Assumptions

Curve Theory and Slopes– Unit Theory with Curve (CRC) Slope of 90, 95, or 100

Prior Quantities Included Buy Quantities– M_SSQ# (SubSystem Quantities)

Matrix Calculated with MatColRow() Functions– Number of Components for Procured Configurations Per Year

Reference Cost Type– Average Unit Cost Based on All Prior Quantities– Average Lot Total Cost Based on Prior Lot Quantity

Break Data (for Each Break)– Unit Number or End of Fiscal Year– Slope Change (Rotation)– Displacement (Percent)– Loss (Number of Units)



Learning Page in ACE



Costs Based on Learning Assumptions

Lot Total Cost Per Component Per Year– Incorporates All Learning Assumptions from Previous Page– Results from Yearly Phasing Report– Unique Id

M_LTC



Cost ModelSiteCost() Function

And M_SSQ



SiteCost() Function

SiteCost() Function– Allocates Annual Costs for Multiple Subsystems (Components) to Multiple Sites

(Configurations)– Calculates lot total cost for each site or platform. Uses several matrices of

subsystem configuration, cost, and schedule. (from ACE Help)

SiteCost ( N_Subs, @Qty, @Conf, @SSQ, @SS_LTC, Site_Num )– N_Subs Represents the Number of Components– Site_Num Identifies the Configuration – @ Indicates a Matrix

Described on next page



SiteCost() Matrix Descriptions

SiteCost(29, @M_QTY, @M_CONF, @M_SSQ, @M_LTC, IVAL)– 29 Components (Subsystems)– M_Qty

Consists of Configuration Procurement Quantities– M_Conf

Contains Component-Configuration Data – M_SSQ

Contains Number of Components in Each Year – M_LTC

Stores the Lot Total Cost by Subsystem per Year– IVal

Identifies the Configuration to be AssessedIndexed from 1 to 18



Assess Cost for Each Configuration

For Each Configuration (18) – Execute SiteCost() to Assess Cost for each Configuration

But Instead of – SITECOST(29, @M_QTY, @M_CONF, @M_SSQ, @M_LTC, 1)– SITECOST(29, @M_QTY, @M_CONF, @M_SSQ, @M_LTC, 2)– SITECOST(29, @M_QTY, @M_CONF, @M_SSQ, @M_LTC, 3)– Etc

Make it Generic– SITECOST(29, @M_QTY, @M_CONF, @M_SSQ, @M_LTC, Ival)

Use Same DEC Column as before with Index IVal– Very Easy to Replicate

No Changes to Equation – Row Repeated 18 times

IVal Represents Particular Configuration



Each Equation – Exactly the Same

Only Thing Different– The Index

Easy to Maintain– Replicate Rows

To View Matrix– Run Phased Rpt

SiteCost() Representation and Results



Cost ModelCost Data Format



Prior Quantities PhaseAverage Unit Cost EMD Displacement Unit/Yr COMP 1 547 14500 0.80 2009 COMP 2 244 9800 0.70 2009 COMP 3 256 3200 0.85 2009 COMP 4 52 960 0.75 2009

Prior Lot PhaseStart at Unit 51 EDM

COMP 5 168 1500 COMP 6 242 2100 COMP 7 218 400 COMP 8 96 800 COMP 9 51 5400 COMP 10 51 900 COMP 11 72 9200 COMP 12 78 350 COMP 13 52 6000 COMP 14 345 3000 COMP 15 76 250 COMP 16 225 9800

Prior Quantities PhaseLRIP1 LRIP2 FRP1 FRP2 FRP3

COMP 17 107 2000.0 2000.0 1800.0 1800.0 1600.0 COMP 18 107 4500.0 4500.0 4500.0 3100.0 3100.0 COMP 19 46 1600.0 1600.0 1400.0 1330.0 1300.0 COMP 20 46 300.0 300.0 300.0 200.0 200.0 COMP 21 83 500.0 500.0 300.0 300.0 300.0 COMP 22 83 6700.0 6700.0 6700.0 5200.0 5200.0 COMP 23 7 1500.0 1500.0 1500.0 1500.0 1500.0 COMP 24 5 6400.0 6400.0 3200.0 3200.0 3200.0 COMP 25 74 150.0 150.0 150.0 150.0 150.0 COMP 26 57 3200.0 3200.0 3200.0 2200.0 2200.0 COMP 27 7 2100.0 2100.0 2100.0 1500.0 1500.0 COMP 28 16 430.0 430.0 320.0 320.0 320.0 COMP 29 17 8800.0 8800.0 8800.0 7400.0 7400.0

Unit Costs Per Phase Per Component

Average Unit Cost

Break

Input Cost Data Formats

Learning Assumptions

Phases

Prior QuantitiesCost Format

Cost Data from Different Suppliers

in Diverse Formats

Supplier Data



Storing Cost Data as Matrix

Cost Data Stored in Matrix – On Yearly Phasing Page– Format of Components 17 – 29 Lends itself to Matrix Input in ACE

Only Components 17 – 29 in MatrixOther Components Input into Equation/Throughput Column

Column Headers– Ignore Fiscal Year Headers– Matrix Column Headers Describe Phases

LRIP1, LRIP2, etcPhases Associated with Fiscal Years

– But not FYs Directly Above



Case and Matrix Functions to Assign Lot Costs

Assign Average Unit Lot Cost to Particular PhaseCase Statement

– Used To Select Cost Associated with Each Phase (or Year)– Five Phases

LRIP1, LRIP2, FRP1, FRP2, FRP 3

Case ( Selector, CaseValue1, ..., CaseValueN ) – Selector Ranges from 1 to 5 Corresponding to Five Phases– Value of the Case Represented by MatVal() Function

Selects Particular Item in Cost Matrix

Case(CHOICE_5, MatVal(@COMP_$_PH,IVAL,PH1),MatVal(@COMP_$_PH,IVAL,PH2), …MatVal(@COMP_$_PH,IVAL,PH5))



Appropriate Cost Selected by MatVal() Function

Case(CHOICE_5, MatVal(@COMP_$_PH,IVAL,PH1),…MatVal(@COMP_$_PH,IVAL,PH5))

MatVal() Function Returns the Cost Value from the Cost Matrix – MatVal ( @Matrix, Row, Col )– Matrix = COMP_$_PH– Row Represented by Index IVal– Column Represented by Variable PH#, where # Ranges from 1 to 5

Example– MatVal(@COMP_$_PH, 6, 4)– Row = Ival = 6– Column = PH4 = 4 = FRP2



System By Site Wizard(The Shortcut)



System by Site Wizard sets up Matrices and MatColRow and SiteCost Functions within the Model

Easier to Model with System by Site Wizard



System by Site Wizard

Creates Input Matrices– Buy Quantities– Component-Configuration

Generates Equations– MatColRow()

To Create M_SSQ Matrix Number of Components for all Configurations per Year

– SiteCost()To Create Cost per Configuration per Year

Populates Learning Page– Cost Data– Learning Parameters



System by Site Wizard : Step 1

Enter Buy Schedule– Start and End Years

Descriptive Label – Used as Prefix to Matrices– I chose “M_” for “Matrix”




Configuration by Year Matrix– Sites = Configurations

Configuration Buy Quantities



Component Unit Prices– Appropriation– Unit Price– Base Year– Units

Learning Data– Slope– Theory– Prior Quantities– Reference Cost Type

Can be Variables




Component by Site Matrix– Sites = Configurations




System By Site Model Results

Buy Quantities

Component-Configurations



System By Site Model Results

MatColRow(): Component Quantities

SiteCost(): Cost per Config

Cost and Learning Data



Results



Reports from POST

Data– Component Costs– Configuration Costs– Total/Average/Phased– Learning Effects

Reports– Time Phased– Pie Charts– Sand Charts– Drill down



Reports from POST: Pie Charts

Total $ by Component COMP 1

COMP 2

COMP 3

COMP 4

COMP 5

COMP 6

COMP 7

COMP 8

COMP 9

COMP 10

COMP 11

COMP 12

COMP 13

COMP 14

COMP 15

COMP 16

COMP 17

COMP 18

COMP 19

COMP 20

COMP 21

COMP 22

COMP 23

COMP 24

COMP 25

COMP 26

COMP 27

Total $ by Configuration

Config1 Config2 Config3 Config4 Config5 Config6 Config7 Config8 Config9 Config10 Config11 Config12 Config13 Config14 Config15 Config16 Config17 Config18

• Most Expensive Component (Total Cost)

• Most Expensive Configuration (Total Cost)

. ..



Average Component Costs

0.000

0.020

0.040

0.060

0.080

0.100

0.120

0.140

COMP 1COMP 2COMP 3COMP 4COMP 5COMP 6COMP 7COMP 8COMP 9COMP 10COMP 11COMP 12COMP 13COMP 14COMP 15COMP 16COMP 17COMP 18COMP 19COMP 20COMP 21COMP 22COMP 23COMP 24COMP 25COMP 26COMP 27COMP 28COMP 29

Uni

tsReports from POST: Drill Down

Average Configuration Costs

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.400

0.450

Con

fig1

Con

fig2

Con

fig3

Con

fig4

Con

fig5

Con

fig6

Con

fig7

Con

fig8

Con

fig9

Con

fig10

Con

fig11

Con

fig12

Con

fig13

Con

fig14

Con

fig15

Con

fig16

Con

fig17

Con

fig18

Uni

ts

• Most Expensive Configuration (Average Cost)

.

• Most Expensive Component (Average Cost)

..



Reports from POST: Sand Charts Phased

Phased Total Cost per Component

$0.

$50.

$100.

$150.

$200.

$250.

$300.

2010 2013 2016 2019 2022

BY2

008

$M

COMP 29COMP 28COMP 27COMP 26COMP 25COMP 24COMP 23COMP 22COMP 21COMP 20COMP 19COMP 18COMP 17COMP 16COMP 15COMP 14COMP 13COMP 12COMP 11COMP 10COMP 9COMP 8COMP 7COMP 6COMP 5COMP 4COMP 3COMP 2COMP 1

Phased Total Manufacturing Costper Configuration

$0.

$50.

$100.

$150.

$200.

$250.

$300.

2010 2013 2016 2019 2022

BY20

08 $

M

Config18Config17Config16Config15Config14Config13Config12Config11Config10Config9Config8Config7Config6Config5Config4Config3Config2Config1

•Largest Procurement Year

. • Most Expensive Component (Total Cost)

.

• Most Expensive Configuration (Total Cost)

.

.



Reports from POST: Phased

T im e P h a s e d R e p o rt fo r B a s e lin e in M fg D e m o R 3 .a c e itC o s ts in B Y2 0 0 8 $ M, F rid a y, 1 4 S e p te m b e r 2 0 0 7 , 1 2 :0 6 p m

T im e P h a se d R e su l ts fo r B a se l in e

W B S To ta l 20 10 20 11 20 12 201 3 201 4 2 015A verag e M an u fac tu ring C os ts 0 .810 0 .0 81 0 .0 75 0 .06 7 0 .05 9 0 .05 6 0 .05 4

C O M P 1 0 .119 0 .0 11 0 .0 11 0 .01 0 0 .00 9 0 .00 8 0 .00 8C O M P 2 0 .068 0 .0 07 0 .0 06 0 .00 6 0 .00 5 0 .00 5 0 .00 5C O M P 3 0 .018 0 .0 02 0 .0 02 0 .00 2 0 .00 2 0 .00 2 0 .00 2C O M P 4 0 .007 0 .0 01 0 .0 01 0 .00 1 0 .00 1 0 .00 1 0 .00 0C O M P 5 0 .013 0 .0 01 0 .0 01 0 .00 1 0 .00 1 0 .00 1 0 .00 1C O M P 6 0 .019 0 .0 02 0 .0 02 0 .00 2 0 .00 1 0 .00 1 0 .00 1C O M P 7 0 .004 0 .0 00 0 .0 00 0 .00 0 0 .00 0 0 .00 0 0 .00 0C O M P 8 0 .006 0 .0 01 0 .0 01 0 .00 1 0 .00 0 0 .00 0 0 .00 0C O M P 9 0 .035 0 .0 04 0 .0 03 0 .00 3 0 .00 3 0 .00 2 0 .00 2C O M P 10 0 .006 0 .0 01 0 .0 01 0 .00 1 0 .00 0 0 .00 0 0 .00 0C O M P 11 0 .069 0 .0 08 0 .0 06 0 .00 6 0 .00 5 0 .00 5 0 .00 5C O M P 12 0 .003 0 .0 00 0 .0 00 0 .00 0 0 .00 0 0 .00 0 0 .00 0C O M P 13 0 .044 0 .0 05 0 .0 04 0 .00 4 0 .00 3 0 .00 3 0 .00 3C O M P 14C O M P 15 0 .002 0 .0 00 0 .0 00 0 .00 0 0 .00 0 0 .00 0 0 .00 0C O M P 16 0 .075 0 .0 08 0 .0 07 0 .00 6 0 .00 6 0 .00 5 0 .00 5C O M P 17C O M P 18 0 .049 0 .0 05 0 .0 05 0 .00 5 0 .00 3 0 .00 3 0 .00 3C O M P 19 0 .019 0 .0 02 0 .0 02 0 .00 1 0 .00 1 0 .00 1 0 .00 1C O M P 20 0 .003 0 .0 00 0 .0 00 0 .00 0 0 .00 0 0 .00 0 0 .00 0C O M P 21 0 .005 0 .0 01 0 .0 01 0 .00 0 0 .00 0 0 .00 0 0 .00 0C O M P 22C O M P 23 0 .021 0 .0 02 0 .0 02 0 .00 2 0 .00 2 0 .00 2 0 .00 1C O M P 24 0 .052 0 .0 06 0 .0 06 0 .00 3 0 .00 3 0 .00 3 0 .00 3C O M P 25 0 .002 0 .0 00 0 .0 00 0 .00 0 0 .00 0 0 .00 0 0 .00 0C O M P 26 0 .033 0 .0 03 0 .0 03 0 .00 3 0 .00 2 0 .00 2 0 .00 2C O M P 27 0 .023 0 .0 02 0 .0 02 0 .00 2 0 .00 2 0 .00 2 0 .00 1C O M P 28 0 .005 0 .0 00 0 .0 00 0 .00 0 0 .00 0 0 .00 0 0 .00 0C O M P 29 0 .111 0 .0 09 0 .0 09 0 .00 9 0 .00 7 0 .00 7 0 .00 7

R ow s F ilte r Ba se Ye a r C a s eY ears S how P rio r/C om p le te

Average Manufactuing CostsOver Time

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

0.080

0.090

2010 2013 2016 2019 2022

Units Baseline

• Average Component CostsOver Time

• Time Phased

• Phased Line



Reports from POST: Phased Line

• Average Component Costs• Different CRC/Learning Parameters

Comp 6

0.000

0.000

0.000

0.001

0.001

0.001

0.001

0.001

0.002

0.002

0.002

2010 2013 2016 2019 2022

Units Baseline

Comp 1

0.000

0.002

0.004

0.006

0.008

0.010

0.012

2010 2013 2016 2019 2022

Uni

ts

Baseline

Comp 3

0.000

0.001

0.001

0.002

0.002

0.003

0.003

2010 2013 2016U

nits

Baseline

Comp 27

0.000

0.001

0.001

0.002

0.002

0.003

2010 2013 2016 2019 2022

Units Baseline



Summary



Summary

Estimate Production Cost of “Messy” Data– Developed a Flexible Cost Model

– Applied Matrix Capabilities

– Employed System By Site Wizard

– Reviewed Types of Reports

Benefits

Quickly Adapt to Change of Program Direction

Input Data & Functions

The Shortcut

Analysis

Quickly Assess Different Scenarios

More Manageable Model

Have Fun!



Backup



Solution Presentation – First Derivatives Example

Recall First Derivatives from Calculus– “the derivative of a function at the value ,

is the slope of the line tangent to the graph of at the point .”*– instantaneous rate of change

marginal cost = rate of change of cost with respect to the number of units purchased

Definition of First Derivative– (based on set of assumptions not shown)

0xf))(,( 00 xfx

xxxxfxxfxf

x −Δ+−Δ+

=→Δ )(

)()(lim)('0

*Grossman, Stanley I, Calculus

Function defined on an open intervalcontaining the point . Limit below exists and is finite.

f

0x

f



Solution Presentation Example – Theory

return

graphical representation of epsilon-delta definition of the limit of a function as x approaches a constant



Solution Presentation Example – Apply Theory

Find the Marginal Cost (or derivative) of the Cost function below– The production costs per day for some widget is given by

where x represents the number of units produced

Apply the definition

– And perform algebraic functionsSuch as expand, combine like elements, manipulate, etc

return

f

xxfxxf

xxxxfxxfxf

xx Δ−Δ+

=−Δ+−Δ+

=→Δ→Δ

)()(lim)(

)()(lim)('00

xxxxxxxxxx

x Δ+−−−Δ++Δ+−Δ+−

=→Δ

)0002.001.0102500())(0002.0)(01.0)(102500(lim3232

0

= . . .



For

Solution Presentation Example – Derive Formulas

return

If where n is a positive integer (i.e. 1,2,3,…)

Then 1)(')(

−=

=n

n

nxxfxxf

Formula Shortcut

f

xxxxxxxxxx

x Δ+−−−Δ++Δ+−Δ+−

→Δ

)0002.001.0102500())(0002.0)(01.0)(102500(lim3232

0

'f

Shortcut

- Instead of

- Use the



Solution Presentation Example – Appreciate Formulas

return

Find the marginal cost when the number of units produced is– 200, 300, and 400

Apply the

– If number of units = 200Marginal cost of 201st unit = ~= $10

– If number of units = 300Marginal cost of 301st unit ~= $38

– If number of units = 400Marginal cost of 401st unit ~=78

Formula

2)200(0006.0)200(02.0)200(10 +−−


1/25/2008Filename.ppt | 64

ACEIT Sys by Site

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