26922810 Excel and Excel QM Examples

Program Name Source Content

1.3 Pritchett Clock Repair Shop Excel QM Breakeven Analysis

1.4 Pritchett Clock Repair Shop Excel QM Goal Seek

2.1 Expected Value and Variance Excel Expected Value and Variance

2.2 Binomial Probabilities Excel Binomial Probabilities

3.1 Thompson Lumber Excel QM Decision Table

3.5 Bayes Theorem for Thompson Lumber Example Excel Bayes Theorem

4.1 Triple A Construction Company Sales Excel QM Regression

4.2 Jenny Wilson Realty Excel QM Multiple Regression

4.3 Jenny Wilson Realty Excel QM Dummy Variables - Regression

4.4 MPG Data Excel QM Linear Regression

4.5 MPG Data Excel QM Nonlinear Regression

4.6 Solved Problem 4-2 Excel Regression

5.1 Wallace Garden Supply Shed Sales Excel QM Weighted Moving Average

5.2 Port of Baltimore Excel QM Exponential Smoothing

5.3 Midwestern Manufacturing's Demand Excel Trend Analysis

5.4 Midwestern Manufacturing's Demand Excel QM Trend Analysis

5.6 Turner Industries Excel Regression

6.1 Sumco Pump Company Excel QM EOQ Model

6.2 Brown Manufacturing Excel QM Production Run Model

6.3 Brass Department Store Excel QM Quantity Discount Model

7.2 Flair Furniture Excel Linear Programming

7.4 Holiday Meal Turkey Ranch Excel Linear Programming

7.6 High note sound company Excel Linear Programming

8.1 Win Big Gambling Club Excel Linear Programming

8.3 Fifth Avenue Industries Excel Linear Programming

8.5 Top Speed Bicycle Company Excel Linear Programming

8.6 Goodman Shipping Excel Linear Programming

9.1 High note sound company Excel Linear Programming

9.2 Manufacturing Example Excel Linear Programming

10.1 Executive Furniture Company Excel QM Transportation

10.2 Birmingham Plant Excel QM Transportation

10.3 Fix-It Shop Assignment Excel QM Assignment

11.2 Harrison Electric IP Analysis Excel Integer programming

11.4 Bagwell Chemical Company Excel Integer programming

11.5 Simkin, Simkin and Steinberg Excel Integer programming

11.7 Great Western Appliance Excel Nonlinear programming

11.8 Hospicare Corp Excel Nonlinear programming

11.9 Thermlock Gaskets Excel Nonlinear programming

11.10 Solved Problem 11-1 Excel 0-1 programming

13.1 Crashing General Foundry Problem Excel Crashing

14.1 Arnold's Muffler Shop Excel QM Single Server (M/M/1) system

14.2 Arnold's Muffler Shop Excel QM Multi-Server (M/M/m) system

14.3 Golding Recycling, Inc. Excel QM Constant Service Rate (M/D/1)

14.4 Department of Commerce Excel QM Finite population queue

15.2 Harry's Tire Shop Excel Simulation (inventory)

15.3 Generating Normal Random Numbers Excel Random #s and Frequency

15.4 Port of New Orleans Barge Unloadings Excel Simulation (waiting line)

15.5 Three Hills Power Company Excel Maintenance Simulation

16.4 Three Grocery Example Excel Markov Analysis

16.5 Accounts Receivable Example Excel Fundamental Matrix & Absorbing States

17.1 ARCO Excel p-Chart Analysis

Module

M1.1 AHP Excel

M5.1 Matrix Multiplication Excel

Dummy Variables - Regression

Constant Service Rate (M/D/1)

Fundamental Matrix & Absorbing States

Pritchett Clock Repair Shop

Breakeven Analysis

Data

Rebuilt Springs

Fixed cost 1000

Variable cost 5

Revenue 10

Results

Breakeven points

Units 200

Dollars 2,000.00$

Graph

Units Costs Revenue

0 1000 0

400 3000 4000

0

1000

2000

3000

4000

5000

0 200 400 600$

Units

Cost-volume analysis

Costs Revenue

Pritchett Clock Repair Shop

Breakeven Analysis

Data

Rebuilt Springs

Fixed cost 1000

Variable cost 5

Revenue 10.71

Volume (optional) 250

Results

Breakeven points

Units 175

Dollars 1,875.00$

Volume Analysis@ 250

Costs 2,250.00$

Revenue 2,678.57$

Profit 428.57$

Graph

Units Costs Revenue

0 1000 0

350 2750 3750

x P(x) xP(x) (x-mean)squared*P(x)

10 0.2 2 54.45

20 0.25 5 10.5625

30 0.25 7.5 3.0625

40 0.3 12 54.675

26.5 122.75

Mean Variance

The Binomial Distribution

n= 5

p= 0.5

r= 4

Cumulative probability P(r<_) 0.9688

P(r) 0.1563

Thompson Lumber

Decision Tables

Data Results

Profit

Favorable

Market

Unfavorable

Market EMV Minimum Maximum Hurwicz

Probability 0.5 0.5 coefficient 0.8

Large Plant 200000 -180000 10000 -180000 200000 124000

Small plant 100000 -20000 40000 -20000 100000 76000

Do nothing 0 0 0 0 0

Maximum 40000 0 200000 124000

Expected Value of Perfect Information

Column best 200000 0 100000 <-Expected value under certainty

40000 <-Best expected value

60000 <-Expected value of perfect information

Regret

Favorable MarketUnfavorable Market Expected Maximum

Probability 0.5 0.5

Large Plant 0 180000 90000 180000

Small plant 100000 20000 60000 100000

Do nothing 200000 0 100000 200000

Minimum 60000 100000

Bayes Theorem for Thompson Lumber Example

Fill in cells B7, B8, and C7

Probability Revisions Given a Positive Survey

State of Nature P(Sur.Pos.|state of nature) Prior Prob. Joint Prob.

Posterior

Probability

FM 0.7 0.5 0.35 0.78

UM 0.2 0.5 0.1 0.22

P(Sur.pos.)= 0.45

Probability Revisions Given a Negative Survey

State of Nature P(Sur.Pos.|state of nature) Prior Prob. Joint Prob.

Posterior

Probability

FM 0.3 0.5 0.15 0.27

UM 0.8 0.5 0.4 0.73

P(Sur.neg.)= 0.55

Triple A Construction CompanySUMMARY OUTPUT

Sales (Y)Payroll (X) Regression Statistics

6 3 Multiple R 0.833333

8 4 R Square 0.694444

9 6 Adjusted R Square0.618056

5 4 Standard Error1.311011

4.5 2 Observations 6

9.5 5

ANOVA

df SS MS F Significance F

Regression 1 15.625 15.625 9.090909 0.039352

Residual 4 6.875 1.71875

Total 5 22.5

CoefficientsStandard Error t Stat P-value Lower 95%

Intercept 2 1.742544 1.147747 0.31505 -2.83808

Payroll (X) 1.25 0.414578 3.015113 0.039352 0.098947

Significance F

Upper 95%Lower 95.0%Upper 95.0%

6.838077 -2.83808 6.838077

2.401053 0.098947 2.401053

SELL PRICE SF AGE

35000 1926 30

47000 2069 40

49900 1720 30

55000 1396 15

58900 1706 32

60000 1847 38

67000 1950 27

70000 2323 30

78500 2285 26

79000 3752 35

87500 2300 18

93000 2525 17

95000 3800 40

97000 1740 12

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.81968

R Square 0.67188

Adjusted R Square0.61222

Standard Error 12156.3

Observations 14

ANOVA


Regression 2 3328484242 1.66E+09 11.26195 0.002179

Residual 11 1625532901 1.48E+08

Total 13 4954017143

CoefficientsStandard Error t Stat P-value Lower 95%Upper 95%Lower 95.0%Upper 95.0%

Intercept 60815.4 12741.04143 4.773193 0.000578 32772.6 88858.29 32772.6 88858.29

SF 21.9097 5.140482535 4.262184 0.001338 10.59556 33.22381 10.59556 33.22381

AGE -1449.34 398.282471 -3.63898 0.003895 -2325.96 -572.729 -2325.96 -572.729

Upper 95.0%

SELL PRICESF AGE X3(Exc) X4(Mint) Condition

35000 1926 30 0 0 Good

47000 2069 40 1 0 Excellent

49900 1720 30 1 0 Excellent

55000 1396 15 0 0 Good

58900 1706 32 0 1 Mint

60000 1847 38 0 1 Mint

67000 1950 27 0 1 Mint

70000 2323 30 1 0 Excellent

78500 2285 26 0 1 Mint

79000 3752 35 0 0 Good

87500 2300 18 0 0 Good

93000 2525 17 0 0 Good

95000 3800 40 1 0 Excellent

97000 1740 12 0 1 Mint

SUMMARY OUTPUT


Multiple R 0.947618

R Square 0.89798


Standard Error7493.777

Observations 14

ANOVA


Regression 4 4.45E+09 1.11E+09 19.80444 0.000174

Residual 9 5.05E+08 56156698

Total 13 4.95E+09


Intercept 48329.23 8713.307 5.5466 0.000358 28618.36 68040.1 28618.36 68040.1

SF 28.2138 3.473758 8.121981 1.96E-05 20.35561 36.07199 20.35561 36.07199

AGE -1981.41 298.0139 -6.64872 9.39E-05 -2655.56 -1307.26 -2655.56 -1307.26

X3(Exc) 16581.32 6089.81 2.722798 0.0235 2805.216 30357.43 2805.216 30357.43

X4(Mint) 23684.62 5324.635 4.448122 0.001605 11639.46 35729.78 11639.46 35729.78

Upper 95.0%

Automobile Weight vs. MPG SUMMARY OUTPUT

MPG (Y) Weight (X1) Regression Statistics

12 4.58 Multiple R 0.86288

13 4.66 R Square 0.74456

15 4.02 Adjusted R Square0.71902

18 2.53 Standard Error5.00757

19 3.09 Observations 12

19 3.11

20 3.18 ANOVA

23 2.68 df SS MS F Significance F

24 2.65 Regression 1 730.909 730.909 29.14802 0.000302

33 1.70 Residual 10 250.7577 25.07577

36 1.95 Total 11 981.6667

42 1.92

CoefficientsStandard Error t Stat P-value Lower 95%Upper 95%

Intercept 47.6193 4.813151 9.89359 1.75E-06 36.89498 58.34371

Weight (X1) -8.246 1.527345 -5.39889 0.000302 -11.6491 -4.84283

Lower 95.0%Upper 95.0%

36.89498 58.34371

-11.6491 -4.84283

Automobile Weight vs. MPG SUMMARY OUTPUT

MPG (Y) Weight (X1) WeightSq.(X2) Regression Statistics

12 4.58 20.98 Multiple R 0.9208

13 4.66 21.72 R Square 0.8478

15 4.02 16.16 Adjusted R Square0.8140

18 2.53 6.40 Standard Error 4.0745

19 3.09 9.55 Observations 12

19 3.11 9.67

20 3.18 10.11 ANOVA

23 2.68 7.18 df SS MS F Significance F

24 2.65 7.02 Regression 2 832.2557 416.1278 25.0661 0.000209

33 1.70 2.89 Residual 9 149.411 16.60122

36 1.95 3.80 Total 11 981.6667

42 1.92 3.69

CoefficientsStandard Error t Stat P-value Lower 95%

Intercept 79.7888 13.5962 5.8685 0.0002 49.0321

Weight (X1) -30.2224 8.9809 -3.3652 0.0083 -50.5386

WeightSq.(X2) 3.4124 1.3811 2.4708 0.0355 0.2881

Significance F

Upper 95%Lower 95.0%Upper 95.0%

110.5454 49.0321 110.5454

-9.9062 -50.5386 -9.9062

6.5367 0.2881 6.5367

Solved Problem 4-2

Advertising ($100) Y Sales X

11 5

6 3

10 7

6 2

12 8

SUMMARY OUTPUT


Multiple R 0.9014

R Square 0.8125

Adjusted R Square 0.7500

Standard Error 1.4142

Observations 5

ANOVA


Regression 1 26 26 13 0.036618

Residual 3 6 2

Total 4 32


Intercept 4 1.5242 2.6244 0.0787 -0.8506 8.8506 -0.8506 8.8506

Sales X 1 0.2774 3.6056 0.0366 0.1173 1.8827 0.1173 1.8827

Upper 95.0%

Wallace Garden Supply Shed Sales

Forecasting Weighted moving averages 3 period moving average

Data Error analysis

Period Demand Weights Forecast Error Absolute Squared

January 10 1

February 12 2

March 13 3

April 16 12.16667 3.833333 3.833333 14.69444

May 19 14.33333 4.666667 4.666667 21.77778

June 23 17 6 6 36

July 26 20.5 5.5 5.5 30.25

August 30 23.83333 6.166667 6.166667 38.02778

September 28 27.5 0.5 0.5 0.25

October 18 28.33333 -10.3333 10.33333 106.7778

November 16 23.33333 -7.33333 7.333333 53.77778

December 14 18.66667 -4.66667 4.666667 21.77778

Total 4.333333 49 323.3333

Average 0.481481 5.444444 35.92593

Bias MAD MSE

SE 6.796358

Next period 15.3333333

Port of Baltimore

Forecasting Exponential smoothing

Alpha 0.1

Data Error Analysis

Period Demand Forecast Error Absolute Squared

Quarter 1 180 175 5 5 25

Quarter 2 168 175.5 -7.5 7.5 56.25

Quarter 3 159 174.75 -15.75 15.75 248.0625

Quarter 4 175 173.175 1.825 1.825 3.330625

Quarter 5 190 173.3575 16.6425 16.6425 276.9728

Quarter 6 205 175.0218 29.97825 29.97825 898.6955

Quarter 7 180 178.0196 1.980425 1.980425 3.922083

Quarter 8 182 178.2176 3.782382 3.782382 14.30642

Total 35.95856 82.45856 1526.54

Average 4.49482 10.30732 190.8175

Bias MAD MSE

SE 15.95065

Next period 178.595856

Midwestern Manufacturing

Time (X) Demand (Y)

1 74

2 79

3 80

4 90

5 105

6 142

7 122

SUMMARY OUTPUT


Multiple R 0.89491

R Square 0.800863



Observations 7

ANOVA


Regression 1 3108.036 3108.036 20.10837 0.006493

Residual 5 772.8214 154.5643

Total 6 3880.857

CoefficientsStandard Error t Stat P-value Lower 95% Upper 95%Lower 95.0%Upper 95.0%

Intercept 56.71429 10.50729 5.39762 0.00295 29.70445 83.72412 29.70445 83.72412

Time (X) 10.53571 2.34950 4.48424 0.00649 4.49613 16.57530 4.49613 16.57530

Upper 95.0%

Midwestern Manufacturing's Demand

Forecasting Regression/Trend analysis

Data Error analysis

Period Demand (y) Period(x) Forecast Error Absolute Squared

1993 74 1 67.25 6.75 6.75 45.5625

1994 79 2 77.78571 1.214286 1.2142857 1.47449

1995 80 3 88.32143 -8.32143 8.3214286 69.24617

1996 90 4 98.85714 -8.85714 8.8571429 78.44898

1997 105 5 109.3929 -4.39286 4.3928571 19.29719

1998 142 6 119.9286 22.07143 22.071429 487.148

1999 122 7 130.4643 -8.46429 8.4642857 71.64413

Total 0.00 60.071429 772.8214

Intercept 56.7142857 Average 0.00 8.5816327 110.4031

Slope 10.5357143 Bias MAD MSE

SE 12.43239

Next period 141 8

Correlation 0.89491

Year Quarter Sales X1 Time PeriodX2 Qtr 2 X3 Qtr 3 X4 Qtr 4

1 1 108 1 0 0 0

2 125 2 1 0 0

3 150 3 0 1 0

4 141 4 0 0 1

2 1 116 5 0 0 0

2 134 6 1 0 0

3 159 7 0 1 0

4 152 8 0 0 1

3 1 123 9 0 0 0

2 142 10 1 0 0

3 168 11 0 1 0

4 165 12 0 0 1

SUMMARY OUTPUT


Multiple R 0.99718

R Square 0.99436



Observations 12

ANOVA


Regression 4 4144.75 1036.188 308.6516 6.03E-08

Residual 7 23.5 3.357143

Total 11 4168.25


Intercept 104.104 1.332194 78.14493 1.48E-11 100.954 107.2543 100.954 107.2543

X1 Time Period2.3125 0.16195 14.27913 1.96E-06 1.92955 2.69545 1.92955 2.69545

X2 Qtr 2 15.6875 1.504767 10.4252 1.62E-05 12.12929 19.24571 12.12929 19.24571

X3 Qtr 3 38.7083 1.530688 25.28819 3.86E-08 35.08883 42.32784 35.08883 42.32784

X4 Qtr 4 30.0625 1.572941 19.11228 2.67E-07 26.34308 33.78192 26.34308 33.78192

Sumco Pump Company

Inventory Economic Order Quantity Model

Data

Demand rate, D 1000

Setup cost, S 10

Holding cost, H 0.5 (fixed amount)

Unit Price, P 0

Results

Optimal Order Quantity, Q* 200

Maximum Inventory 200

Average Inventory 100

Number of Setups 5

Holding cost $50.00

Setup cost $50.00

Unit costs $0.00

Total cost, Tc $100.00

COST TABLE Start at 25 Increment by 15

Q Setup cost Holding costTotal cost

25 400 6.25 406.25

40 250 10 260

55 181.8182 13.75 195.5682

70 142.8571 17.5 160.3571

85 117.6471 21.25 138.8971

100 100 25 125

115 86.95652 28.75 115.7065

130 76.92308 32.5 109.4231

145 68.96552 36.25 105.2155

160 62.5 40 102.5

175 57.14286 43.75 100.8929

190 52.63158 47.5 100.1316

205 48.78049 51.25 100.0305

220 45.45455 55 100.4545

235 42.55319 58.75 101.3032

250 40 62.5 102.5

265 37.73585 66.25 103.9858

280 35.71429 70 105.7143

295 33.89831 73.75 107.6483

310 32.25806 77.5 109.7581

325 30.76923 81.25 112.0192

050

100150200250300350400450

25 115 205 295

Co

st

($)

Order Quantity (Q)

Inventory: Cost vs Quantity

Setup cost

Holding cost

Total cost

340 29.41176 85 114.4118

355 28.16901 88.75 116.919

370 27.02703 92.5 119.527

Brown Manufacturing

Inventory Production Order Quantity Model

Data

Demand rate, D 10000

Setup cost, S 100

Holding cost, H 0.5 (fixed amount)

Daily production rate, p 80

Daily demand rate, d 60

Unit price, P 0

Results

Optimal production quantity, Q* 4000

Maximum Inventory 1000

Average Inventory 500

Number of Setups 2.5

Holding cost 250

Setup cost 250

Unit costs 0

Total cost, Tc 500

COST TABLE Start at 1000 Increment by333.3333

Q Setup cost Holding costTotal cost

1000 1000 62.5 1062.5

1333.333 750 83.33333 833.3333

1666.667 600 104.1667 704.1667

2000 500 125 625

2333.333 428.5714 145.8333 574.4048

2666.667 375 166.6667 541.6667

3000 333.3333 187.5 520.8333

3333.333 300 208.3333 508.3333

3666.667 272.7273 229.1667 501.8939

4000 250 250 500

4333.333 230.7692 270.8333 501.6026

4666.667 214.2857 291.6667 505.9524

5000 200 312.5 512.5

5333.333 187.5 333.3333 520.8333

5666.667 176.4706 354.1667 530.6373

6000 166.6667 375 541.6667

6333.333 157.8947 395.8333 553.7281

6666.667 150 416.6667 566.6667

7000 142.8571 437.5 580.3571

7333.333 136.3636 458.3333 594.697

7666.667 130.4348 479.1667 609.6014

8000 125 500 625

0

200

400

600

800

1000

1200

10002666.6666674333.33333360007666.666667

Co

st

($)

Order Quantity (Q)


8333.333 120 520.8333 640.8333

8666.667 115.3846 541.6667 657.0513


Setup cost

Holding cost

Total cost

Brass Department Store

Inventory Quantity Discount Model

Data

Demand rate, D 5000

Setup cost, S 49

Holding cost %, I 20%

Range 1 Range 2 Range 3

Minimum quantity 0 1000 2000

Unit Price, P 5 4.8 4.75

Results

Range 1 Range 2 Range 3

Q* (Square root formula) 700 714.4345083 718.1848465

Order Quantity 700 1000 2000

Holding cost $350.00 $480.00 $950.00

Setup cost $350.00 $245.00 $122.50

Unit costs $25,000.00 $24,000.00 $23,750.00

Total cost, Tc $25,700.00 $24,725.00 $24,822.50 minimum

Optimal Order Quantity 1000

=

$24,725.00

Flair Furniture

Tables Chairs

Left Hand

Side

Right Hand

Side Slack

Objective function 70 50 4100

Carpentry 4 3 240 <= 240 0

Painting 2 1 100 <= 100 0

Solution Values 30 40

Holiday Meal Turkey Ranch

Brand 1 Brand 2

Left Hand

Side

Right Hand

Side Surplus

Objective function 2 3 31.2

Ingredient A 5 10 90 >= 90

Ingredient B 4 3 48 >= 48 0

Ingredient C 0.5 0 4.2 >= 1.5 2.7

Solution Values 8.4 4.8

High note sound company

CD PlayersReceivers

Value 0 20

Total

Profit 50 120 2400

Used Sign Available

Electrician hours 2 4 80 <= 80

Audio technician hours 3 1 20 <= 60

Win Big Gambling Club

1 minute

TV spots

newspaper

ads

30 second

radio spots

1 minute

radio spots

Solution 1.96875 5 6.20689655 0

Variables X1 X2 X3 X4

Audience reached per ad 5000 8500 2400 2800

Maximum TV 1

Maximum Newspaper 1

Maximum 30-second radio 1

Maximum 1 min. radio 1

Cost per ad 800 925 290 380

Radio dollars 290 380

Radio spots 1 1

RHS

67240.302

1.96875 <= 12

5 <= 5

6.2068966 <= 25

0 <= 20

8000 <= 8000

1800 <= 1800

6.2068966 >= 5

Fifth Avenue Industries

Variety

Number

(X)

Selling

price

Monthly

minimum

Monthly

demand

Material

(yards) silk polyester cotton

All silk 6400 6.7 6000 7000 0.125 100%

All polyester 14000 3.55 10000 14000 0.08 100%

Poly-cotton

blend 1 16000 4.31 13000 16000 0.1 50% 50%

Poly-cotton

blend 2 8500 4.81 6000 8500 0.1 30% 70%

Total revenue 202425 800 2175 1395

Material Cost Available Used

Silk 21 800 800

Polyester 6 3000 2175

Cotton 9 1600 1395

Total Cost 42405

Total Profit 160020

Top Speed Bicycle Company

Transportation

Data

COSTS New York Chicago Los AngelesSupply

New Orleans 2 3 5 20000

Omaha 3 1 4 15000

Demand 10000 8000 15000 33000 \ 35000

Shipments

Shipments New York Chicago Los AngelesRow Total

New Orleans 10000 0 8000 18000

Omaha 0 8000 7000 15000

Column Total 10000 8000 15000 33000 \ 33000

Total Cost 96000

Goodman Shipping

Item

Percent

loaded

Max

percent

loaded Value ($) weight (lbs)

1 0.333333 1 22500 7500

2 1 1 24000 7500

3 0 1 8000 3000

4 0 1 9500 3500

5 0 1 11500 4000

6 0 1 9750 3500

Total 31,500$ 10000

Weight Capacity 10000

High note sound company

CD PlayersReceivers

Value 0 20

Total

Profit 50 120 2400

Used Sign Available

Electrician hours 2 4 80 <= 80

Audio technician hours 3 1 20 <= 60

Manufacturing Example

mower blower

variable-> 100 200

Total profit

profit 30 80 19000

used available

labor hours 2 4 1000 < 1000

steel (lbs) 6 2 1000 < 1200

snowblower engines 1 200 < 200

Executive Furniture Company

Transportation

Data

COSTS AlbuquerqueBoston Cleveland Supply

Des Moines 5 4 3 100

Evansville 8 4 3 300

Fort Lauderdale 9 7 5 300

Demand 300 200 200 700 \ 700

Shipments

Shipments AlbuquerqueBoston Cleveland Row Total

Des Moines 100 0 0 100

Evansville 0 200 100 300

Fort Lauderdale 200 0 100 300

Column Total 300 200 200 700 \ 700

Total Cost 3900

Birmingham Plant

Transportation

Data

COSTS Detroit Dallas New York Los AngelesSupply

Cincinnati 73 103 88 108 15000

Salt Lake 85 80 100 90 6000

Pittsburgh 88 97 78 118 14000

Birmingham 84 79 90 99 11000

Demand 10000 12000 15000 9000 46000 \ 46000

Shipments

Shipments Detroit Dallas New York Los AngelesColumn Total

Cincinnati 10000 0 1000 4000 15000

Salt Lake 0 1000 0 5000 6000

Pittsburgh 0 0 14000 0 14000

Birmingham 0 11000 0 0 11000

Column Total 10000 12000 15000 9000 46000 \ 46000

Total Cost 3741000

Fix-It Shop Assignment

Fix-It Shop Assignment

Assignment

Data

COSTS Project 1 Project 2 Project 3

Adams 11 14 6

Brown 8 10 11

Cooper 9 12 7

Assignments

Shipments Project 1 Project 2 Project 3 Row Total

Adams 0 0 1 1

Brown 0 1 0 1

Cooper 1 0 0 1

Column Total 1 1 1 3

Total Cost 25

Harrison Electric IP Analysis

Chandeliers Fans

Solution 5 0

Total

Profit 7 6 35

Used Sign Limit

wiring hours 2 3 10 < 12

assembly hours 6 5 30 < 30

Bagwell Chemical Company

xyline (bags) hexall (lbs)

value 44 20

profit 85 1.5 3770

used sign available

ingredient a 30 0.5 1330 <= 2000

ingredient b 18 0.4 800 <= 800

ingredient c 2 0.1 90 <= 200

Simkin, Simkin and Steinberg

Stock Company Name Invest Return Cost

1 Trans-Texas Oil 0 50 480

2 British Petroleum 0 80 540

3 Dutch Shell 1 90 680

4 Houston Drilling 1 120 1000

5 Texas Petroleum 1 110 700

6 San Diego Oil 1 40 510

7 California Petro 0 75 900

Total 360 2890

Limit 3000

Bound

Texas Constraint 2 >= 2

Foreign oil constraint 1 <= 1

California Constraint 1 = 1

Great Western Appliance

MicrotoasterSelf-clean Total

Number 0 1000 1000 < 1000

Profit 0 271000 271,000.00$

used Sign capacity

Hours 0.5 0.4 400 < 500

Hospicare Corpx1 x2

value 6.066259 4.100253

terms x1 x1^2 x1*x2 x2 x2^3 1/x2

values 6.066259 36.79949 24.87319 4.100253 68.93374 0.243887

total

revenue 13 6 5 1 248.846

constraint 1 2 4 90 < 90

constraint 2 1 1 75 < 75

constraint 3 8 -2 40.3296 < 61

Thermlock Gaskets

x1 x2

value 3.325326 14.67227

total

cost 5 7 119.3325

constraints

x1 x1^2 x1^3 x2 x2^2

value 3.325326 11.05779 36.77076 14.67227 215.2756 Total

Constraint 1 3 0.25 4 0.3 136.0122 > 125

Constraint 2 13 1 80 > 80

Constraint 3 0.7 1 17 > 17

0-1 integer Program

x1 x2 x3

values 1 1 0

total

maximize 50 45 48 95

Limit

constraint 1 19 27 34 46 < 80

22 13 12 35 < 40

1 1 1 2 < 2

Crashing General Foundry ProblemYA YB YC YD YE YF YG YH XST XA XB XC XD XE XF XG XH XFIN

Values 0 0 1 0 0 0 2 0 0 2 3 3 7 7 6 10 12 12

Minimize cost 1000 2000 1000 1000 1000 500 2000 3000

A crash max. 1

B crash max. 1

C crash max. 1

D crash max. 1

E crash max. 1

F crash max. 1

G crash max. 1

H crash max. 1

Due date 1

Start 1

A constraint 1 -1 1

B constraint 1 -1 1

C constraint 1 -1 1

D constraint 1 -1 1

E constraint 1 -1 1

F constraint 1 -1 1

G constraint 1 1 -1 1

G constraint 2 1 -1 1

H constraint 1 1 -1 1

H constraint 2 1 -1 1

Finish constraint -1 1

Totals

5000

0 < 1

0 < 2

1 < 1

0 < 1

0 < 2

0 < 1

2 < 3

0 < 1

12 < 12

0 = 0

2 > 2

3 > 3

2 > 2

4 > 4

4 > 4

3 > 3

5 > 5

5 > 5

6 > 2

2 > 2

0 > 0

Arnold's Muffler Shop

Waiting Lines M/M/1 (Single Server Model)

Data Results

Arrival rate (l) 2 Average server utilization(r) 0.666667Service rate (m) 3 Average number of customers in the queue(Lq) 1.333333

Average number of customers in the system(L) 2

Average waiting time in the queue(Wq) 0.666667

Average time in the system(W) 1

Probability (% of time) system is empty (P0) 0.333333

Probabilities

Number Probability Cumulative Probability

0 0.333333 0.333333

1 0.222222 0.555556

2 0.148148 0.703704

3 0.098765 0.802469

4 0.065844 0.868313

5 0.043896 0.912209

6 0.029264 0.941472

7 0.019509 0.960982

8 0.013006 0.973988

9 0.008671 0.982658

10 0.005781 0.988439

11 0.003854 0.992293

12 0.002569 0.994862

13 0.001713 0.996575

14 0.001142 0.997716

15 0.000761 0.998478

16 0.000507 0.998985

17 0.000338 0.999323

18 0.000226 0.999549

19 0.000150 0.999699

20 0.000100 0.999800

Arnold's Muffler Shop

Waiting Lines M/M/s

Data Results

Arrival rate (l) 2 Average server utilization(r) 0.33333

Service rate (m) 3 Average number of customers in the queue(Lq) 0.08333

Number of servers(s) 2 Average number of customers in the system(L) 0.75


Average time in the system(W) 0.375


Probabilities

Number Probability Cumulative Probability

0 0.500000 0.500000

1 0.333333 0.833333

2 0.111111 0.944444

3 0.037037 0.981481

4 0.012346 0.993827

5 0.004115 0.997942

6 0.001372 0.999314

7 0.000457 0.999771

8 0.000152 0.999924

9 0.000051 0.999975

10 0.000017 0.999992

11 0.000006 0.999997

12 0.000002 0.999999

13 0.000001 1.000000

14 0.000000 1.000000

15 0.000000 1.000000

16 0.000000 1.000000

17 0.000000 1.000000

18 0.000000 1.000000

19 0.000000 1.000000

20 0.000000 1.000000

Computations

n or s (lam/mu)^n/n!Cumsum(n-1)term2 P0(s)

0 1

1 0.666667 1 2 0.33333

2 0.222222 1.666667 0.333333333 0.5

3 0.049383 1.888889 0.063492063 0.5122

4 0.00823 1.938272 0.009876543 0.51331

5 0.001097 1.946502 0.001266223 0.51341

6 0.000122 1.947599 0.000137174 0.51342

7 1.16E-05 1.947721 1.2835E-05 0.51342

8 9.68E-07 1.947733 1.05569E-06 0.51342

9 7.17E-08 1.947734 7.74175E-08 0.51342

10 4.78E-09 1.947734 5.12021E-09 0.51342

11 2.9E-10 1.947734 3.08314E-10 0.51342

12 1.61E-11 1.947734 1.70369E-11 0.51342

13 8.25E-13 1.947734 8.69754E-13 0.51342

14 3.93E-14 1.947734 4.12575E-14 0.51342

15 1.75E-15 1.947734 1.82758E-15 0.51342

16 7.28E-17 1.947734 7.59283E-17 0.51342

17 2.85E-18 1.947734 2.96998E-18 0.51342

18 1.06E-19 1.947734 1.09751E-19 0.51342

19 3.71E-21 1.947734 3.84312E-21 0.51342

20 1.24E-22 1.947734 1.27871E-22 0.51342

21 3.92E-24 1.947734 4.05276E-24 0.51342

22 1.19E-25 1.947734 1.22628E-25 0.51342

23

24

25

26

27

28

29

30

Rho(s) Lq(s) L(s) Wq(s) W(S)

0.666667 1.333333 2 0.666667 1

0.333333 0.083333 0.75 0.041667 0.375

0.222222 0.009292 0.675958 0.004646 0.337979

0.166667 0.001014 0.667681 0.000507 0.33384

0.133333 0.0001 0.666767 5E-05 0.333383

0.111111 8.8E-06 0.666675 4.4E-06 0.333338

0.095238 6.94E-07 0.666667 3.47E-07 0.333334

0.083333 4.93E-08 0.666667 2.46E-08 0.333333

0.074074 3.18E-09 0.666667 1.59E-09 0.333333

0.066667 1.88E-10 0.666667 9.39E-11 0.333333

0.060606 1.02E-11 0.666667 5.11E-12 0.333333

0.055556 5.15E-13 0.666667 2.57E-13 0.333333

0.051282 2.41E-14 0.666667 1.21E-14 0.333333

0.047619 1.06E-15 0.666667 5.3E-16 0.333333

0.044444 4.36E-17 0.666667 2.18E-17 0.333333

0.041667 1.69E-18 0.666667 8.47E-19 0.333333

0.039216 6.22E-20 0.666667 3.11E-20 0.333333

0.037037 2.17E-21 0.666667 1.08E-21 0.333333

0.035088 7.17E-23 0.666667 3.59E-23 0.333333

0.033333 2.26E-24 0.666667 1.13E-24 0.333333

0.031746 6.82E-26 0.666667 3.41E-26 0.333333

0.030303 1.97E-27 0.666667 9.84E-28 0.333333

Garcia-Golding Recycling

Waiting Lines M/D/1 (Constant Service Times)

Data Results

Arrival rate (l) 8 Average server utilization(r) 0.666667Service rate (m) 12 Average number of customers in the queue(Lq) 0.666667

Average number of customers in the system(L) 1.333333




Waiting cost/hour 60.00$

Waiting cost/trip 5.00$

Department of Commerce

Waiting Lines M/M/s with a finite population

Data Results

Arrival rate (l) per

customer 0.05 Average server utilization(r) 0.436048

Service rate (m) 0.5 Average number of customers in the queue(Lq) 0.203474

Number of servers 1 Average number of customers in the system(L) 0.639522

Population size (N) 5 Average waiting time in the queue(Wq) 0.933264



Effective arrival rate 0.218024

Probabilities

Number, n

Probability,

P(n)

Cumulative

Probability Number waiting

Arrival

rate(n)

0 0.5639522 0.5639522 0 0.25

1 0.2819761 0.8459283 0 0.2

2 0.1127904 0.9587187 1 0.15

3 0.0338371 0.9925558 2 0.1

4 0.0067674 0.9993233 3 0.05

5 0.0006767 1 4 0

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

1.7732

Term 1

Sum term

1 Term 2

Sum term

2

Decum

term 2 P0(s)

1 1 1 1 0.7732

0.5 1.5 0.5 1.5 0.2732 0.563952

0.2 1.7 0.0732

0.06 1.76 0.0132

0.012 1.772 0.0012

0.0012 1.7732 0

Harry's Tire Shop NOTE: The random numbers appearing here may not be the same as the ones in the book, but the formulas are the same.

Probability

Probability

Range

(Lower)

Cumulative

Probability

Tires

Demand Day

Random

Number

Simulated

Demand

0.05 0 0.05 0 1 0.738713 4

0.1 0.05 0.15 1 2 0.809414 4

0.2 0.15 0.35 2 3 0.858616 5

0.3 0.35 0.65 3 4 0.906845 5

0.2 0.65 0.85 4 5 0.632865 3

0.15 0.85 1 5 6 0.871298 5

7 0.17927 2

8 0.739672 4

9 0.527331 3

10 0.257875 2

Average 3.7

Results (Frequency table)

Tires

Demanded Frequency Percentage Cum %

0 0 0% 0%

1 0 0% 0%

2 2 20% 20%

3 2 20% 40%

4 3 30% 70%

5 3 30% 100%

10

NOTE: The random numbers appearing here may not be the same as the ones in the book, but the formulas are the same.

Generating Normal Random Numbers NOTE: The random numbers appearing here may not be the same as the ones in the book, but the formulas are the same.

Random number Value Frenquency Percentage

38.56168904 26 0 0.0%

44.12934062 28 2 1.0%

39.09006016 30 3 1.5%

41.6115212 32 4 2.0%

36.8373438 34 8 4.0%

40.58881682 36 18 9.0%

45.16354566 38 24 12.0%

47.41344557 40 38 19.0%

34.57334599 42 37 18.5%

36.0474607 44 23 11.5%

42.1638933 46 22 11.0%

28.29700386 48 11 5.5%

38.14649298 50 6 3.0%

42.23390822 52 3 1.5%

41.85412671 54 1 0.5%

35.95991143 56 0 0.0%

27.93157837 200

38.54188857

39.04520022

32.56023403

41.69639146

44.43350295

41.85227064

38.45075418

37.38882091

33.02101696

40.6400646

41.17258569

39.96474019

41.03583802

44.60003945

38.06981023

42.90673701

37.07801997

32.84127465

41.80699589

41.67911025

49.24258993

35.01932776

43.61010545

41.81771246

50.80814037

38.77385236

38.47929316

37.71896993

35.92948329

43.44322161

39.95048214

41.89463451

37.76545142

38.09549431

44.33478259

36.13992556

34.12232602

42.03601649

36.71482384

29.13328035

42.92556993

37.50066263

35.02111028

42.33221803

40.24424266

38.8368427

40.98538447

27.67315395

34.09959069

39.24256618

29.58638652

49.5076796

31.74448455

45.69617468

47.35126958

44.46185606

46.56239048

36.10574416

39.36494594

42.12464207

45.0290262

45.91150619

36.42252659

46.13615538

36.04178886

41.97013999

45.60078043

34.70077225

45.39929756

34.11849742

38.70581248

38.747506

50.64820379

45.88826842

36.40261979

41.52208587

46.59614633

49.75444815

48.48194393

38.97037886

40.33469476

35.48822395

41.0830677

41.00359209

42.48147104

43.57190573

41.16914865

51.45406355

45.79309542

37.73215968

37.13860654

40.97192721

39.76302815

44.99998136

48.97407901

35.47674677

38.92208945

37.73568588

37.15233765

39.76609951

46.98934684

33.36900325

41.5515104

45.15152291

31.75704356

39.34025643

41.60487736

36.07407901

38.6140063

36.74786838

33.06146144

42.75324176

42.5026408

32.99124216

33.13558609

42.64159038

42.74632693

35.05647801

39.97289129

39.89324781

40.2956706

38.14531751

41.2648517

39.41162201

43.12350197

40.15107936

34.59976578

48.8346183

47.74501279

52.36157989

41.00668786

40.02543857

40.39739927

38.25853047

38.88513525

38.84859408

34.50344166

41.36399548

39.75417349

42.35035309

39.68634974

41.37830095

33.51514677

47.01137633

36.86512154

46.11033393

43.66033294

44.06863988

41.0921877

38.53390409

40.47577984

36.82718645

42.81969651

37.035601

43.74497596

38.45984057

41.77411443

42.40898258

45.11910123

40.77840551

38.56061648

43.14300434

35.15652821

39.35622989

39.23034706

31.84024945

40.24890939

47.83578473

41.78150918

35.80741397

38.02931441

46.72580016

42.96416483

30.69024827

36.97738421

44.1269921

45.39807655

44.47722189

45.89792101

37.93462946

44.28650007

35.61303521

35.06684899


Port of New Orleans Barge Unloadings NOTE: The random numbers appearing here may not be the same as the ones in the book, but the formulas are the same.

Day

Previously

delayed

Random

number Arrivals

Total to

be

unoaded

Random

Number

Possibly

unloaded Unloaded

1 0 0.108295 0 0 0.160394 2 0

2 0 0.100507 0 0 0.483036 3 0

3 0 0.320609 2 2 0.702392 4 2

4 0 0.182938 1 1 0.524397 3 1

5 0 0.576297 3 3 0.766404 4 3

6 0 0.682204 3 3 0.82367 4 3

7 0 0.244693 1 1 0.646211 3 1

8 0 0.864116 4 4 0.158178 2 2

9 2 0.353314 2 4 0.830843 4 4

10 0 0.008447 0 0 0.064438 2 0

Barge Arrivals Unloading rates

Demand Probability Lower CumulativeDemand Number Probability Lower

0 0.13 0 0.13 0 1 0.05 0

1 0.17 0.13 0.3 1 2 0.15 0.05

2 0.15 0.3 0.45 2 3 0.5 0.2

3 0.25 0.45 0.7 3 4 0.2 0.7

4 0.2 0.7 0.9 4 5 0.1 0.9

5 0.1 0.9 1 5


CumulativeUnloading

0.05 1

0.2 2

0.7 3

0.9 4

1 5

Three Hills Power NOTE: The random numbers appearing here may not be the same as the ones in the book, but the formulas are the same.

Breakdown

number

Random

number

Time

between

breakdowns

Time of

breakdowns

Time

repairperson

is free

Random

Number Repair time

Repair

ends

1 0.0529581 1 1 1 0.3852438 2 3

2 0.9245766 3 4 4 0.8913291 3 7

3 0.5936416 2 6 7 0.3614929 2 9

4 0.9111224 3 9 9 0.2881283 2 11

5 0.6038654 2.5 11.5 11.5 0.0588177 1 12.5

6 0.0172306 0.5 12 12.5 0.3399594 2 14.5

7 0.0516984 1 13 14.5 0.0860723 1 15.5

8 0.533433 2 15 15.5 0.8584862 3 18.5

9 0.8751594 3 18 18.5 0.7751288 2 20.5

10 0.3091988 2 20 20.5 0.5317927 2 22.5

Demand Table Repair times

Time between breakdownsProbability Lower Cumulative Demand Time Probability

0.5 0.05 0 0.05 0.5 1 0.28

1 0.06 0.05 0.11 1 2 0.52

1.5 0.16 0.11 0.27 1.5 3 0.2

2 0.33 0.27 0.6 2

2.5 0.21 0.6 0.81 2.5

3 0.19 0.81 1 3


Lower CumulativeLead time

0 0.28 1

0.28 0.8 2

0.8 1 3

Three Grocery Example

State Probabilities

American Food StoreFood Mart Atlas Foods

Time #1 #2 #3 Matrix of Transition Probabilities

0 0.4 0.3 0.3 0.8 0.1 0.1

1 0.41 0.31 0.28 0.1 0.7 0.2

2 0.415 0.314 0.271 0.2 0.2 0.6

3 0.4176 0.3155 0.2669

4 0.41901 0.31599 0.265

5 0.419807 0.316094 0.264099

6 0.4202748 0.3160663 0.2636589

Accounts Receivable Example

1 0 0 0

P= I : 0 = 0 1 0 0

A : B 0.6 0 0.2 0.2

0.4 0.1 0.3 0.2

I - B = 0.8 -0.2

-0.3 0.8

F = (I - B) inverse 1.37931 0.344828

0.517241 1.37931

FA = 0.965517 0.034483

0.862069 0.137931

ARCO Quality Control

Number of samples 20

Sample size 100

Data Results

# Defects % Defects Total Sample Size 2000

Sample 1 6 0.06 Total Defects 80

Sample 2 5 0.05 Percentage defects 0.04

Sample 3 0 0 Std dev of p-bar 0.019596

Sample 4 1 0.01

Sample 5 4 0.04 Upper Control Limit 0.098788

Sample 6 2 0.02 Center Line 0.04

Sample 7 5 0.05 Lower Control Limit 0

Sample 8 3 0.03

Sample 9 3 0.03

Sample 10 2 0.02

Sample 11 6 0.06

Sample 12 1 0.01

Sample 13 8 0.08

Sample 14 7 0.07

Sample 15 5 0.05

Sample 16 4 0.04

Sample 17 11 0.11 Above UCL

Sample 18 3 0.03

Sample 19 0 0

Sample 20 4 0.04

Graph information

Sample 1 0.06 0 0

Sample 2 0.05 0 0

Sample 3 0 0 0

Sample 4 0.01 0 0

Sample 5 0.04 0 0

Sample 6 0.02 0 0

Sample 7 0.05 0 0

Sample 8 0.03 0 0

Sample 9 0.03 0 0

Sample 10 0.02 0 0

Sample 11 0.06 0 0

Sample 12 0.01 0 0

Sample 13 0.08 0 0

Sample 14 0.07 0 0

Sample 15 0.05 0 0

Sample 16 0.04 0 0

Sample 17 0.11 0 0

Sample 18 0.03 0 0

Sample 19 0 0 0

Sample 20 0.04 0 0

AHP n= 3

Hardware Sys.1 Sys.2 Sys.3 Sys.1 Sys.2 Sys.3 Priority Wt. sum vector Consistency vector

Sys.1 1 3 9 Sys.1 0.6923 0.7200 0.5625 0.6583 2.0423 3.1025 Lambda

Sys.2 0.3333 1 6 Sys.2 0.2308 0.2400 0.3750 0.2819 0.8602 3.0512 CI

Sys.3 0.1111 0.1667 1 Sys.3 0.0769 0.0400 0.0625 0.0598 0.1799 3.0086 CR

Column Total 1.4444 4.1667 16

Software Sys.1 Sys.2 Sys.3 Sys.1 Sys.2 Sys.3 Priority Wt. sum vector

Sys.1 1 0.5 0.125 Sys.1 0.0909 0.0769 0.0943 0.0874 0.2623 3.0014 Lambda

Sys.2 2 1 0.2 Sys.2 0.1818 0.1538 0.1509 0.1622 0.4871 3.0028 CI

Sys.3 8 5 1 Sys.3 0.7273 0.7692 0.7547 0.7504 2.2605 3.0124 CR

Column Total 11 6.5 1.325

Vendor Sys.1 Sys.2 Sys.3 Sys.1 Sys.2 Sys.3 Priority Wt. sum vector

Sys.1 1 1 6 Sys.1 0.4615 0.4286 0.6000 0.4967 1.5330 3.0863 Lambda

Sys.2 1 1 3 Sys.2 0.4615 0.4286 0.3000 0.3967 1.2132 3.0582 CI

Sys.3 0.1667 0.3333 1 Sys.3 0.0769 0.1429 0.1000 0.1066 0.3216 3.0172 CR

Column Total 2.1667 2.3333 10

Factor Hard. Soft. Vendor Hardware Software Vendor Priority Wt. sum vector

Hardware 1 0.125 0.3333 Hardware 0.0833 0.0857 0.0769 0.0820 0.2460 3.0004 Lambda

Software 8 1 3 Software 0.6667 0.6857 0.6923 0.6816 2.0468 3.0031 CI

Vendor 3 0.3333 1 Vendor 0.2500 0.2286 0.2308 0.2364 0.7096 3.0011 CR

Column Total 12 1.4583 4.3333

n RI Hardware Software Vendor Priority

2 0.00 Sys.1 0.658 0.087 0.497 0.231

3 0.58 Sys.2 0.282 0.162 0.397 0.227

4 0.90 Sys.3 0.060 0.750 0.107 0.542

5 1.12

6 1.24

7 1.32

8 1.41

Consistency vector

3.0541

0.0270

0.0466

3.005543075

0.0028

0.0048

3.0539

0.0269

0.0464

3.0015

0.0008

0.0013

Matrix Multiplication

A= 1 2 3 B= 2 1

1 2 0 1 1

3 2

AxB = 13 9

4 3

Matrix Inverse

A= 2 1 A-inverse= 1.5 -0.5

4 3 -2 1

Matrix Determinant

A= 3 4 det(A)= -10

4 2

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