quantitative management

5/21/2018 Quantitative Management

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Program Name Source Content1.3 Pritchett Clock Repair Shop Excel QM Breakeven Analysis1.4 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

2.3 Normal distribution Excel Normal distribution2.4 F Distribution Excel F distribution probabilities2.5 Exponential Distribution Excel Exponential probabilities2.6 Poisson distribution Excel Poisson probabilities3.1 Thompson Lumber Excel Decision Table3.5 Bayes Theorem for Thompson Lumber Example Excel Bayes Theorem4.1 Triple A Construction Company Sales Excel Regression4.2 Jenny Wilson Realty Excel Multiple Regression

4.3 Jenny Wilson Realty Excel Dummy Variables - Regressio4.4 MPG Data Excel Linear Regression4.5 MPG Data Excel Nonlinear Regression4.6 Solved Problem 4-2 Excel Regression

4.8 Triple A Construction Company Sales Excel QM Regression5.1 Wallace Garden Supply Shed Sales Excel QM Weighted Moving Average5.2 Port of Baltimore Excel QM Exponential Smoothing5.3 Midwestern Manufacturing's Demand Excel QM Expo. Smoothing with Trend5.4 Midwestern Manufacturing's Demand Excel Trend Analysis5.5 Midwestern Manufacturing's Demand Excel QM Trend Analysis

5.6 Turner Industries Excel QM Multiplicative Decomposition5.7 Turner Industries Excel Multiple Regression6.1 Sumco Pump Company Excel QM EOQ Model6.2 Brown Manufacturing Excel QM Production Run Model6.3 Brass Department Store Excel QM Quantity Discount Model6.4 Hinsdale Company Safety Stock Excel QM Safety Stock7.2 Flair Furniture Excel Linear Programming7.4 Holiday Meal Turkey Ranch Excel Linear Programming7.6 High note sound company Excel Linear Programming7.7 Flair Furniture Excel QM Linear Programming8.1 Win Big Gambling Club Excel Linear Programming

8.2 Management Science Associates Excel Linear Programming8.3 Fifth Avenue Industries Excel Linear Programming8.4 Greenberg Motors Excel Linear Programming8.5 Labor Planning Example Excel Linear Programming8.6 ICT Portfolio Selection Excel Linear Programming

8.5xx Top Speed Bicycle Company Excel Linear Programming8.7 Goodman Shipping Excel Linear Programming8.8 Whole Foods Nutrition Problem Excel Linear Programming

8.9 Low Knock Oil Company Excel Linear Programming8.10 Top Speed Bicycle Company Excel Linear Programming9.1 Transportation Example Excel Linear Programming9.2 Fix-It Shop Excel QM Linear Programming9.3 Frosty Machines Transshipment Problem Excel Linear Programming9.4 Transportation Problem - Birmingham Excel QM Transportation9.5 Fix-It Shop Assignment Excel QM Assignment9.1 Executive Furniture Company Excel QM Transportation9.2 Birmingham Plant Excel QM Transportation


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10.2 Harrison Electric IP Analysis Excel Integer programming10.4 Bagwell Chemical Company Excel Integer programming10.5 Quemo Chemical Company Excel Integer programming

10.6 Sitka Manufacturing Company Excel Integer programming10.7 Simkin, Simkin and Steinberg Excel Integer programming10.9 Great Western Appliance Excel Nonlinear programming

10.10 Hospicare Corp Excel Nonlinear programming10.11 Thermlock Gaskets Excel Nonlinear programming10.12 Solved Problem 10-1 Excel 0-1 programming10.13 Solved Problem 10-3 Excel Nonlinear programming12.1 PERT - General Foundry Example Excel QM Crashing12.2 Crashing General Foundry Problem Excel Crashing

12.extra Crashing General Foundry Problem Excel QM Crashing13.1 Arnold's Muffler Shop Excel QM Single Server (M/M/1) system

13.2 Arnold's Muffler Shop Excel QM Multi-Server (M/M/m) system13.3 Golding Recycling, Inc. Excel QM Constant Service Rate (M/D/1)13.4 Department of Commerce Excel QM Finite population14.2 Harry's Tire Shop Excel Simulation (inventory)

14.3 Generating Normal Random Numbers Excel Random #s and Frequency14.4 Harry's Tire Shop Excel QM Simulation (inventory)14.5 Port of New Orleans Barge Unloadings Excel Simulation (waiting line)14.6 Three Hills Power Company Excel Maintenance Simulation15.3 Three Grocery Example Excel Markov Analysis15.4 Accounts Receivable Example Excel Fundamental Matrix & Absorbi

16.1 Box Filling Example Excel QM Quality = x-bar chart16.2 Super Cola Example Excel QM Quality = x-bar chart16.3 ARCO Excel QM p-Chart Analysis16.4 Red Top Cab Company Excel QM c-Chart Analysis

ModuleM1.1 AHP ExcelM5.1 Matrix Multiplication Excel


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g States


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Pritchett Clock Repair Shop

Breakeven Analysis

Data

Rebuilt Springs

Fixed cost 1000Variable cost 5Revenue 10

Results

Breakeven pointsUnits 200

Dollars 2,000.00$

Graph

Units Costs Revenue0 1000 0

400 3000 4000

0

1000

2000

3000

4000

5000

0 200 400 600

$

Units

Cost-volume analysis

Costs Revenue


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Pritchett Clock Repair Shop

Breakeven Analysis

Data

Rebuilt Springs

Fixed cost 1000Variable cost 5Revenue 10.71Volume (optional) 250

Results

Breakeven pointsUnits 175

Dollars 1,875.00$

Volume Analysis@ 250Costs 2,250.00$Revenue 2,678.57$

Profit 428.57$

Graph

Units Costs Revenue0 1000 0

350 2750 3750


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X P(X) XP(X) (X - E(X))2P(X)

5 0.1 0.5 0.441

4 0.2 0.8 0.242

3 0.3 0.9 0.003

2 0.3 0.6 0.243

1 0.1 0.1 0.361

E(X) = XP(X) = 2.9 1.290 = Variance

1.136 = Standard deviati

To see the formulas, hold down the CTRL key and press the ` (Grave accent) key


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n


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The Binomial Distribution

X = random variable for number of successes

n= 5 number of trials

p= 0.5 probability of a succes

r= 4 specific number of successes

Cumulative probability P(X < r) = 0.96875

Probability of exactly rs P(X = r) = 0.15625


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X is a normal random variablewith mean, , and standard deviation, .

= 100

= 20

x= 75

P(X x) = 0.89435


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F Distribution with df1 and df2 degrees of freedom

To find F given df1 = 5

df2 = 6

= 0.05

F-value = 4.39

To find the probability to the right of a calculated value,fdf1 = 5

df2 = 6

f= 4.2

P(F > f) = 0.0548


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Exponential distribution - the random variable (X) is time

Average number per time period = = 3 per hour

t= 0.5000 hours

P(X t) = 0.2231


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Poisson distribution - the random variable is the number of occurrences per time period

= 2

x P(X) P(X < x)0 0.1353 0.13531 0.2707 0.40602 0.7293 0.6767


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Thompson Lumber

Decision Tables

Data Results

Profit

FavorableMarket

UnfavorableMarket EMV Minimum Maximum Hurwicz

Probability 0.5 0.5 coefficient 0.8

Large Plant 200000 -180000 10000 -180000 200000 124000Small plant 100000 -20000 40000 -20000 100000 76000Do nothing 0 0 0 0 0

Maximum 40000 0 200000 124000

Expected Value of Perfect InformationColumn best 200000 0 100000


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Bayes Theorem for Thompson Lumber Example

Fill in cells B7, B8, and C7

Probability Revisions Given a Positive SurveyState of

Nature P(Sur.Pos.Prior Prob. Joint Prob

Posterior

ProbabilityFM 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 SurveyState of

Nature P(Sur.Pos.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


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Triple A Construction Company SUMMARY OUTPUT

Sales (Y) Payroll (X) Regression Statistics

6 3 Multiple R 0.8333

8 4 R Square 0.6944

9 6 Adjusted R 0.6181

5 4 Standard E 1.3110

4.5 2 Observatio 6

9.5 5

ANOVA

df SS MS F gnificance

Regression 1 15.6250 15.6250 9.0909 0.0394

Residual 4 6.8750 1.7188Total 5 22.5

Coefficient ndard Err t Stat P-value ower 95%

Intercept 2 1.7425 1.1477 0.3150 -2.8381

Payroll (X) 1.25 0.4146 3.0151 0.0394 0.0989


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F

pper 95% wer 95.0 pper 95.0%

6.8381 -2.8381 6.8381

2.4011 0.0989 2.4011


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Jenny Wilson Realty

SELL PRICE SF AGE

95000 1926 30

119000 2069 40

124800 1720 30

135000 1396 15

142800 1706 32

145000 1847 38

159000 1950 27

165000 2323 30

182000 2285 26

183000 3752 35

200000 2300 18

211000 2525 17

215000 3800 40

219000 1740 12

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.8197

R Square 0.6719

Adjusted R Square 0.6122

Standard Error 24313

Observations 14

ANOVA

df SS MS F Significance F

Regression 2 1.3314E+10 6.7E+09 11.2619 0.002178765

Residual 11 6502131603 5.9E+08

Total 13 1.9816E+10

Coefficient tandard Erro t Stat P-value Lower 95% Upper 95%

Intercept 146631 25482.0829 5.7543 0.0001 90545.2073 202716.5798

SF 43.819 10.2810 4.2622 0.0013 21.1911 66.4476AGE -2898.7 796.5649 -3.6390 0.0039 -4651.9139 -1145.4586


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Lower 95.0% Upper 95.0%

90545.2073 202716.5798

21.1911 66.4476-4651.9139 -1145.4586


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Jenny Wilson Realty

SELL PRICE SF AGE X3 (Exc.) X4 (Mint) Condition

95000 1926 30 0 0 Good

119000 2069 40 1 0 Excellent

124800 1720 30 1 0 Excellent

135000 1396 15 0 0 Good

142800 1706 32 0 1 Mint

145000 1847 38 0 1 Mint

159000 1950 27 0 1 Mint

165000 2323 30 1 0 Excellent

182000 2285 26 0 1 Mint

183000 3752 35 0 0 Good

200000 2300 18 0 0 Good

211000 2525 17 0 0 Good

215000 3800 40 1 0 Excellent

219000 1740 12 0 1 Mint

SUMMARY OUTPUT


Multiple R 0.9476

R Square 0.8980

Adjusted R Sq 0.8526

Standard Erro 14987.5545

Observations 14

ANOVA

df SS MS F ignificance F

Regression 4 1.78E+10 4.45E+09 19.804436 0.000174

Residual 9 2.02E+09 2.25E+08

Total 13 1.98E+10

Coefficients andard Err t Stat P-value Lower 95%Upper 95%ower 95.0 pper 95.0

Intercept 121658.45 17426.61 6.981 0.000 82236.71 ######## 82236.71 ########

SF 56.43 6.95 8.122 0.000 40.71 72.14 40.71 72.14

AGE -3962.82 596.03 -6.649 0.000 -5311.13 -2614.51 -5311.13 -2614.51

X3 (Exc.) 33162.65 12179.62 2.723 0.023 5610.43 60714.87 5610.43 60714.87

X4 (Mint) 47369.25 10649.27 4.448 0.002 23278.93 71459.57 23278.93 71459.57


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Automobile Weight vs. MPG SUMMARY OUTPUT

MPG (Y) eight (X1) Regression Statistics12 4.58 Multiple R 0.8628813 4.66 R Square 0.7445615 4.02 Adjusted R 0.71902

18 2.53 Standard 5.0075719 3.09 Observatio 12

19 3.1120 3.18 ANOVA

23 2.68 df SS MS F ignificance F 24 2.65 Regressio 1 730.909 730.909 29.14802 0.00030233 1.70 Residual 10 250.7577 25.0757736 1.95 Total 11 981.6667

42 1.92

Coefficient andard Err t Stat P-value Lower 95%Upper 95%

Intercept 47.6193 4.813151 9.89359 1.75E-06 36.89498 58.34371Weight (X1 -8.246 1.527345 -5.39889 0.000302 -11.6491 -4.84283


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ower 95.0 pper 95.0%

36.89498 58.34371-11.6491 -4.84283


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Automobile Weight vs. MPG SUMMARY OUTPUT

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

12 4.58 20.98 Multiple R 0.920813 4.66 21.72 R Square 0.847815 4.02 16.16 Adjusted R 0.8140

18 2.53 6.40 Standard 4.074519 3.09 9.55 Observatio 12

19 3.11 9.6720 3.18 10.11 ANOVA

23 2.68 7.18 df SS MS F 24 2.65 7.02 Regressio 2 832.2557 416.1278 25.066133 1.70 2.89 Residual 9 149.411 16.6012236 1.95 3.80 Total 11 981.6667

42 1.92 3.69

Coefficient andard Err t Stat P-value

Intercept 79.7888 13.5962 5.8685 0.0002Weight (X1 -30.2224 8.9809 -3.3652 0.0083

WeightSq. 3.4124 1.3811 2.4708 0.0355


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ignificance F

0.000209

Lower 95%Upper 95% ower 95.0 pper 95.0%

49.0321 110.5454 49.0321 110.5454-50.5386 -9.9062 -50.5386 -9.9062

0.2881 6.5367 0.2881 6.5367


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Solved Problem 4-2

Advertising ($100) Y Sales X11 56 310 7

6 212 8

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.9014R Square 0.8125

Adjusted R Square 0.7500Standard Error 1.4142Observations 5

ANOVA


Regression 1 26 26 13 0.036618Residual 3 6 2Total 4 32

Coefficient andard Err t Stat P-value Lower 95%Upper 95% ower 95.0

Intercept 4 1.5242 2.6244 0.0787 -0.8506 8.8506 -0.8506Sales X 1 0.2774 3.6056 0.0366 0.1173 1.8827 0.1173


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pper 95.0%

8.85061.8827


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Triple A Construction

Forecasting Regression/Trend analysis

Data Forecasts and Error AnalysisPeriod Demand (y) Period(x) Forecast Error Absolute Squared Abs Pct ErrPeriod 1 6 3 5.75 0.25 0.25 0.0625 04.17%Period 2 8 4 7 1 1 1 12.50%Period 3 9 6 9.5 -0.5 0.5 0.25 05.56%Period 4 5 4 7 -2 2 4 40.00%Period 5 4.5 2 4.5 0 0 0 00.00%Period 6 9.5 5 8.25 1.25 1.25 1.5625 13.16%

Total 0 5 6.875 75.38%

Intercept 2 Average 0 0.833333 1.145833 12.56%Slope 1.25 Bias MAD MSE MAPE

SE 1.311011

Next period 10.75 7Correlatio 0.833333


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Wallace Garden Supply

Forecasting Weighted moving averages - 3 period moving average

Data Forecasts and Error Analysis

Period Demand Weights Forecast Error Absolute Squared Abs Pct ErrJanuary 10 1February 12 2March 13 3April 16 12.1667 3.8333 3.8333 14.6944 23.96%May 19 14.3333 4.6667 4.6667 21.7778 24.56%June 23 17 6 6 36 26.09%July 26 20.5 5.5 5.5 30.25 21.15%

August 30 23.8333 6.1667 6.1667 38.0278 20.56%September 28 27.5 0.5 0.5 0.25 01.79%October 18 28.3333 -10.3333 10.3333 106.7778 57.41%November 16 23.3333 -7.3333 7.3333 53.7778 45.83%

December 14 18.6667 -4.6667 4.6667 21.7778 33.33%Total 4.3333 49.0000 323.3333 254.68%

Average 0.4815 5.4444 35.9259 28.30%Bias MAD MSE MAPE

SE 6.79636

Next period 15.3333333


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Port of Baltimore

Forecasting Exponential smoothing

Alpha 0.1Data Forecasts and Error Analysis

Period Demand Forecast Error Absolute Squared Abs Pct ErrQuarter 1 180 175 5 5 25 02.78%Quarter 2 168 175.5 -7.5 7.5 56.25 04.46%Quarter 3 159 174.75 -15.75 15.75 248.0625 09.91%Quarter 4 175 173.175 1.825 1.825 3.330625 01.04%Quarter 5 190 173.3575 16.6425 16.6425 276.9728 08.76%Quarter 6 205 175.0218 29.97825 29.97825 898.6955 14.62%

Quarter 7 180 178.0196 1.980425 1.980425 3.922083 01.10%Quarter 8 182 178.2176 3.782382 3.782382 14.30642 0.02078232

Total 35.95856 82.45856 1526.54 44.75%

Average 4.49482 10.30732 190.8175 05.59%

Bias MAD MSE MAPESE 15.95065

Next period 178.595856


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Midwestern Manufacturing

Forecasting Trend adjusted exponential smoothing

Alpha 0.3

Beta 0.4Data Forecasts and Error Analysis

Period Demand

SmoothedForecast,Ft

SmoothedTrend, Tt

ForecastIncludingTrend,FITt Error Absolute Squared

Period 1 74 74 74 0 0 0Period 2 79 74 0 74 5 5 25Period 3 80 75.5 0.6 76.1 4.5 4.5 20.25Period 4 90 77.27 1.068 78.338 12.73 12.73 162.0529Period 5 105 81.8366 2.46744 84.30404 23.1634 23.1634 536.5431

Period 6 142 90.51283 4.950955 95.46378 51.48717 51.4872 2650.929

Period 7 122 109.4246 10.5353 119.9599 12.57535 12.5754 158.1395Next period 120.572 10.78011 131.3521

Total 109.4559 109.456 3552.914

Average 15.63656 15.6366 507.5592Bias MAD MSE

SE 26.65676


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Abs PctErr

00.00%06.33%05.63%14.14%22.06%

36.26%

0.103077

94.73%

13.53%MAPE


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Time (X) Demand (Y)1 742 793 804 90

5 1056 1427 122

SUMMARY OUTPUT


Multiple R 0.89491R Square 0.800863Adjusted R 0.761036

Standard 12.43239Observatio 7

ANOVA


Regressio 1 3108.036 3108.036 20.10837 0.006493Residual 5 772.8214 154.5643Total 6 3880.857

Coefficientsandard Err t Stat P-value Lower 95%Upper 95% ower 95.0 pper 95.0%

Intercept 56.71429 10.50729 5.397615 0.002948 29.70445 83.72412 29.70445 83.72412Time (X) 10.53571 2.349501 4.484236 0.006493 4.496131 16.5753 4.496131 16.5753


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Forecasting Regression/Trend analysis

Data Forecasts and Error AnalysisPeriod Demand (y) Period(x) Forecast Error Absolute SquaredYear 1 74 1 67.25 6.75 6.75 45.5625Year 2 79 2 77.7857 1.2143 1.2143 1.4745Year 3 80 3 88.3214 -8.3214 8.3214 69.2462Year 4 90 4 98.8571 -8.8571 8.8571 78.4490Year 5 105 5 109.3929 -4.3929 4 .3929 19.2972Year 6 142 6 119.9286 22.0714 22.0714 487.1480Year 7 122 7 130.4643 -8.4643 8 .4643 71.6441

Total -4.26326E-14 60.0714 772.8214

Intercept 56.7142857 Average -6.09037E-15 8.5816 110.4031Slope 10.5357143 Bias MAD MSE

SE 12.43239Next period 141 8

Correlatio 0.89491


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Abs Pct Err09.12%01.54%10.40%09.84%04.18%15.54%06.94%

57.57%

08.22%MAPE


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Turner Industries

Forecasting Multiplicative decomposition

4 seasons

DataPeriod Demand (y) Time (x) Average Ratio Seasonal Smoothed UnadjustedPeriod 1 108 1 0.8491 127.1979 127.1187Period 2 125 2 0.9626 129.8589 129.4621Period 3 150 3 131 132.000 1.136 1.1315 132.5660 131.8056Period 4 141 4 133 134.125 1.051 1.0571 133.3841 134.1490Period 5 116 5 135.25 136.375 0.851 0.8491 136.6200 136.4924Period 6 134 6 137.5 138.875 0.965 0.9626 139.2087 138.8359

Period 7 159 7 140.25 141.125 1.127 1.1315 140.5199 141.1793Period 8 152 8 142 143.000 1.063 1.0571 143.7899 143.5227Period 9 123 9 144 145.125 0.848 0.8491 144.8643 145.8662Period 10 142 10 146.25 147.875 0.960 0.9626 147.5197 148.2096

Period 11 168 11 149.5 1.1315 148.4739 150.5530Period 12 165 12 1.0571 156.0878 152.8965

Average Intercept 124.7753Slope 2.3434

RatiosSeason 1 Season 2 Season 3 Season 4

1.1364 1.05130.8506 0.9649 1.1267 1.06290.8475 0.9603

Average 0.8491 0.9626 1.1315 1.0571

ForecastsPeriod Unadjusted Seasonal Adjusted

13 155.240 0.849 131.81014 157.583 0.963 151.68715 159.927 1.132 180.95916 162.270 1.057 171.535


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Forecasts and Error AnalysisAdjusted Error |Error| Error^2 Abs Pct Err

107.9327 0.0673 0.0673 0.0045 00.06%124.6181 0.3819 0.3819 0.1458 00.31%149.1396 0.8604 0.8604 0.7403 00.57%141.8086 -0.8086 0.8086 0.6538 00.57%115.8917 0.1083 0.1083 0.0117 00.09%133.6411 0.3589 0.3589 0.1288 00.27%

159.7461 -0.7461 0.7461 0.5567 00.47%151.7175 0.2825 0.2825 0.0798 00.19%123.8507 -0.8507 0.8507 0.7236 00.69%142.6641 -0.6641 0.6641 0.4410 00.47%

170.3526 -2.3526 2.3526 5.5346 01.40%161.6265 3.3735 3.3735 11.3807 02.04%

Total 0.0107 10.8547 20.4014 07.14%0.0009 0.9046 1.7001 00.59%

Bias MAD MSE MAPESE 1.8439709


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Year Quarter Sales Time Peri X2 Qtr 2 X3 Qtr 3 X4 Qtr 41 1 108 1 0 0 0

2 125 2 1 0 0

3 150 3 0 1 04 141 4 0 0 1

2 1 116 5 0 0 0

2 134 6 1 0 03 159 7 0 1 04 152 8 0 0 1

3 1 123 9 0 0 02 142 10 1 0 03 168 11 0 1 04 165 12 0 0 1

SUMMARY OUTPUT


Multiple R 0.99718

R Square 0.99436Adjusted R 0.99114Standard E 1.83225Observatio 12

ANOVA


Regressio 4 4144.75 1036.188 308.6516 6.03E-08Residual 7 23.5 3.357143Total 11 4168.25

Coefficient andard Err t Stat P-value Lower 95%Upper 95% ower 95.0 pper 95.0%

Intercept 104.104 1.332194 78.14493 1.48E-11 100.954 107.2543 100.954 107.2543X1 Time P 2.3125 0.16195 14.27913 1.96E-06 1.92955 2.69545 1.92955 2.69545X2 Qtr 2 15.6875 1.504767 10.4252 1.62E-05 12.12929 19.24571 12.12929 19.24571X3 Qtr 3 38.7083 1.530688 25.28819 3.86E-08 35.08883 42.32784 35.08883 42.32784X4 Qtr 4 30.0625 1.572941 19.11228 2.67E-07 26.34308 33.78192 26.34308 33.78192


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Sumco Pump Company

Inventory Economic Order Quantity Model

Data

Demand rate, D 1000Setup cost, S 10Holding cost, H 0.5 (fixed amount)Unit Price, P 0

Results

Optimal Order Quantity, Q 200

Maximum Inventory 200Average Inventory 100Number of Setups 5

Holding cost $50.00Setup cost $50.00

Unit costs $0.00

Total cost, Tc $100.00

COST TABLE Start at 25 Increment 15

Q Setup cost Holding co Total cost

25 400 6.25 406.2540 250 10 26055 181.8182 13.75 195.568270 142.8571 17.5 160.357185 117.6471 21.25 138.8971

100 100 25 125115 86.95652 28.75 115.7065130 76.92308 32.5 109.4231145 68.96552 36.25 105.2155

160 62.5 40 102.5175 57.14286 43.75 100.8929190 52.63158 47.5 100.1316

205 48.78049 51.25 100.0305220 45.45455 55 100.4545235 42.55319 58.75 101.3032250 40 62.5 102.5265 37.73585 66.25 103.9858280 35.71429 70 105.7143295 33.89831 73.75 107.6483

310 32.25806 77.5 109.7581325 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


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340 29.41176 85 114.4118355 28.16901 88.75 116.919370 27.02703 92.5 119.527


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Brown Manufacturing

Inventory Production Order Quantity Model

Data

Demand rate, D 10000Setup cost, S 100Holding cost, H 0.5 (fixed amount)Daily production rate, p 80

Daily demand rate, d 60Unit price, P 0

Results

Optimal production quantity, Q* 4000Maximum Inventory 1000Average Inventory 500Number of Setups 2.5

Holding cost 250Setup cost 250

Unit costs 0

Total cost, Tc 500

COST TABLE Start at 1000 Increment 333.3333

Q Setup cost Holding co Total cost1000 1000 62.5 1062.5

1333.333 750 83.33333 833.33331666.667 600 104.1667 704.1667

2000 500 125 6252333.333 428.5714 145.8333 574.40482666.667 375 166.6667 541.6667

3000 333.3333 187.5 520.83333333.333 300 208.3333 508.33333666.667 272.7273 229.1667 501.8939

4000 250 250 500

4333.333 230.7692 270.8333 501.60264666.667 214.2857 291.6667 505.9524

5000 200 312.5 512.5

5333.333 187.5 333.3333 520.83335666.667 176.4706 354.1667 530.6373

6000 166.6667 375 541.66676333.333 157.8947 395.8333 553.72816666.667 150 416.6667 566.6667

7000 142.8571 437.5 580.35717333.333 136.3636 458.3333 594.697

7666.667 130.4348 479.1667 609.60148000 125 500 625

0

200

400

600

800

1000

1200

10002666.6666674333.33333360007666.666667

Cost($)

Order Quantity (Q)

Inventory: Cost vs Quantity


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8333.333 120 520.8333 640.83338666.667 115.3846 541.6667 657.0513


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Setup cost

Holding cost

Total cost


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Brass Department Store

Inventory Quantity Discount Model

Data

Demand rate, D 5000Setup cost, S 49Holding cost %, I 20%

Range 1 Range 2 Range 3

Minimum quantity 0 1000 2000Unit Price, P 5 4.8 4.75

Results

Range 1 Range 2 Range 3Q* (Square root formula) 700 714.4345083 718.1848465Order Quantity 700 1000 2000

Holding cost $350.00 $480.00 $950.00Setup 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


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=

$24,725.00


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6.4

Inventory

Model: Demand during leadtime and its standard deviation given Model: Daily demand and its standard deviation ar

Data Data

Average demand during lead time, 350 Average daily demand

Standard deviation of dLT 10 Standard deviation of daily demand, d

Service level (% of demand met) 95.00% Lead time days Service level (% of demand met) 97

Results Results

Z-value 1.64 Z-value

Safety stock 16.45 Average demand during lead time

Standard deviation of demand during lead tim

Safety stock 1

Reorder Point 7

Models: Either daily demand, lead time or both are variable

Data

Average daily demand 25Standard deviation of daily demand 0

Average lead time (in days) 6

Standard deviation of lead time, LT 3

Service level (% of demand met) 98.00%

Results

Z-value 2.05

Average demand during lead time 150

Standard deviation of demand during lead time, dLT 75.00

Safety stock 154.03

Reorder point 304.03

Safety stock - Normal distribution

Enter 0 if demand is constant

Enter 0 if lead time is constant

241862962.xls.ms_office


47/137

Flair Furniture

Variables T (Tables) C (Chairs)

Units Produced 30 40 Profit

Objective function 70 50 4100

Constraints LHS (Hours used) RHS

Carpentry 4 3 240 < 240

Painting 2 1 100 < 100


48/137

Holiday Meal Turkey Ranch

Variables Brand 1 Brand 2

Units Produced 8.4 4.8 Cost

Objective function 2 3 31.2

Constraints LHS (Amt. of Ing.) RHS

Ingredient A 5 10 90 > 90

Ingredient B 4 3 48 > 48

Ingredient C 0.5 0 4.2 > 1.5


49/137

High Note Sound Company

Variables CD Player Receivers

Units Produced 0 20 Profit

Objective function 50 120 2400

Constraints LHS (Hrs. Used) RHS

Electrician Hours 2 4 80 < 80

Audio Tech Hours 3 1 20 < 60


50/137

7.7

Linear Programming

Signs< less than or equal to

= equals (You need to enter an apostrophe first.)> greater than or equal to

Data Results

x 1 x 2 LHS Slack/SurplusObjective 70 50 sign RHS 4100

Constraint 1 4 3 < 240 240 0Constraint 2 2 1 < 100 100 0

Results

Variables 30 40Objective 4100

Page 50


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Win Big Gambling ClubRadio Radio

TV Newspaper 30 sec. 1 min.

Variables X1 X2 X3 X4

Solution 1.9688 5 6.2069 0

Audience per ad 5000 8500 2400 2800

Constraints

Max. TV 1

Max. Newspaper 1

Max. 30-sec. radio 1

Max. 1 min. radio 1

Cost 800 925 290 380

Radio dollars 290 380

Radio spots 1 1


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F G H

Total Audience

67240.3017

LHS RHS

1.9688 < 12

5 < 5

6.2069 < 25

0 < 20

8000 < 8000

1800 < 1800

6.2069 > 5


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Management Science Associates

Variable X1 X2 X3 X4 X5 X6

Solution 0 600 140 1000 0 560 Total Cost

Min. Cost 7.5 6.8 5.5 6.9 7.25 6.1 15166

Constraints LHS RHS

Total Households 1 1 1 1 1 1 2300 > 2,300

30 and Younger 1 0 0 1 0 0 1000 > 1,000

31-50 0 1 0 0 1 0 600 > 600

Border States 0.85 0.85 0.85 -0.15 -0.15 -0.15 395 > 0

51+ Border States 0 0 0.8 0 0 -0.2 0 < 0


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A B C D E F G

Fifth Avenue Industries

All silk All poly. Blend 1 Blend 2


Values 5112 14000 16000 8500 Total Profit

Profit 16.24 8.22 8.77 8.66 412028.88

Constraints LHS

Silk available 0.125 0.066 1200 2240 115

2560 > 2240 3202560 < 2560 0

2560 < 2560 0

2355 < 2560 205

2560 < 2560 0

476.92 < 3300

1322.22 < 3300

757.69 < 3300

750 < 3300


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A B C D E F G H I J

Labor Planning Example

Variables F P1 P2 P3 P4 P5

Values 10 0 7 2 5 0 Total Cost

Cost 100 32 32 32 32 32 1448

Constraints LHS Sign RHS

9 a.m. - 10 a.m. 1 1 10 > 10

10 a.m. - 11 a.m. 1 1 1 17 > 12

11 a.m. - noon 0.5 1 1 1 14 > 14

noon - 1 p.m. 0.5 1 1 1 1 19 > 16

1 p.m. - 2 p.m. 1 1 1 1 1 24 > 18

2 p.m. - 3 p.m. 1 1 1 1 17 > 17

3 p.m. - 4 p.m. 1 1 1 15 > 15

4 p.m. - 5 p.m. 1 1 10 > 10

Max. Full time 1 10 < 12

Total PT hours 4 4 4 4 4 56 < 56


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K L M N O

Slack/Surplus

0

5

0

3

6

0

0

0

2

0


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A B C D E F G H

ICT Portfolio Selection

Variable X1 X2 X3 X4

Solution 750000 950000 1500000 1800000 Total Return

Max. Return 0.07 0.11 0.19 0.15 712000

LHS RHS

Trade 1 750000 < 1,000,000

Bonds 1 950000 < 2,500,000

Gold 1 1500000 < 1,500,000

Construction 1 1800000 < 1,800,000

Min. Gold+Constr -0.55 -0.55 0.45 0.45 550000 > 0

Min. Trade 0.85 -0.15 -0.15 -0.15 0 > 0

Total Invested 1 1 1 1 5000000 < 5000000


62/137

Goodman Shipping

Variables X1 X2 X3 X4 X5 X6

Values 0.3333 1 0 0 0 0 Total Value

Load Value $ 22500 24000 8000 9500 11500 9750 31500


Total weight 7500 7500 3000 3500 4000 3500 10000 < 10000

% Item 1 1 0.3333333 < 1

% Item 2 1 1 < 1

% Item 3 1 0 < 1

% Item 4 1 0 < 1

% Item 5 1 0 < 1

% Item 6 1 0 < 1


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A B C D E F G H

Whole Foods Nutrition Problem

Grain A Grain B Grain C

Variable Xa Xb Xc

Solution 0.025 0.05 0.05 Total Cost

Minimize 0.33 0.47 0.38 0.05075


Protein 22 28 21 3 > 3

Riboflavin 16 14 25 2.35 > 2

Phosphorus 8 7 9 1 > 1

Magnesium 5 0 6 0.425 > 0.425

Total Weight 1 1 1 0.125 = 0.125


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I J

Slack/Surplus

0

0.35

0

0

0


65/137

Low Knock Oil Company

X100 Reg X100 Econ X220 Reg X220 Econ

Variable X1 X2 X3 X4

Solution 15000 26666.67 10000 5333.33 Total Cost

Cost 30 30 34.8 34.8 1783600

Constraints LHS Sign

Demand Regular 1 1 25000 >

Demand Economy 1 1 32000 >

Ing. A in Regular -0.1 0.15 0 >

Ing. B in Economy 0.05 -0.25 0


66/137

RHS Slack/Surplus

25000 0

32000 0

0 0

0 0


67/137

Top Speed Bicycle CompanyN.O. to N.O. to N.O. to Omaha to Omaha to Omaha to

NY Chicago LA NY Chicago LA

Variables X11 X12 X13 X21 X22 X23

Values 10000 0 8000 0 8000 7000 Total Cost

Cost 2 3 5 3 1 4 96000

Constraints LHS

NY Demand 1 1 10000

Chi. Demand 1 1 8000

LA Demand 1 1 15000

N.O. Supply 1 1 1 18000

Omaha Supply 1 1 1 15000


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Sign RHS

= 10000

= 8000

= 15000

< 20000

< 15000


69/137

Shipping Cost Per Unit

From\To Albuquerque Boston Cleveland

Des Moines 5 4 3

Evansville 8 4 3

Fort Lauderdale 9 7 5

Solution - Number of units shipped

Albuquerque Boston Cleveland Total shipped Supply

Des Moines 100 0 0 100 100

Evansville 0 200 100 300 300

Fort Lauderdale 200 0 100 300 300

Total received 300 200 200

Demand 300 200 200

Total cost = 3900


70/137

Cost for Assignments

Person\Project Project 1 Project 2 Project 3

Adams 11 14 6

Brown 8 10 11

Cooper 9 12 7

Made

Project 1 Project 2 Project 3 Total pr Supply

Adams 0 0 1 1 1

Brown 0 1 0 1 1

Cooper 1 0 0 1 1

Total assigned to 1 1 1

Total workers 1 1 1

Total cost = 25


71/137

Frosty Machines Transshipment Problem

Shipping Cost Per Unit

From\To Chicago Buffalo NYC Phil. St.Louis

Toronto 4 7

Detroit 5 7

Chicago 6 4 5Buffalo 2 3 4

Solution - Number of units shipped

Chicago Buffalo NYC Phil. St.Louis tal shipp Supply

Toronto 650 150 800 800

Detroit 0 300 300 700

Chicago 0 350 300 650

Buffalo 450 0 0 450

Total received 650 450 450 350 300

Demand 450 350 300

Total cost = 9550


72/137

9.4

Birmingham

Transportation

Data

COSTS Dest 1 Dest 2 Dest 3 Dest 4 SupplyOrigin 1 73 103 88 108 15000Origin 2 85 80 100 90 6000Origin 3 88 97 78 118 14000Origin 4 84 79 90 99 11000Demand 10000 12000 15000 9000 46000 \ 46000

ShipmentsShipments Dest 1 Dest 2 Dest 3 Dest 4 Row Total

Origin 1 10000 0 1000 4000 15000

Origin 2 0 1000 0 5000 6000

Origin 3 0 0 14000 0 14000

Origin 4 0 11000 0 0 11000

Column Total 10000 12000 15000 9000 46000 \ 46000

Total Cost 3741000

Page 72


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9.4

Page 73


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9.5

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A B C D E F G

Fix-It Shop Assignment

Assignment

Data

COSTS Project 1 Project 2 Project 3

Adams 11 14 6Brown 8 10 11Cooper 9 12 7

Assignments

Shipments Project 1 Project 2 Project 3 Row Total Adams 1 1

Brown 1 1

Cooper 1 1

Column Total 1 1 1 3

Total Cost 25

Page 74


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9.5

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Page 75


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Harrison Electric Integer Programming AnalysisChandeliers Fans

Variables X1 X2

Values 5 0 Total Profit

Profit 7 6 35


Wiring hours 2 3 10 < 12

Assembly hours 6 5 30 < 30


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Bagwell Chemical Company

Xyline (bags) Hexall (lbs)

Variables X Y

Values 44 20 Total Profit

Profit 85 1.5 3770

Constraints LHS sign RHS

Ingredient A 30 0.5 1330 < 2000

Ingredient B 18 0.4 800 < 800

Ingredient C 2 0.1 90 < 200


78/137

Quemo Chemical Company

Catalytic Conv. Software Warehouse Expan.

Variables X1 X2 X3

Values 1 0 1 NPV

Net Present Value 25000 18000 32000 57000

Constraints LHS

Year 1 8000 6000 12000 20000

Year 2 7000 4000 8000 15000


79/137

sign RHS

< 20000

< 16000


80/137

Sitka Manufacturing Company

Baytown Lake Charles Mobile Baytown units


Values 0 1 1 0

Cost 340000 270000 290000 32

Constraints

Minimum capacity 1

Maximum in Baytown -21000 1

Maximum in L. C. -20000

Maximum in Mobile -19000


81/137

L. Charles units Mobile units

X5 X6

19000 19000 Cost

33 30 1757000

LHS Sign RHS

1 1 38000 > 38000

0 < 0

1 -1000 < 0

1 0 < 0


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`


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Simkin, Simkin and Steinberg

Variables X1 X2 X3 X4 X5 X6 X7

Values 0 0 1 1 1 1 0 Return

Return($1,000s) 50 80 90 120 110 40 75 360

Constraints LHS Sign

Texas 1 1 1 2 >

Foreigh Oil 1 1 1

Tensile Strength 13 1 80 >

Elasticity 0.7 1 17 >


88/137

RHS

125

80

17


89/137

Solved Problem 10-1

Variables X1 X2 X3

Values 1 1 0 Total

Maximize 50 45 48 95


Constraint 1 19 27 34 46 < 80

Constraint 2 22 13 12 35 < 40

Constraint 3 1 1 1 2 < 2

Constraint 4 1 -1 0 0 < 0


90/137

Forecasting - Exponential Smoothing

=0.3478 Ft+1= Ft+ (Yt-Ft)

Time Period (t) Demand (Yt) Forecast (Ft) Error = Yt- Ft |error|

1 110 110 0 -

2 156 110 46.000 46.0003 126 125.9999998 0.000 0.000

4 138 125.9999999 12.000 12.000

5 124 130.1739129 -6.174 6.174

6 125 128.026465 -3.026 3.026

7 160 126.9737815 33.026 33.026

8 138.4611617 MAD= 16.704

F1is assumed to be a perfect forecast.

MAD is based on time periods 2 through 7

`


91/137

General Foundry

Project Management Precedences; 3 time estimates

Data

Activity Optimistic Likely Pessimistic Mean Std dev Variance

A 1 2 3 2 0.333333 0.111111B 2 3 4 3 0.333333 0.111111C 1 2 3 2 0.333333 0.111111D 2 4 6 4 0.666667 0.444444E 1 4 7 4 1 1F 1 2 9 3 1.333333 1.777778G 3 4 11 5 1.333333 1.777778H 1 2 3 2 0.333333 0.111111

Precedences Immediate Predecessors (1 per column)Activity Time Pred 1 Pred 2A 2B 3

C 2 AD 4 BE 4 CF 3 CG 5 D EH 2 F G

Results

ActivityEarlyStart

EarlyFinish

LateStart

LateFinish Slack Variance

A 0 2 0 2 0 0.111111B 0 3 12 15 12

C 2 4 2 4 0 0.111111D 0 4 4 8 4E 4 8 4 8 0 1F 4 7 10 13 6G 8 13 8 13 0 1.777778H 13 15 13 15 0 0.111111

Project 15 Project 3.111111

Std.dev 1.763834

Early start computationsA 0 0B 0 0C 2 0

D 0 0E 4 0F 4 0G 4 8H 7 13

Late finish computationsA B C D E F G H

A 15 15 15 15 15 15 15 15B 15 15 15 15 15 15 15 15C 2 15 15 15 15 15 15 15

0 2 4 6

H

G

F

E

D

C

B

A

Gant

Critical Activity


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D 15 15 15 15 15 15 15 15

E 15 15 4 15 15 15 15 15F 15 15 10 15 15 15 15 15G 15 15 15 8 8 15 15 15H 15 15 15 15 15 13 13 15

2 15 4 8 8 13 13 15

Graph Critical Ac Noncritical Slack 9 Graph Critical Acti NoncriticalA 0 2 0 0 8 H 13 2 0B 0 0 3 12 7 G 8 5 0C 2 2 0 0 6 F 4 0 3

D 0 0 4 4 5 E 4 4 0E 4 4 0 0 4 D 0 0 4F 4 0 3 6 3 C 2 2 0G 8 5 0 0 2 B 0 0 3H 13 2 0 0 1 A 0 2 0


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8 10 12 14 16

ime

Chart

Noncritical Activity Slack


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Slack 006

040

120


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Crashing

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A B C D E F G H I J K L M

Project Management Crashing

Results

Data Normal time 15 Minimum crash cost to meet project goal 5,000.0$

Project goal 12 Minimum time 7 Project time

Immediate Predecessors (1 per column) Intermediate Computation

Activity

Normal

Time

Normal

Cost

Crash

Time Crash Cost Pred 1 Pred 2 Pred 3 Pred 4

Crash

days

Crash

cost/day Crash limit

A 2 22,000$ 1 23,000$ 0 1000

B 3 30,000$ 1 34,000$ 0 2000

C 2 26,000$ 1 27,000$ A 0 1000

D 4 48,000$ 3 49,000$ B 0 1000

E 4 56,000$ 2 58,000$ C 1 1000

F 3 30,000$ 2 30,500$ C 0 500

G 5 80,000$ 2 86,000$ D E 2 2000

H 2 16,000$ 1 19,000$ F G 0 3000

0 0



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Crashing

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

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

Minimize cost 1000 2000 1000 1000 1000 500 2000 3000

A crash max. 1

B crash max. 1C crash max. 1D crash max. 1E crash max. 1F crash max. 1G crash max. 1H crash max. 1Due dateStart 1A constraint 1 -1 1

B constraint 1 -1 1C constraint 1 -1 1D constraint 1 -1 1

E constraint 1 -1 1F constraint 1 -1 1G constraint 1 1 -1 1G constraint 2 1 -1 1H constraint 1 1 -1H constraint 2 1 -1Finish constraint


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XH XFIN12 12 Totals

5000

0 < 1

0 < 21 < 10 < 10 < 20 < 12 < 30 < 1

1 12 < 120 = 02 > 2

3 > 32 > 24 > 4

4 > 43 > 35 > 55 > 5

1 6 > 21 2 > 2-1 1 0 > 0


99/137

Arnold's Muffler Shop

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

Data ResultsArrival rate (l) 2 Average server utilization() 0.6666667

Service rate (m) 3 Average number of customers in the queue(Lq) 1.3333333

Average number of customers in the system(Ls) 2

Average waiting time in the queue(Wq) 0.6666667

Average time in the system(Ws) 1

Probability (% of time) system is empty (P0) 0.3333333

Probabilities

Number Probability

Cumulative

Probability

0 0.333333 0.3333331 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 0.99486213 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


100/137

Arnold's Muffler Shop

Waiting Lines M/M/s

Data Results

Arrival rate (l) 2 Average server utilization(r) 0.33333Service 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) 0.375Probability (% of time) system is empty (P0) 0.5

Probabilities

Number Probability Cumulative Probability0 0.500000 0.5000001 0.333333 0.8333332 0.111111 0.944444

3 0.037037 0.9814814 0.012346 0.9938275 0.004115 0.9979426 0.001372 0.9993147 0.000457 0.9997718 0.000152 0.9999249 0.000051 0.999975

10 0.000017 0.99999211 0.000006 0.99999712 0.000002 0.99999913 0.000001 1.00000014 0.000000 1.000000

15 0.000000 1.00000016 0.000000 1.00000017 0.000000 1.00000018 0.000000 1.00000019 0.000000 1.00000020 0.000000 1.000000

Computationsn or s (lam/mu)^nCumsum(n term2 P0(s)

0 11 0.666667 1 2 0.33333

2 0.222222 1.666667 0.333333333 0.53 0.049383 1.888889 0.063492063 0.51224 0.00823 1.938272 0.009876543 0.513315 0.001097 1.946502 0.001266223 0.513416 0.000122 1.947599 0.000137174 0.513427 1.16E-05 1.947721 1.2835E-05 0.513428 9.68E-07 1.947733 1.05569E-06 0.513429 7.17E-08 1.947734 7.74175E-08 0.51342

10 4.78E-09 1.947734 5.12021E-09 0.5134211 2.9E-10 1.947734 3.08314E-10 0.51342


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12 1.61E-11 1.947734 1.70369E-11 0.5134213 8.25E-13 1.947734 8.69754E-13 0.5134214 3.93E-14 1.947734 4.12575E-14 0.51342

15 1.75E-15 1.947734 1.82758E-15 0.5134216 7.28E-17 1.947734 7.59283E-17 0.5134217 2.85E-18 1.947734 2.96998E-18 0.51342

18 1.06E-19 1.947734 1.09751E-19 0.5134219 3.71E-21 1.947734 3.84312E-21 0.5134220 1.24E-22 1.947734 1.27871E-22 0.5134221 3.92E-24 1.947734 4.05276E-24 0.5134222 1.19E-25 1.947734 1.22628E-25 0.51342232425

26272829

30


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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 0.3750.222222 0.009292 0.675958 0.004646 0.3379790.166667 0.001014 0.667681 0.000507 0.333840.133333 0.0001 0.666767 5E-05 0.3333830.111111 8.8E-06 0.666675 4.4E-06 0.3333380.095238 6.94E-07 0.666667 3.47E-07 0.3333340.083333 4.93E-08 0.666667 2.46E-08 0.3333330.074074 3.18E-09 0.666667 1.59E-09 0.3333330.066667 1.88E-10 0.666667 9.39E-11 0.3333330.060606 1.02E-11 0.666667 5.11E-12 0.333333


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0.055556 5.15E-13 0.666667 2.57E-13 0.3333330.051282 2.41E-14 0.666667 1.21E-14 0.3333330.047619 1.06E-15 0.666667 5.3E-16 0.333333

0.044444 4.36E-17 0.666667 2.18E-17 0.3333330.041667 1.69E-18 0.666667 8.47E-19 0.3333330.039216 6.22E-20 0.666667 3.11E-20 0.333333

0.037037 2.17E-21 0.666667 1.08E-21 0.3333330.035088 7.17E-23 0.666667 3.59E-23 0.3333330.033333 2.26E-24 0.666667 1.13E-24 0.3333330.031746 6.82E-26 0.666667 3.41E-26 0.3333330.030303 1.97E-27 0.666667 9.84E-28 0.333333


104/137

Garcia-Golding Recycling

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

Data ResultsArrival rate (l) 8 Average server utilization() 0.66667Service rate (m) 12 Average number of customers in the queue( 0.66667

Average number of customers in the system( 1.33333


Average time in the system(Ws) 0.16667



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Department of Commerce

Waiting Lines M/M/s with a finite population

Data ResultsArrival rate (l) percustomer 0.05 Average server utilization() 0.43605

Service rate (m) 0.5 Average number of customers in the queue( 0.20347

Number of servers 1 Average number of customers in the system( 0.63952

Population size (N) 5 Average waiting time in the queue(Wq) 0.93326

Average time in the system(Ws) 2.93326


Effective arrival rate 0.21802

Probabilities

Number, nProbability,P(n)

CumulativeProbability Number waiting

Arrivalrate(n)

0 0.5639522 0.5639522 0 0.251 0.2819761 0.8459283 0 0.22 0.1127904 0.9587187 1 0.153 0.0338371 0.9925558 2 0.14 0.0067674 0.9993233 3 0.05

5 0.0006767 1 4 06

789

10111213141516

1718

1920212223242526

27


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282930

31


107/137

1.7732

Term 1Sum term1 Term 2

Sum term2

Decumterm 2 P0(s)

1 1 1 1 0.77320.5 1.5 0.5 1.5 0.2732 0.563952

0.2 1.7 0.07320.06 1.76 0.0132

0.012 1.772 0.0012

0.0012 1.7732 0


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109/137

Harry's Tire Shop NOTE: The random numbers appearing here may not be the same as the

Probability

ProbabilityRange(Lower)

CumulativeProbability

TiresDemand Day

RandomNumber

SimulatedDemand

0.05 0 0.05 0 1 0.749013 40.1 0.05 0.15 1 2 0.02899 00.2 0.15 0.35 2 3 0.884811 50.3 0.35 0.65 3 4 0.899167 50.2 0.65 0.85 4 5 0.280993 2

0.15 0.85 1 5 6 0.185889 2

7 0.804419 48 0.823777 49 0.828614 4

10 0.516824 3

Average 3.3Results (Frequency table)

Tires

Demanded Frequency Percentage Cum %0 1 10% 10%1 0 0% 10%

2 2 20% 30%3 1 10% 40%4 4 40% 80%5 2 20% 100%

10


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nes in the book, but the formulas are the same.


111/137

Generating Normal Random Numbers NOTE: The random numbers appearing here may not be the

Random number Value Frenquency Percentage

38.33354342 26 0 0.0%42.89283202 28 0 0.0%36.49922691 30 2 1.0%

36.67324261 32 5 2.5%45.14502646 34 12 6.0%45.72902181 36 21 10.5%50.97116406 38 38 19.0%46.26590129 40 27 13.5%

42.9651911 42 22 11.0%40.96517241 44 37 18.5%38.55602342 46 14 7.0%

43.06190751 48 8 4.0%43.87541925 50 6 3.0%39.56478684 52 6 3.0%42.13737029 54 2 1.0%

41.39973832 56 0 0.0%43.00174013 20034.2558161743.0955849636.7844488241.0944902233.0131466242.9769505953.4502542743.30170651

43.0507186143.7653313236.0935961349.6746342536.5981160836.81494395

42.146403747.1741548641.1733469234.4342925940.09943849

38.8198725133.3027605932.4734524735.85863836

42.9016355135.9353224644.4935401448.5472811934.55690611

40.7259057143.3210374

43.8158129850.40370106


112/137

37.5829748434.3869431137.65492797

39.7885607237.4677955

43.38597442

42.6179430947.98650113

35.643691939.7954461942.1869948137.8075269630.6724267842.22248811

42.2988788835.8626949941.5960531841.87531808

32.0909009435.4132651237.5995395436.7292453336.7739134233.91758675

35.8455867335.7610027952.2992796734.4535724932.0811465835.6104609529.6606363240.8162470144.0649487132.3411157938.21071496

38.4117330837.9573449443.2070964549.1007876635.1301440233.5781518241.2857909745.24384441

37.6101915836.5140885

41.5068683338.6613473746.1687682933.6110250144.4879240648.7945777336.67585305


113/137

39.7571252249.06770628

39.0065734

43.4720066337.8326497937.70117172

40.1219230137.8367967

35.5608142239.0130517739.64257038

40.49517138.4738750437.65895096

36.1532517241.5140933937.8485136635.76568223

30.7680201451.0194717138.1405888233.3219583932.8665140340.69205971

43.0427331441.1391085241.22180875

35.2407141.6360954836.3429971843.8114175236.7721109944.7456071847.2049091734.33502251

42.8346469536.9200377445.7275477547.9837384638.9175627738.7090675729.9912693544.83920704

39.1717756744.2817892530.6399690442.58332931

45.714996245.1661156736.1554877737.19684988

44.4819806


114/137

36.6634504238.70631398

30.1666704

43.3764789343.9269902837.93613195

42.1917960436.9791444239.6136809540.9728302440.8288144939.5062875341.5629889534.30379299

38.9320693443.1893346436.7338235236.73538256

35.3956102446.4965465250.0416403339.5762187139.9391034343.19220467

42.1421957246.4015225

33.3746352342.7311857139.7434825336.9185484736.5939172636.4948719248.0531400235.6165471442.29824094

42.1089660837.0079338341.8344167531.6440471339.8250613150.5159708539.1735413144.26856174

37.2868124343.0601827550.3728464742.93730679


115/137

same as the ones in the book, but the formulas are the same.


116/137

Harry's Auto Tire

Simulation

Data Expected Valuean om um er

Sorter Category name Value Frequency Probabilityumu at ve

Probabilitya ue

Frequency

0 Category 1 0 10 0.05 0.05 0

5 Category 2 1 20 0.1 0.15 20

15 Category 3 2 40 0.2 0.35 80

35 Category 4 3 60 0.3 0.65 180

65 Category 5 4 40 0.2 0.85 160

85 Category 6 5 30 0.15 1 150

Total 200 Expected

Simulation trials

Trial Random Number Value

1 49.75356111 3

2 42.54379616 3

3 11.05226624 1

4 62.55635162 3

5 71.66883241 4

6 5.916177498 1

7 93.94754024 5

8 25.57671549 2

9 47.28165517 3

10 78.25374746 4

11 67.34389427 4

12 18.13195089 2

13 96.69770853 5

14 30.23377211 2

15 70.05263663 4

16 41.15417291 3

17 38.03756793 3

18 93.90717526 5

19 77.94485754 420 19.80755946 2

21 28.13252851 2

22 69.21506643 4

23 0.500312304 0

24 29.91855277 2

25 45.08914438 3

26 20.1850716 2


117/137

27 1.568146042 0

28 35.06759342 3

29 29.44608384 2

30 1.650394772 0

31 11.78977206 1

32 15.07957347 233 49.64593402 3

34 85.86405494 5

35 47.01974311 3

36 81.18770223 4

37 91.12932558 5

38 35.01939474 3

39 49.82957379 3

40 97.62708078 5

41 35.38745003 3

42 55.2655906 3

43 27.25784406 2

44 98.59225737 5

45 13.3603896 1

46 57.0922683 3

47 39.49034515 3

48 82.70432574 4

49 81.73496458 4

50 48.4168796 3

51 5.863838022 1

52 87.13600433 5

53 16.89980093 254 2.052130368 0

55 40.21688124 3

56 37.72639478 3

57 47.27940932 3

58 31.53012169 2

59 97.05275029 5

60 90.89529571 5

61 50.72574086 3

62 21.14036658 2

63 64.16164814 3

64 68.31199018 4

65 15.14762553 2

66 82.39940644 4

67 86.71623896 5

68 45.19804529 3

69 16.52826671 2

70 8.316273711 1


118/137

71 20.23592569 2

72 85.07156223 5

73 46.33581234 3

74 68.58760209 4

75 6.748065244 1

76 97.12916056 577 59.55417353 3

78 26.77037407 2

79 58.35692882 3

80 86.64030945 5

81 10.00555475 1

82 86.94189832 5

83 51.61687751 3

84 17.43080505 2

85 49.99018171 3

86 95.76494308 5

87 58.52407969 3

88 23.68511265 2

89 49.55284676 3

90 0.340067186 0

91 86.79362625 5

92 54.92428559 3

93 90.45528737 5

94 18.49070424 2

95 5.184897201 1

96 77.14237858 4

97 29.9787242 298 26.52452622 2

99 19.19253761 2

100 38.64569639 3

101 77.03571206 4

102 66.71100413 4

103 88.30709644 5

104 51.2834334 3

105 96.11143092 5

106 68.49919457 4

107 25.18914031 2

108 30.94094365 2

109 65.82397601 4

110 90.49745425 5

111 37.12518443 3

112 97.43232255 5

113 90.54847083 5

114 96.82279681 5


119/137

115 15.55244215 2

116 42.05266869 3

117 76.42958958 4

118 45.42886023 3

119 75.14345752 4

120 14.42240401 1121 11.67018516 1

122 77.92921924 4

123 7.568238403 1

124 41.38309457 3

125 51.17274962 3

126 63.30237324 3

127 83.47502272 4

128 89.7935231 5

129 67.02763785 4

130 78.51442916 4

131 78.72777997 4

132 88.57089009 5

133 70.84061384 4

134 14.60441895 1

135 67.85007945 4

136 6.488823404 1

137 88.78264186 5

138 5.592798114 1

139 82.81251917 4

140 82.66463588 4

141 53.7984944 3142 51.06985285 3

143 55.61096172 3

144 5.25268015 1

145 1.275888173 0

146 9.779698475 1

147 36.19418236 3

148 99.79366023 5

149 64.18938138 3

150 33.24194216 2

151 39.74711287 3

152 52.73839263 3

153 3.324150796 0

154 81.94526538 4

155 75.10110078 4

156 13.20101822 1

157 33.512987 2

158 65.64648951 4


120/137

159 38.09242202 3

160 92.973034 5

161 96.85448947 5

162 99.76201734 5

163 67.83226315 4

164 52.25961874 3165 20.85287215 2

166 68.59143199 4

167 49.77202874 3

168 95.91308979 5

169 9.165848618 1

170 38.46528614 3

171 13.80354625 1

172 94.71454518 5

173 5.801084689 1

174 19.89390111 2

175 5.42482997 1

176 36.18840513 3

177 53.21520803 3

178 1.238436612 0

179 18.30744158 2

180 73.61210468 4

181 35.82893115 3

182 96.46123105 5

183 82.29677538 4

184 91.59234161 5

185 95.61315697 5186 57.96658021 3

187 63.51237763 3

188 45.92114184 3

189 23.81579413 2

190 15.72112027 2

191 14.42842134 1

192 55.76924652 3

193 43.8503737 3

194 19.96860346 2

195 73.40036979 4

196 11.75425553 1

197 43.4889831 3

198 93.41557714 5

199 18.95066131 2

200 65.14750415 4


121/137

Simulation results

Value

mu a on

Occurrences Percentage

ccurences

Value

0 8 0.04 0

1 24 0.12 24

2 35 0.175 70

3 59 0.295 177

4 37 0.185 148

5 37 0.185 185

Totals 200 1 604

Average 3.02


122/137

Port of New Orleans Barge Unloadings NOTE: The random numbers app

DayPreviouslydelayed

Randomnumber Arrivals

Total tobeunoaded

RandomNumber

Possiblyunloaded Unloaded

1 0 0.799987 4 4 0.522887 3 32 1 0.459957 3 4 0.491463 3 33 1 0.07101 0 1 0.236792 3 14 0 0.818166 4 4 0.221964 3 35 1 0.458993 3 4 0.534902 3 36 1 0.883063 4 5 0.982718 5 57 0 0.253188 1 1 0.586948 3 18 0 0.73145 4 4 0.575971 3 39 1 0.828907 4 5 0.868945 4 4

10 1 0.597244 3 4 0.211498 3 3

Barge Arrivals Unloading rates

Demand Probability Lower CumulativeDemand Number Probability Lower

0 0.13 0 0.13 0 1 0.05 01 0.17 0.13 0.3 1 2 0.15 0.052 0.15 0.3 0.45 2 3 0.5 0.23 0.25 0.45 0.7 3 4 0.2 0.74 0.2 0.7 0.9 4 5 0.1 0.9

5 0.1 0.9 1 5


123/137

aring here may not be the same as the ones in the book, but the formulas are the same.

CumulativeUnloading

0.05 10.2 20.7 30.9 4

1 5


124/137

Three Hills Power Company

Breakdown

number

Random

number

Time between

breakdowns

Time of

breakdowns

Time repairperson

is free

Random

Number Repair time

Repair

ends

1 0.3677 2 2 2 0.5662 2 4

2 0.2270 1.5 3.5 4 0.8556 3 7

3 0.5249 2 5.5 7 0.0661 1 8

4 0.6042 2.5 8 8 0.4632 2 10

5 0.7671 2.5 10.5 10.5 0.5069 2 12.5

6 0.3627 2 12.5 12.5 0.4491 2 14.5

7 0.0144 0.5 13 14.5 0.2288 1 15.5

8 0.4744 2 15 15.5 0.8321 3 18.5

9 0.7058 2.5 17.5 18.5 0.8228 3 21.5

10 0.6338 2.5 20 21.5 0.4145 2 23.5

Demand Table Repair times

Time

betweenbreakdowns Probability Lower Cumulative Demand Time Probability

0.5 0.05 0 0.05 0.5 1 0.28

1.0 0.06 0.05 0.11 1 2 0.52

1.5 0.16 0.11 0.27 1.5 3 0.20

2.0 0.33 0.27 0.6 2

2.5 0.21 0.6 0.81 2.5

3.0 0.19 0.81 1 3

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


125/137

Lower Cumulative Lead time

0.00 0.28 1

0.28 0.80 2

0.80 1.00 3


126/137

Three Grocery Example

State ProbabilitiesAmerican Food SFood 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 0.22 0.415 0.314 0.271 0.2 0.2 0.6

3 0.4176 0.3155 0.26694 0.41901 0.31599 0.2655 0.419807 0.316094 0.2640996 0.4202748 0.3160663 0.2636589


127/137

Accounts Receivable Example

1 0 0 0P= I : 0 = 0 1 0 0

A : B 0.6 0 0.2 0.20.4 0.1 0.3 0.2

I - B = 0.8 -0.2-0.3 0.8

F = (I - B) inverse 1.37931 0.3448280.517241 1.37931

FA = 0.965517 0.0344830.862069 0.137931


128/137

Box Filling Example

Quality Control x bar chart

Number of 1Sample siz 36

Populationstandarddeviation 2

Data Results

Mean

Sample 1 16 x-bar valu 16

Average 16 z value 3

Sigma x b 0.33333

Upper co 17

Center lin 16Lower co 15


129/137

Super Cola Example

Quality Control x bar chart

Number of 1

Sample size 5

Data Results

Mean Range Xbar Range

Sample 1 16.01 0.25 x-bar value 16.01

Average 16.01 0.25

R bar 0.25

Upper cont 16.15425 0.52875

Center line 16.01 0.25

Table Lower cont 15.86575 0

Sample

size, n

Mean

Factor, A2

UpperRange,

D4

LowerRange,

D32 1.88 3.268 03 1.023 2.574 0

4 0.729 2.282 05 0.577 2.115 06 0.483 2.004 07 0.419 1.924 0.0768 0.373 1.864 0.1369 0.337 1.816 0.184

10 0.308 1.777 0.22311 0.285 1.744 0.25612 0.266 1.716 0.284

13 0.249 1.692 0.30814 0.235 1.671 0.32915 0.223 1.652 0.34816 0.212 1.636 0.36417 0.203 1.621 0.37918 0.194 1.608 0.39219 0.187 1.596 0.40420 0.18 1.586 0.41421 0.173 1.575 0.42522 0.167 1.566 0.43423 0.162 1.557 0.443

24 0.157 1.548 0.45225 0.153 1.541 0.459


130/137

ARCO

Quality Control p chart

Number of 20

Sample siz 100

Data Results

# Defects % Defects Total Samp 2000

Sample 1 6 0.06 Total Defe 80

Sample 2 5 0.05 Percentag 0.04

Sample 3 0 0 Std dev of 0.019596

Sample 4 1 0.01 z value 3

Sample 5 4 0.04

Sample 6 2 0.02 Upper Con 0.098788

Sample 7 5 0.05 Center Lin 0.04

Sample 8 3 0.03 Lower Con 0

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 0.11Above UCL

Sample 18 3 0.03

Sample 19 0 0Sample 20 4 0.04

Graph information

Sample 1 0.06 0 0.04 0.098788

Sample 2 0.05 0 0.04 0.098788

Sample 3 0 0 0.04 0.098788

Sample 4 0.01 0 0.04 0.098788

Sample 5 0.04 0 0.04 0.098788

Sample 6 0.02 0 0.04 0.098788

Sample 7 0.05 0 0.04 0.098788

Sample 8 0.03 0 0.04 0.098788

Sample 9 0.03 0 0.04 0.098788

Sample 10 0.02 0 0.04 0.098788

Sample 11 0.06 0 0.04 0.098788

Sample 12 0.01 0 0.04 0.098788

0

0.02

0.04

0.06

0.08

0.1

0.12

1 3 5 7 9 11 13 15 17 1

Mean

Sample

p-chart


131/137

Sample 13 0.08 0 0.04 0.098788

Sample 14 0.07 0 0.04 0.098788

Sample 15 0.05 0 0.04 0.098788

Sample 16 0.04 0 0.04 0.098788

Sample 17 0.11 0 0.04 0.098788

Sample 18 0.03 0 0.04 0.098788

Sample 19 0 0 0.04 0.098788Sample 20 0.04 0 0.04 0.098788


132/137

9


133/137

Red Top Cab Company

Quality Control c chart

Number of 9

Data Results

# Defects Total unit 9

Sample 1 3 Total Def 54

Sample 2 0 Defect rat 6

Sample 3 8 Standard 2.44949

Sample 4 9 z value 3

Sample 5 6

Sample 6 7 Upper Co 13.3485

Sample 7 4 Center Li 6

Sample 8 9Lower Co 0Sample 9 8

ph informationSample 1 3 0 6 13.34847Sample 2 0 0 6 13.34847

Sample 3 8 0 6 13.34847Sample 4 9 0 6 13.34847Sample 5 6 0 6 13.34847

Sample 6 7 0 6 13.34847Sample 7 4 0 6 13.34847Sample 8 9 0 6 13.34847Sample 9 8 0 6 13.34847

0

5

10

15

1 2 3 4

Mean

c


134/137

5 6 7 8 9

Sample

-chart


135/137

AHP n= 3

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

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

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 Lamb

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 Lamb

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 Lamb

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


136/137

or

3.0541

0.0270

0.0466

3.005543075

0.0028

0.0048

3.0539

0.0269

0.0464

3.0015

0.0008

0.0013


137/137

Matrix Multiplication

A= 1 2 3 B= 2 11 2 0 1 1

3 2

AxB = 13 94 3

Matrix Inverse

A= 2 1 A-inverse= 1.5 -0.54 3 -2 1

Matrix Determinant

A= 3 4 det(A)= -104 2

quantitative management

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