Download - 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
Regression Statistics
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
df SS MS F ignificance F
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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Midwestern Manufacturing
Time (X) Demand (Y)1 742 793 804 90
5 1056 1427 122
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.89491R Square 0.800863Adjusted R 0.761036
Standard 12.43239Observatio 7
ANOVA
df SS MS F ignificance F
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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Midwestern Manufacturing
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
Regression Statistics
Multiple R 0.99718
R Square 0.99436Adjusted R 0.99114Standard E 1.83225Observatio 12
ANOVA
df SS MS F ignificance F
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
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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
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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
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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
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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
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A B C D E
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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15
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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11
12
A B C D E F G H I J
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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25
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27
28
29
30
A B C D E F G
Fifth Avenue Industries
All silk All poly. Blend 1 Blend 2
Variables X1 X2 X3 X4
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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25
26
27
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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21
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23
24
25
26
27
K L M N O
Slack/Surplus
0
5
0
3
6
0
0
0
2
0
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14
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
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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
Constraints LHS Sign RHS
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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7
8
9
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11
12
13
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
Constraints LHS Sign RHS
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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1
2
3
4
5
6
7
8
9
10
11
12
13
I J
Slack/Surplus
0
0.35
0
0
0
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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
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RHS Slack/Surplus
25000 0
32000 0
0 0
0 0
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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
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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
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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
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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
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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
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9.4
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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
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9.5
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H I
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Harrison Electric Integer Programming AnalysisChandeliers Fans
Variables X1 X2
Values 5 0 Total Profit
Profit 7 6 35
Constraints LHS Sign RHS
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
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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
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sign RHS
< 20000
< 16000
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Sitka Manufacturing Company
Baytown Lake Charles Mobile Baytown units
Variables X1 X2 X3 X4
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
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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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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 >
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RHS
125
80
17
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Solved Problem 10-1
Variables X1 X2 X3
Values 1 1 0 Total
Maximize 50 45 48 95
Constraints LHS Sign RHS
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
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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
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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
3
4
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20
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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4
5
6
7
89
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N
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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
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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
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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 waiting time in the queue(Wq) 0.04167
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
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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 waiting time in the queue(Wq) 0.08333
Average time in the system(Ws) 0.16667
Probability (% of time) system is empty (P0) 0.33333
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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
Probability (% of time) system is empty (P0) 0.56395
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
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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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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.
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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
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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
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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
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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
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same as the ones in the book, but the formulas are the same.
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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Lower Cumulative Lead time
0.00 0.28 1
0.28 0.80 2
0.80 1.00 3
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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
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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
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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
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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
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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
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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
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9
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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
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5 6 7 8 9
Sample
-chart
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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
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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
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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