xls qm simulacion

Program Name Source Content1.3 Pritchett Clock Repair Shop Excel QM Breakeven Analysis1.4 Pritchett Clock Repair Shop Excel QM Goal Seek2.1 Expected Value and Variance Excel Expected Value and Variance

2.2 Binomial Probabilities Excel Binomial Probabilities2.3 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 Regression4.3 Jenny Wilson Realty Excel Dummy Variables - Regression4.4 MPG Data Excel Linear Regression4.5 MPG Data Excel Nonlinear Regression4.6 Solved Problem 4-2 Excel Regression4.8 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 Analysis5.6 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 Programming8.2 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 Programming8.9 Low Knock Oil Company Excel Linear Programming

8.10 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

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

10.5 Quemo Chemical Company Excel Integer programming10.6 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) system13.2 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 population 14.2 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 & Absorbing States16.1 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

Dummy Variables - Regression

Constant Service Rate (M/D/1)

Fundamental Matrix & Absorbing States

Pritchett Clock Repair Shop

Breakeven Analysis

DataRebuilt Springs

Fixed cost 1000Variable cost 5Revenue 10

ResultsBreakeven points

Units 200Dollars $ 2,000.00

GraphUnits Costs Revenue

0 1000 0400 3000 4000

0 50 100 150 200 250 300 350 400 4500

1000

2000

3000

4000

5000

Cost-volume analysis

Costs Revenue

Units

$

Enter the fixed and variable costs and the selling price in the data area.Enter the fixed and variable costs and the selling price in the data area.

Pritchett Clock Repair Shop

Breakeven Analysis

DataRebuilt Springs

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

ResultsBreakeven points

Units 175Dollars $ 1,875.00

Volume Analysis@ 250 Costs $ 2,250.00 Revenue $ 2,678.57 Profit $ 428.57

GraphUnits Costs Revenue

0 1000 0350 2750 3750

Enter the fixed and variable costs and the selling price in the data area.Enter the fixed and variable costs and the selling price in the data area.

X P(X) XP(X)5 0.1 0.5 0.4414 0.2 0.8 0.2423 0.3 0.9 0.0032 0.3 0.6 0.2431 0.1 0.1 0.361

E(X) = ΣXP(X) = 2.9 1.2901.136

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

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

= Variance= Standard deviation

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

The Binomial DistributionX = random variable for number of successes

n= 5 number of trialsp= 0.5 probability of a succesr= 4 specific number of successes

Cumulative probability 0.96875

P(X = r) = 0.15625P(X < r) =

Probability of exactly r successes

X is a normal random variable with mean, μ, and standard deviation, σ.

μ = 100σ = 20

75

0.10565

0.89435

x =

P(X < x) = P(X > x) =

F Distribution with df1 and df2 degrees of freedom

df1 = 5df2 = 6

0.05

F-value = 4.39

df1 = 5df2 = 6

4.2

P(F > f) = 0.0548

To find F given α

α =

To find the probability to the right of a calculated value, f

f =

Exponential distribution - the random variable (X) is time3 per hour

0.5000 hours

0.7769P(X > t) = 0.2231

Average number per time period = μ = t =

P(X < t) =

Poisson distribution - the random variable is the number of occurrences per time period2

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

λ =

Thompson Lumber

Decision Tables

Data Results

Profit EMV Minimum Maximum HurwiczProbability 0.5 0.5 coefficient 0.8Large 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 <-Expected value under certainty

40000 <-Best expected value60000 <-Expected value of perfect information

RegretFavorable MUnfavorable Market Expected Maximum

Probability 0.5 0.5Large Plant 0 180000 90000 180000Small plant 100000 20000 60000 100000Do nothing 200000 0 100000 200000

Minimum 60000 100000

Favorable Market

Unfavorable Market

Enter the profits or costs in the main body of the data table. Enter probabilities in the first row if you want to compute the expected value.Enter the profits or costs in the main body of the data table. Enter probabilities in the first row if you want to compute the expected value.

Bayes Theorem for Thompson Lumber Example

Fill in cells B7, B8, and C7

Probability Revisions Given a Positive Survey

P(Sur.Pos.|Prior Prob. Joint Prob.FM 0.7 0.5 0.35 0.78UM 0.2 0.5 0.1 0.22

P(Sur.pos.)= 0.45

Probability Revisions Given a Negative Survey

P(Sur.Pos.|Prior Prob. Joint Prob.FM 0.3 0.5 0.15 0.27UM 0.8 0.5 0.4 0.73

P(Sur.neg.)= 0.55

State of Nature

Posterior Probability

State of Nature

Posterior Probability

Triple A Construction Company SUMMARY OUTPUT

Sales (Y) Payroll (X) Regression Statistics6 3 Multiple R 0.8333

8 4 R Square 0.6944

9 6 Adjusted R 0.6181

5 4 Standard Er 1.3110

4.5 2 Observatio 6

9.5 5ANOVA

df SS MS F

Regression 1 15.6250 15.6250 9.0909

Residual 4 6.8750 1.7187

Total 5 22.5

CoefficientsStandard Error t Stat P-value

Intercept 2 1.7425 1.1477 0.3150

Payroll (X) 1.25 0.4146 3.0151 0.0394

Significance F

0.0394

Lower 95%Upper 95%Lower 95.0%Upper 95.0%

-2.8381 6.8381 -2.8381 6.8381

0.0989 2.4011 0.0989 2.4011

Jenny Wilson Realty

SELL PRICE SF AGE95000 1926 30

119000 2069 40124800 1720 30135000 1396 15142800 1706 32145000 1847 38159000 1950 27165000 2323 30182000 2285 26183000 3752 35200000 2300 18211000 2525 17215000 3800 40219000 1740 12

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.81968R Square 0.67188Adjusted R Square 0.61222Standard Error 24312.6Observations 14

ANOVAdf SS MS F Significance F

Regression 213313936968 6.66E+09 11.26195 0.00217876517Residual 11 6502131603 5.91E+08Total 1319816068571

CoefficientsStandard Error t Stat P-value Lower 95% Upper 95%Intercept 146631 25482.0829 5.7543 0.0001 90545.2073 202716.5798SF 43.8194 10.2810 4.2622 0.0013 21.1911 66.4476AGE -2898.69 796.5649 -3.6390 0.0039 -4651.9139 -1145.4586

Lower 95.0% Upper 95.0%90545.2073 202716.5798

21.1911 66.4476-4651.9139 -1145.4586

Jenny Wilson Realty

SELL PRICE SF AGE X3 (Exc.) X4 (Mint) Condition95000 1926 30 0 0 Good

119000 2069 40 1 0 Excellent124800 1720 30 1 0 Excellent135000 1396 15 0 0 Good142800 1706 32 0 1 Mint145000 1847 38 0 1 Mint159000 1950 27 0 1 Mint165000 2323 30 1 0 Excellent182000 2285 26 0 1 Mint183000 3752 35 0 0 Good200000 2300 18 0 0 Good211000 2525 17 0 0 Good215000 3800 40 1 0 Excellent219000 1740 12 0 1 Mint

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.9476R Square 0.8980Adjusted R Squ 0.8526Standard Error 14987.5545Observations 14


Regression 4 1.779E+10 4.449E+09 19.804436 0.000174Residual 9 2.022E+09224626791Total 13 1.982E+10

CoefficientsStandard Error t Stat P-value Lower 95% Upper 95%Lower 95.0%Intercept 121658.45 17426.61 6.981 0.000 82236.71 161080.19 82236.71SF 56.43 6.95 8.122 0.000 40.71 72.14 40.71AGE -3962.82 596.03 -6.649 0.000 -5311.13 -2614.51 -5311.13X3 (Exc.) 33162.65 12179.62 2.723 0.023 5610.43 60714.87 5610.43X4 (Mint) 47369.25 10649.27 4.448 0.002 23278.93 71459.57 23278.93

Upper 95.0%161080.19

72.14-2614.5160714.8771459.57

Automobile Weight vs. MPG SUMMARY OUTPUT

MPG (Y) Weight (X1) Regression Statistics12 4.58 Multiple R 0.86287813 4.66 R Square 0.74455915 4.02 Adjusted R 0.71901518 2.53 Standard Er5.00757119 3.09 Observatio 1219 3.1120 3.18 ANOVA23 2.68 df SS MS F Significance F24 2.65 Regression 1 730.90901 730.90901 29.148024 0.000301933 1.70 Residual 10 250.75766 25.07576636 1.95 Total 11 981.6666742 1.92

CoefficientsStandard Error t Stat P-value Lower 95%Intercept 47.61934 4.8131509 9.8935905 1.753E-06 36.894975Weight (X1)-8.24597 1.5273451 -5.398891 0.0003019 -11.64911

Significance F

Upper 95%Lower 95.0%Upper 95.0%58.343712 36.894975 58.343712-4.842833 -11.64911 -4.842833

Automobile Weight vs. MPG SUMMARY OUTPUT

MPG (Y) Weight (X1) WeightSq.(X2) Regression Statistics12 4.58 20.98 Multiple R 0.920813 4.66 21.72 R Square 0.847815 4.02 16.16 Adjusted R 0.814018 2.53 6.40 Standard Er 4.074519 3.09 9.55 Observatio 1219 3.11 9.6720 3.18 10.11 ANOVA23 2.68 7.18 df SS MS F24 2.65 7.02 Regression 2 832.25568 416.12784 25.06609833 1.70 2.89 Residual 9 149.41099 16.60122136 1.95 3.80 Total 11 981.6666742 1.92 3.69

CoefficientsStandard Error t Stat P-valueIntercept 79.7888 13.5962 5.8685 0.0002Weight (X1) -30.2224 8.9809 -3.3652 0.0083WeightSq.( 3.4124 1.3811 2.4708 0.0355

Significance F0.0002094

Lower 95%Upper 95%Lower 95.0%Upper 95.0%49.0321 110.5454 49.0321 110.5454

-50.5386 -9.9062 -50.5386 -9.90620.2881 6.5367 0.2881 6.5367

Solved Problem 4-2

Advertising ($100) Y Sales X11 56 3

10 76 2

12 8

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.9014R Square 0.8125Adjusted R Square 0.7500Standard Error 1.4142Observations 5


Regression 1 26 26 13 0.0366184Residual 3 6 2Total 4 32

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

Upper 95.0%8.85061.8827

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 0.8333333 1.1458333 12.56%Slope 1.25 Bias MAD MSE MAPE

SE 1.3110111Next period 10.75 7

Correlation0.8333333

If this is trend analysis then simply enter the past demands in the demand column. If this is causal regression then enter the y,x pairs with y first and enter a new value of x at the bottom in order to forecast y.

Wallace Garden Supply

Forecasting Weighted moving averages - 3 period moving average

Data Forecasts and Error AnalysisPeriod 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 MAPESE 6.79636

Next period 15.3333333

Enter the data in the shaded area. Enter weights in INCREASING order from top to bottom.

Port of Baltimore

Forecasting Exponential smoothing

Alpha 0.1Data Forecasts and Error AnalysisPeriod 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 276.97281 08.76%Quarter 6 205 175.02175 29.97825 29.97825 898.69547 14.62%Quarter 7 180 178.01958 1.980425 1.980425 3.9220832 01.10%Quarter 8 182 178.21762 3.7823825 3.7823825 14.306417 0.02078232

Total 35.958557 82.458557 1526.5399 44.75%Average 4.4948197 10.30732 190.81749 05.59%


Next period 178.595856

Enter alpha (between 0 and 1), enter the past demands in the shaded column then enter a starting forecast. If the starting forecast is not in the first period then delete the error analysis for all rows above the starting forecast.

Enter alpha (between 0 and 1), enter the past demands in the shaded column then enter a starting forecast. If the starting forecast is not in the first period then delete the error analysis for all rows above the starting forecast.

Midwestern Manufacturing

Forecasting Trend adjusted exponential smoothing

Alpha 0.3Beta 0.4Data Forecasts and Error Analysis

Period Demand Error Absolute SquaredPeriod 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 536.5431Period 6 142 90.512828 4.9509552 95.463783 51.487172 51.48717 2650.9289Period 7 122 109.42465 10.535301 119.95995 12.575352 12.57535 158.13947

Next period 120.57196 10.780107 131.35207Total 109.45592 109.4559 3552.9144

Average 15.636561 15.63656 507.55919Bias MAD MSE

SE 26.65676

Smoothed Forecast, Ft

Smoothed Trend, Tt

Forecast Including Trend, FITt

Enter alpha and beta (between 0 and 1), enter the past demands in the shaded column then enter a starting forecast. If the starting forecast is not in the first period then delete the error analysis for all rows above the starting forecast.

00.00%06.33%05.63%14.14%22.06%36.26%

0.1030767

94.73%13.53%

MAPE

Abs Pct Err


Time (X) Demand (Y)1 742 793 804 905 1056 1427 122

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.8949096R Square 0.8008632Adjusted R 0.7610359Standard Er12.432389Observatio 7


Regression 1 3108.0357 3108.0357 20.108369 0.0064933Residual 5 772.82143 154.56429Total 6 3880.8571

CoefficientsStandard Error t Stat P-value Lower 95%Upper 95%Lower 95.0%Upper 95.0%Intercept 56.714286 10.507286 5.3976151 0.002948 29.704447 83.724124 29.704447 83.724124Time (X) 10.535714 2.3495006 4.4842356 0.0064933 4.4961307 16.575298 4.4961307 16.575298

Upper 95.0%


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 -4.2632564E-14 60.0714 772.8214Intercept 56.7142857 Average -6.0903663E-15 8.5816 110.4031Slope 10.5357143 Bias MAD MSE

SE 12.432389Next period 141 8

Correlation0.8949096

If this is trend analysis then simply enter the past demands in the demand column. If this is causal regression then enter the y,x pairs with y first and enter a new value of x at the bottom in order to forecast y.

Abs Pct Err09.12%01.54%10.40%09.84%04.18%15.54%06.94%57.57%08.22%

MAPE

Turner Industries

Forecasting Multiplicative decomposition

4 seasons

DataPeriod Demand (y) Time (x) Average Ratio Seasonal SmoothedPeriod 1 108 1 0.8491 127.1979Period 2 125 2 0.9626 129.8589Period 3 150 3 131 132.000 1.136 1.1315 132.5660Period 4 141 4 133 134.125 1.051 1.0571 133.3841Period 5 116 5 135.25 136.375 0.851 0.8491 136.6200Period 6 134 6 137.5 138.875 0.965 0.9626 139.2087Period 7 159 7 140.25 141.125 1.127 1.1315 140.5199Period 8 152 8 142 143.000 1.063 1.0571 143.7899Period 9 123 9 144 145.125 0.848 0.8491 144.8643Period 10 142 10 146.25 147.875 0.960 0.9626 147.5197Period 11 168 11 149.5 1.1315 148.4739Period 12 165 12 1.0571 156.0878

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

Enter past demands in the data area. Do not change the time period numbers!

Forecasts and Error AnalysisUnadjusted Adjusted Error |Error| Error^2 Abs Pct Err

127.1187 107.9327 0.0673 0.0673 0.0045 00.06%129.4621 124.6181 0.3819 0.3819 0.1458 00.31%131.8056 149.1396 0.8604 0.8604 0.7403 00.57%134.1490 141.8086 -0.8086 0.8086 0.6538 00.57%136.4924 115.8917 0.1083 0.1083 0.0117 00.09%138.8359 133.6411 0.3589 0.3589 0.1288 00.27%141.1793 159.7461 -0.7461 0.7461 0.5567 00.47%143.5227 151.7175 0.2825 0.2825 0.0798 00.19%145.8662 123.8507 -0.8507 0.8507 0.7236 00.69%148.2096 142.6641 -0.6641 0.6641 0.4410 00.47%150.5530 170.3526 -2.3526 2.3526 5.5346 01.40%152.8965 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%


Year Quarter Sales X1 Time PeriodX2 Qtr 2 X3 Qtr 3 X4 Qtr 41 1 108 1 0 0 0

2 125 2 1 0 03 150 3 0 1 04 141 4 0 0 1

2 1 116 5 0 0 02 134 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 StatisticsMultiple R 0.997177R Square 0.994362Adjusted R 0.991141Standard Er1.832251Observatio 12


Regression 4 4144.75 1036.1875 308.6516 6.028E-08Residual 7 23.5 3.3571429Total 11 4168.25

CoefficientsStandard Error t Stat P-value Lower 95%Upper 95%Lower 95.0%Upper 95.0%Intercept 104.1042 1.3321935 78.144928 1.479E-11 100.95403 107.2543 100.95403 107.2543X1 Time Pe 2.3125 0.1619496 14.279132 1.964E-06 1.92955 2.69545 1.92955 2.69545X2 Qtr 2 15.6875 1.5047667 10.425204 1.625E-05 12.129292 19.245708 12.129292 19.245708X3 Qtr 3 38.70833 1.5306881 25.288192 3.86E-08 35.088831 42.327835 35.088831 42.327835X4 Qtr 4 30.0625 1.5729413 19.112283 2.673E-07 26.343085 33.781915 26.343085 33.781915

Sumco Pump Company

Inventory Economic Order Quantity Model

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

ResultsOptimal Order Quantity, Q* 200Maximum Inventory 200Average Inventory 100Number of Setups 5

Holding cost $50.00 Setup cost $50.00

Unit costs $0.00

$100.00

COST TABLE Start at 25 Increment b 15

Q Setup cost Holding cosTotal cost25 400 6.25 406.2540 250 10 26055 181.81818 13.75 195.5681870 142.85714 17.5 160.3571485 117.64706 21.25 138.89706

100 100 25 125115 86.956522 28.75 115.70652130 76.923077 32.5 109.42308145 68.965517 36.25 105.21552160 62.5 40 102.5175 57.142857 43.75 100.89286190 52.631579 47.5 100.13158205 48.780488 51.25 100.03049220 45.454545 55 100.45455235 42.553191 58.75 101.30319250 40 62.5 102.5265 37.735849 66.25 103.98585280 35.714286 70 105.71429295 33.898305 73.75 107.64831310 32.258065 77.5 109.75806325 30.769231 81.25 112.01923340 29.411765 85 114.41176355 28.169014 88.75 116.91901

Total cost, Tc

2540557085100

115

130

145

160

175

190

205

220

235

250

265

280

295

310

325

340

355

370

0

100

200

300

400

500

Inventory: Cost vs Quantity

Setup cost

Holding cost

Total cost

Order Quantity (Q)

Co

st (

$)

Enter the data in the shaded areaEnter the data in the shaded area

370 27.027027 92.5 119.52703

Brown Manufacturing

Inventory Production Order Quantity Model

DataDemand rate, D 10000Setup cost, S 100Holding cost, H 0.5 (fixed amount)Daily production rate, p 80Daily demand rate, d 60Unit price, P 0

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

Holding cost 250Setup cost 250

Unit costs 0

500

COST TABLE Start at 1000 Increment b333.33333

Q Setup cost Holding cosTotal cost1000 1000 62.5 1062.5

1333.3333 750 83.333333 833.333331666.6667 600 104.16667 704.16667

2000 500 125 6252333.3333 428.57143 145.83333 574.404762666.6667 375 166.66667 541.66667

3000 333.33333 187.5 520.833333333.3333 300 208.33333 508.333333666.6667 272.72727 229.16667 501.89394

4000 250 250 5004333.3333 230.76923 270.83333 501.602564666.6667 214.28571 291.66667 505.95238

5000 200 312.5 512.55333.3333 187.5 333.33333 520.833335666.6667 176.47059 354.16667 530.63725

6000 166.66667 375 541.666676333.3333 157.89474 395.83333 553.728076666.6667 150 416.66667 566.66667

7000 142.85714 437.5 580.357147333.3333 136.36364 458.33333 594.696977666.6667 130.43478 479.16667 609.60145

8000 125 500 6258333.3333 120 520.83333 640.833338666.6667 115.38462 541.66667 657.05128

Total cost, Tc

1000

1333.33333333333

1666.66666666666

2000

2333.33333333333

2666.66666666666

3000

3333.33333333333

3666.66666666666

4000

4333.33333333333

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Order Quantity (Q)

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Enter the data in the shaded area. You may have to do some work to enter the daily production rate.Enter the data in the shaded area. You may have to do some work to enter the daily production rate.

1000

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Setup cost

Holding cost

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Enter the data in the shaded area. You may have to do some work to enter the daily production rate.Enter the data in the shaded area. You may have to do some work to enter the daily production rate.

Brass Department Store

Inventory Quantity Discount Model

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

Range 1 Range 2 Range 3Minimum quantity 0 1000 2000Unit Price, P 5 4.8 4.75

ResultsRange 1 Range 2 Range 3

Q* (Square root formula) 700 714.4345083118 718.1848464596Order Quantity 700 1000 2000

Holding cost $350.00 $480.00 $950.00 Setup cost $350.00 $245.00 $122.50

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

$25,700.00 $24,725.00 $24,822.50 minimumOptimal Order Quantity 1000Total cost, Tc

=

$24,725.00

6.4

document.xlsx

Inventory Safety stock - Normal distribution

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

Data DataAverage demand during lead time, µ 350 Average daily demand 15

10 3Service level (% of demand met) 95.00% Lead time days 4

Service level (% of demand met) 97.00%

Results ResultsZ-value 1.64 Z-value 1.88Safety stock 16.45 Average demand during lead time 60

6.00Safety stock 11.28Reorder Point 71.28

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

DataAverage daily demand 25Standard deviation of daily demand 0 Enter 0 if demand is constantAverage lead time (in days) 6

3 Enter 0 if lead time is constantService level (% of demand met) 98.00%

ResultsZ-value 2.05Average demand during lead time 150

75.00Safety stock 154.03Reorder point 304.03

Standard deviation of σdLT Standard deviation of daily demand, σd

Standard deviation of demand during lead time, σdLT

Standard deviation of lead time, σLT

Standard deviation of demand during lead time, σdLT

Select a model and then enter the data in the shaded area. The model on the bottom left represents the 3 models described in the textbook under Other Probabilistic Models

Select a model and then enter the data in the shaded area. The model on the bottom left represents the 3 models described in the textbook under Other Probabilistic Models

Flair Furniture

Variables T (Tables) C (Chairs)Units Produced 30 40 ProfitObjective function 70 50 4100

Constraints LHS (Hours used) RHSCarpentry 4 3 240 < 240Painting 2 1 100 < 100

Holiday Meal Turkey Ranch

Variables Brand 1 Brand 2Units Produced 8.4 4.8 CostObjective function 2 3 31.2

Constraints LHS (Amt. of Ing.) RHSIngredient A 5 10 90 > 90Ingredient B 4 3 48 > 48Ingredient C 0.5 0 4.2 > 1.5

High Note Sound Company

Variables CD Player ReceiversUnits 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

7.7

Linear Programming

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

Data Resultsx 1 x 2 LHS Slack/Surplus

Objective 70 50 sign RHS 4100Constraint 1 4 3 < 240 240 0Constraint 2 2 1 < 100 100 0

ResultsVariables 30 40Objective 4100

Enter the values in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE.If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.

Win Big Gambling ClubRadio Radio

TV Newspaper 30 sec. 1 min. Variables X1 X2 X3 X4Solution 1.9688 5 6.2069 0Audience per ad 5000 8500 2400 2800

ConstraintsMax. TV 1Max. Newspaper 1Max. 30-sec. radio 1Max. 1 min. radio 1Cost 800 925 290 380Radio dollars 290 380Radio spots 1 1

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Total Audience67240.3017

LHS RHS1.9688 < 12

5 < 56.2069 < 25

0 < 208000 < 80001800 < 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 CostMin. Cost 7.5 6.8 5.5 6.9 7.25 6.1 15166

Constraints LHS RHSTotal Households 1 1 1 1 1 1 2300 > 2,30030 and Younger 1 0 0 1 0 0 1000 > 1,00031-50 0 1 0 0 1 0 600 > 600Border States 0.85 0.85 0.85 -0.15 -0.15 -0.15 395 > 051+ Border States 0 0 0.8 0 0 -0.2 0 < 0

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Fifth Avenue Industries

All silk All poly. Blend 1 Blend 2Variables X1 X2 X3 X4Values 5112 14000 16000 8500 Total ProfitProfit 16.24 8.22 8.77 8.66 412028.88

Constraints LHSSilk available 0.125 0.066 1200 <Polyester available 0.08 0.05 1920 <Cotton available 0.05 0.044 1174 <Maximum silk 1 5112 <Maximum polyester 1 14000 <Maximum blend 1 1 16000 <Maximum blend 2 1 8500 <Minimum silk 1 5112 >Minimum polyester 1 14000 >Minimum blend 1 1 16000 >Minimum blend 2 1 8500 >

Calculations to determine the profit per tie.

Silk Polyester Blend 1 Blend 1Selling Price per tie 19.24 8.7 9.52 10.64 Cost of material per yard

0.125 0 0 0.066 24

0 0.08 0.05 0 6

0 0 0.05 0.044 9Material cost per tie 3 0.48 0.75 1.98Profit per tie 16.24 8.22 8.77 8.66

Yards of silk used in tie

Yards of polyester used in tie

Yards of cotton used in tie

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RHS Slack/Surplus1200 03000 10801600 4267000 1888

14000 016000 0

8500 05000 112

10000 400013000 3000

5000 3500

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Greenberg Motors

Variable A1 A2 A3 A4 B1 B2 B3 B4 IA1 IA2 IA3 IA4 IB1 IB2 IB3 IB4Solution 1276.9 223.1 1757.7 792.3 1000 2522.2 77.8 1700 476.9 0 757.7 450 0 1322.2 0 300Min. Cost 20 20 22 22 15 15 16.5 16.5 0.36 0.36 0.36 0.36 0.26 0.26 0.26 0.26

Demand ConstraintsJan. GM3A 1 -1Feb. GM3A 1 1 -1Mar. GM3A 1 1 -1Apr. GM3A 1 1 -1Jan. GM3B 1 -1Feb. GM3B 1 1 -1Mar. GM3B 1 1 -1Apr. GM3B 1 1 -1Inv.GM3A Apr. 1Inv.GM3B Apr. 1Labor Hour ConstraintsHrs Min. Jan. 1.3 0.9Hrs Min. Feb. 1.3 0.9Hrs Min. Mar. 1.3 0.9Hrs Min. Apr. 1.3 0.9Hrs Max. Jan. 1.3 0.9Hrs Max. Feb. 1.3 0.9Hrs Max.Mar. 1.3 0.9Hrs Max. Apr. 1.3 0.9Storage ConstraintsJan. Inv. Limit 1 1Feb. Inv. Limit 1 1Mar. Inv. Limit 1 1Apr. Inv. Limit 1 1

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Jan Feb Mar AprGM3A Units Pro 1276.9 223.1 1757.7 792.3GMBA Units Pro 1000.0 2522.2 77.8 1700.0GM3A Inventory 476.9 0.0 757.7 450.0GM3B Inventory 0.0 1322.2 0.0 300.0Labor Hours Use 2560.0 2560.0 2355.0 2560.0

A B C D E F G H I J K L M N O P Q33

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Total Cost169294.9

LHS Sign RHS800 = 800700 = 700

1000 = 10001100 = 11001000 = 10001200 = 12001400 = 14001400 = 1400

450 = 450300 = 300

Slack/Surplus2560 > 2240 3202560 > 2240 3202355 > 2240 1152560 > 2240 3202560 < 2560 02560 < 2560 02355 < 2560 2052560 < 2560 0

476.92 < 33001322.22 < 3300

757.69 < 3300750 < 3300

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Labor Planning Example

Variables F P1 P2 P3 P4 P5Values 10 0 7 2 5 0 Total CostCost 100 32 32 32 32 32 1448

Constraints LHS Sign RHS9 a.m. - 10 a.m. 1 1 10 > 1010 a.m. - 11 a.m. 1 1 1 17 > 1211 a.m. - noon 0.5 1 1 1 14 > 14noon - 1 p.m. 0.5 1 1 1 1 19 > 161 p.m. - 2 p.m. 1 1 1 1 1 24 > 182 p.m. - 3 p.m. 1 1 1 1 17 > 173 p.m. - 4 p.m. 1 1 1 15 > 154 p.m. - 5 p.m. 1 1 10 > 10Max. Full time 1 10 < 12Total PT hours 4 4 4 4 4 56 < 56

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Slack/Surplus0503600020

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ICT Portfolio Selection

Variable X1 X2 X3 X4 Solution 750000 950000 1500000 1800000 Total ReturnMax. Return 0.07 0.11 0.19 0.15 712000

LHS RHSTrade 1 750000 < 1,000,000Bonds 1 950000 < 2,500,000Gold 1 1500000 < 1,500,000Construction 1 1800000 < 1,800,000Min. Gold+Constr. -0.55 -0.55 0.45 0.45 550000 > 0Min. Trade 0.85 -0.15 -0.15 -0.15 0 > 0Total Invested 1 1 1 1 5000000 < 5000000

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Goodman Shipping

Variables X1 X2 X3 X4 X5 X6Values 0.33333 1 0 0 0 0 Total ValueLoad Value $ 22500 24000 8000 9500 11500 9750 31500

Constraints LHS Sign RHSTotal weight 7500 7500 3000 3500 4000 3500 10000 < 10000

% Item 1 1 0.33333333 < 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

Whole Foods Nutrition Problem

Grain A Grain B Grain CVariable Xa Xb Xc Solution 0.025 0.05 0.05 Total CostMinimize 0.33 0.47 0.38 0.05075

Constraints LHS Sign RHSProtein 22 28 21 3 > 3Riboflavin 16 14 25 2.35 > 2Phosphorus 8 7 9 1 > 1Magnesium 5 0 6 0.425 > 0.425Total Weight 1 1 1 0.125 = 0.125

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Slack/Surplus0

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Low Knock Oil Company

X100 Reg X100 Econ X220 Reg X220 EconVariable X1 X2 X3 X4 Solution 15000 26666.67 10000 5333.33 Total CostCost 30 30 34.8 34.8 1783600

Constraints LHS SignDemand 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 <

RHS Slack/Surplus25000 032000 0

0 00 0

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

NY Chicago LA NY Chicago LAVariables X11 X12 X13 X21 X22 X23Values 10000 0 8000 0 8000 7000 Total CostCost 2 3 5 3 1 4 96000

Constraints LHSNY Demand 1 1 10000Chi. Demand 1 1 8000LA Demand 1 1 15000N.O. Supply 1 1 1 18000Omaha Supply 1 1 1 15000

Sign RHS= 10000= 8000= 15000< 20000< 15000

Shipping Cost Per UnitFrom\To Albuquerque Boston Cleveland

Des Moines 5 4 3Evansville 8 4 3Fort Lauderdale 9 7 5

Solution - Number of units shippedAlbuquerque Boston Cleveland Total shipped Supply

Des Moines 100 0 0 100 100Evansville 0 200 100 300 300Fort Lauderdale 200 0 100 300 300Total received 300 200 200Demand 300 200 200

Total cost = 3900

Cost for AssignmentsPerson\Project Project 1 Project 2 Project 3

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

MadeProject 1 Project 2 Project 3 Total pro Supply

Adams 0 0 1 1 1Brown 0 1 0 1 1Cooper 1 0 0 1 1Total assigned to 1 1 1Total workers 1 1 1

Total cost = 25

Frosty Machines Transshipment Problem

Shipping Cost Per UnitFrom\To Chicago Buffalo NYC Phil. St.Louis

Toronto 4 7Detroit 5 7Chicago 6 4 5Buffalo 2 3 4

Solution - Number of units shippedChicago Buffalo NYC Phil. St.LouisTotal shippedSupply

Toronto 650 150 800 800Detroit 0 300 300 700Chicago 0 350 300 650Buffalo 450 0 0 450Total received 650 450 450 350 300Demand 450 350 300

Total cost = 9550

9.4

Birmingham

Transportation

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

ShipmentsShipments Dest 1 Dest 2 Dest 3 Dest 4 Row Total Origin 1 10000 0 1000 4000 15000Origin 2 0 1000 0 5000 6000Origin 3 0 0 14000 0 14000Origin 4 0 11000 0 0 11000Column Total 10000 12000 15000 9000 46000 \ 46000 Total Cost 3741000

Enter the transportation data in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE.If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.

9.4

Enter the transportation data in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE.If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.

9.5

Fix-It Shop Assignment

Assignment

DataCOSTS Project 1 Project 2 Project 3Adams 11 14 6 Brown 8 10 11 Cooper 9 12 7

AssignmentsShipments 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

Enter the assignment costs in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE.If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.

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Harrison Electric Integer Programming AnalysisChandeliers Fans

Variables X1 X2Values 5 0 Total ProfitProfit 7 6 35

Constraints LHS Sign RHSWiring hours 2 3 10 < 12Assembly hours 6 5 30 < 30

Bagwell Chemical CompanyXyline (bags) Hexall (lbs)

Variables X Y Values 44 20 Total ProfitProfit 85 1.5 3770

Constraints LHS sign RHSIngredient A 30 0.5 1330 < 2000Ingredient B 18 0.4 800 < 800Ingredient C 2 0.1 90 < 200

Quemo Chemical CompanyCatalytic Conv. Software Warehouse Expan.

Variables X1 X2 X3Values 1 0 1 NPVNet Present Value 25000 18000 32000 57000

Constraints LHSYear 1 8000 6000 12000 20000Year 2 7000 4000 8000 15000

sign RHS< 20000< 16000

Sitka Manufacturing CompanyBaytown Lake Charles Mobile Baytown units

Variables X1 X2 X3 X4Values 0 1 1 0

Cost 340000 270000 290000 32

ConstraintsMinimum capacity 1

Maximum in Baytown -21000 1Maximum in L. C. -20000

Maximum in Mobile -19000

L. Charles units Mobile unitsX5 X6

19000 19000 Cost33 30 1757000

LHS Sign RHS1 1 38000 > 38000

0 < 01 -1000 < 0

1 0 < 0

Simkin, Simkin and Steinberg

Variables X1 X2 X3 X4 X5 X6 X7Values 0 0 1 1 1 1 0 Return

50 80 90 120 110 40 75 360Constraints LHS

Texas 1 1 1 2Foreigh Oil 1 1 1California 1 1 1$3 Million 480 540 680 1000 700 510 900 2890

Return ($1,000s)

Sign RHS> 2< 1= 1< 3000

Great Western ApplianceMicro Self-Clean

Variables X1 X2Values 0 1000

Terms X1 X2Calculated Values 0 1000 1000000 Profit

Profit 28 21 0.25 271000

Constraints LHS Sign RHSCapacity 1 1 1000 < 1000

Hours Available 0.5 0.4 400 < 500

X22

Hospicare Corp

Variables X1 X2Values 6.0663 4.1003

Terms X1 X1*X2 X2 1/X2Calculated Values 6.0663 36.7995 24.8732 4.1003 68.9337 0.2439 Total Profit

Profit 13 0 6 5 1 248.8457

Constraints LHS Sign RHSNursing 2 4 90.00 < 90X-Ray 1 1 75.00 < 75

Budget 8 -2 40.33 < 61

X12 X23

Thermlock Gaskets

Variables X1 X2Values 3.325 14.672 Total CostCost 5 7 119.333

X1 X2Value 3.325 11.058 36.771 14.672 215.276Constraints LHS SignHardness 3 0.25 4 0.3 136.012 >Tensile Strength 13 1 80 >Elasticity 0.7 1 17 >

X12 X13 X22

RHS1258017

Solved Problem 10-1

Variables X1 X2 X3Values 1 1 0 Total

Maximize 50 45 48 95

Constraints LHS Sign RHSConstraint 1 19 27 34 46 < 80Constraint 2 22 13 12 35 < 40Constraint 3 1 1 1 2 < 2Constraint 4 1 -1 0 0 < 0

Forecasting - Exponential Smoothing

0.3478

Time Period (t) |error|1 110 110 0 -2 156 110 46.000 46.0003 126 125.999999780957 0.000 0.0004 138 125.999999857146 12.000 12.0005 124 130.173912893171 -6.174 6.1746 125 128.026464959728 -3.026 3.0267 160 126.973781509886 33.026 33.0268 138.461161697009 MAD= 16.704

MAD is based on time periods 2 through 7

`

α = Ft+1 = Ft + α(Yt-Ft) Demand (Yt) Forecast (Ft) Error = Yt - Ft

F1 is assumed to be a perfect forecast.

General Foundry

Project Management Precedences; 3 time estimates

DataActivity Optimistic Likely Pessimistic Mean Std dev VarianceA 1 2 3 2 0.3333333 0.1111111B 2 3 4 3 0.3333333 0.1111111C 1 2 3 2 0.3333333 0.1111111D 2 4 6 4 0.6666667 0.4444444E 1 4 7 4 1 1F 1 2 9 3 1.3333333 1.7777778G 3 4 11 5 1.3333333 1.7777778H 1 2 3 2 0.3333333 0.1111111Precedences Immediate Predecessors (1 per column)Activity Time Pred 1 Pred 2A 2B 3C 2 AD 4 BE 4 CF 3 CG 5 D EH 2 F G

Results

Activity Slack VarianceA 0 2 0 2 0 0.1111111B 0 3 12 15 12C 2 4 2 4 0 0.1111111D 0 4 4 8 4E 4 8 4 8 0 1F 4 7 10 13 6G 8 13 8 13 0 1.7777778H 13 15 13 15 0 0.1111111

Project 15 Project 3.1111111Std.dev 1.7638342

Early start computationsA 0 0B 0 0C 2 0D 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 15D 15 15 15 15 15 15 15 15E 15 15 4 15 15 15 15 15

Early Start

Early Finish

Late Start

Late Finish

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Gantt Chart

Column H Critical ActivityNoncritical Activity Slack

Time

Enter the times in the appropriate column(s). Enter the precedences, one per column. (Do not try to use commas).

F 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 ActiNoncritical Slack 9 Graph Critical ActiA 0 2 0 0 8 H 13 2B 0 0 3 12 7 G 8 5C 2 2 0 0 6 F 4 0D 0 0 4 4 5 E 4 4E 4 4 0 0 4 D 0 0F 4 0 3 6 3 C 2 2G 8 5 0 0 2 B 0 0H 13 2 0 0 1 A 0 2

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Gantt Chart

Column H Critical ActivityNoncritical Activity Slack

Time

Enter the times in the appropriate column(s). Enter the precedences, one per column. (Do not try to use commas).

Noncritical ASlack0 00 03 60 04 40 03 120 0

Crashing

document.xlsx

Project Management Crashing

ResultsData Normal time 15 Minimum crash cost to meet project goal $ 5,000.00 Project goal 12 Minimum time 7 Project time 12

Immediate Predecessors (1 per column) Intermediate Computations

Activity Crash Cost Pred 1 Pred 2 Pred 3 Pred 4 Crash limitA 2 $ 22,000 1 $ 23,000 0 1000 1B 3 $ 30,000 1 $ 34,000 0 2000 2C 2 $ 26,000 1 $ 27,000 A 0 1000 1D 4 $ 48,000 3 $ 49,000 B 0 1000 1E 4 $ 56,000 2 $ 58,000 C 1 1000 2F 3 $ 30,000 2 $ 30,500 C 0 500 1G 5 $ 80,000 2 $ 86,000 D E 2 2000 3H 2 $ 16,000 1 $ 19,000 F G 0 3000 1

0 0 0

Normal Time

Normal Cost

Crash Time

Crash days

Crash cost/day

Enter the data in the shaded area. Then go to the DATA Tab on the ribbon, click on Solver in the Data Analysis Group and then click SOLVE.If SOLVER is not on the Data Tab then please see the Help file (Solver) for instructions.

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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 10Minimize cost 1000 2000 1000 1000 1000 500 2000 3000A crash max. 1B 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 1B constraint 1 -1 1C constraint 1 -1 1D constraint 1 -1 1E 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

XH XFIN12 12 Totals

50000 < 10 < 21 < 10 < 10 < 20 < 12 < 30 < 1

1 12 < 120 = 02 > 23 > 32 > 24 > 44 > 43 > 35 > 55 > 5

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

Arnold's Muffler Shop

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

Data Results2 0.666666673 1.33333333

20.66666667

10.33333333

Probabilities

Number Probability0 0.333333 0.3333331 0.222222 0.5555562 0.148148 0.7037043 0.098765 0.8024694 0.065844 0.8683135 0.043896 0.9122096 0.029264 0.9414727 0.019509 0.9609828 0.013006 0.9739889 0.008671 0.982658

10 0.005781 0.98843911 0.003854 0.99229312 0.002569 0.99486213 0.001713 0.99657514 0.001142 0.99771615 0.000761 0.99847816 0.000507 0.99898517 0.000338 0.99932318 0.000226 0.99954919 0.000150 0.99969920 0.000100 0.999800

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

Average number of customers in the system(Ls)Average waiting time in the queue(Wq)Average time in the system(Ws)Probability (% of time) system is empty (P0)

Cumulative Probability

The arrival RATE and service RATE both must be rates and use the same time unit. Given a time such as 10 minutes, convert it to a rate such as 6 per hour.The arrival RATE and service RATE both must be rates and use the same time unit. Given a time such as 10 minutes, convert it to a rate such as 6 per hour.

The arrival RATE and service RATE both must be rates and use the same time unit. Given a time such as 10 minutes, convert it to a rate such as 6 per hour.

Arnold's Muffler Shop

Waiting Lines M/M/s

Data Results2 0.33333

3 0.08333Number of servers(s) 2 Average number of customers in the system(L) 0.75

0.04167Average time in the system(W) 0.375

0.5ProbabilitiesNumber Probability Cumulative Probability

0 0.500000 0.5000001 0.333333 0.8333332 0.111111 0.9444443 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 1.00000015 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)^n/Cumsum(n-term2 P0(s)

0 11 0.6666667 1 2 0.333332 0.2222222 1.6666667 0.333333333333333 0.53 0.0493827 1.8888889 0.0634920634920635 0.51224 0.0082305 1.9382716 0.00987654320987654 0.513315 0.0010974 1.9465021 0.00126622348844571 0.513416 0.0001219 1.9475995 0.000137174211248285 0.513427 1.161E-05 1.9477214 1.28350139179682E-05 0.513428 9.677E-07 1.947733 1.05569378546059E-06 0.513429 7.168E-08 1.947734 7.74175442671098E-08 0.51342

10 4.779E-09 1.947734 5.12020795417393E-09 0.5134211 2.896E-10 1.947734 3.08313597240581E-10 0.5134212 1.609E-11 1.947734 1.70369367459144E-11 0.5134213 8.252E-13 1.947734 8.69753527569206E-13 0.5134214 3.929E-14 1.947734 4.12575391282828E-14 0.51342

Arrival rate (l) Average server utilization(r)

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

Average waiting time in the queue(Wq)

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


15 1.746E-15 1.947734 1.82757648408783E-15 0.5134216 7.276E-17 1.947734 7.59282983727312E-17 0.5134217 2.854E-18 1.947734 2.96998446015785E-18 0.5134218 1.057E-19 1.947734 1.09750556974159E-19 0.5134219 3.708E-21 1.947734 3.84311714656988E-21 0.5134220 1.236E-22 1.947734 1.27871411410371E-22 0.5134221 3.924E-24 1.947734 4.05275511573854E-24 0.5134222 1.189E-25 1.947734 1.22628006974231E-25 0.513422324252627282930

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

0.6666667 1.3333333 2 0.6666667 10.3333333 0.0833333 0.75 0.0416667 0.3750.2222222 0.0092915 0.6759582 0.0046458 0.33797910.1666667 0.0010139 0.6676806 0.000507 0.33384030.1333333 0.0001 0.6667667 5E-05 0.33338330.1111111 8.803E-06 0.6666755 4.402E-06 0.33333770.0952381 6.937E-07 0.6666674 3.468E-07 0.33333370.0833333 4.927E-08 0.6666667 2.464E-08 0.33333340.0740741 3.18E-09 0.6666667 1.59E-09 0.33333330.0666667 1.878E-10 0.6666667 9.389E-11 0.33333330.0606061 1.021E-11 0.6666667 5.106E-12 0.33333330.0555556 5.145E-13 0.6666667 2.573E-13 0.33333330.0512821 2.414E-14 0.6666667 1.207E-14 0.3333333

0.047619 1.059E-15 0.6666667 5.296E-16 0.3333333

0.0444444 4.364E-17 0.6666667 2.182E-17 0.33333330.0416667 1.695E-18 0.6666667 8.475E-19 0.33333330.0392157 6.224E-20 0.6666667 3.112E-20 0.3333333

0.037037 2.167E-21 0.6666667 1.084E-21 0.33333330.0350877 7.175E-23 0.6666667 3.587E-23 0.33333330.0333333 2.264E-24 0.6666667 1.132E-24 0.3333333

0.031746 6.822E-26 0.6666667 3.411E-26 0.33333330.030303 1.967E-27 0.6666667 9.837E-28 0.3333333

Garcia-Golding Recycling

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

Data Results8 0.666667

12 0.666667

1.333333

0.083333

0.166667

0.333333

Arrival rate (l) Average server utilization(r)


Average number of customers in the system(Ls)


Average time in the system(Ws)



The arrival RATE and service RATE both must be rates and use the same time unit. Given a time such as 10 minutes, convert it to a rate such as 6 per hour.

Department of Commerce

Waiting Lines M/M/s with a finite population

Data Results

0.05 0.436048

0.5 0.203474

Number of servers 1 0.639522

Population size (N) 5 0.933264

2.933264

0.563952Effective arrival rate 0.218024

Probabilities

Number, n Number waiting0 0.56395218 0.56395218 0 0.251 0.28197609 0.84592827 0 0.22 0.11279044 0.9587187 1 0.153 0.03383713 0.99255583 2 0.14 0.00676743 0.99932326 3 0.055 0.00067674 1 4 06789

101112131415161718192021222324252627282930

Arrival rate (l) per customer Average server utilization(r)


Average number of customers in the system(Ls)


Average time in the system(Ws)


Probability, P(n)


Arrival rate(n)

The arrival rate is for each member of the population. If they go for service every 20 minutes then enter 3 (per hour).The arrival rate is for each member of the population. If they go for service every 20 minutes then enter 3 (per hour).

The arrival rate is for each member of the population. If they go for service every 20 minutes then enter 3 (per hour).

1.7732

Term 1 Term 2 P0(s)1 1 1 1 0.7732

0.5 1.5 0.5 1.5 0.2732 0.56395220.2 1.7 0.0732

0.06 1.76 0.01320.012 1.772 0.0012

0.0012 1.7732 0

Sum term 1

Sum term 2

Decum term 2

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

Probability Day0.05 0 0.05 0 1 0.8395261 4

0.1 0.05 0.15 1 2 0.6821572 40.2 0.15 0.35 2 3 0.8972836 50.3 0.35 0.65 3 4 0.6513231 40.2 0.65 0.85 4 5 0.1968093 2

0.15 0.85 1 5 6 0.6711921 47 0.9969362 58 0.972367 59 0.1425137 1

10 0.4643349 3Average 3.7

Results (Frequency table)

Frequency Percentage Cum %0 0 0% 0%1 1 10% 10%2 1 10% 20%3 1 10% 30%4 4 40% 70%5 3 30% 100%

10

Probability Range (Lower)


Tires Demand

Random Number

Simulated Demand

Tires Demanded

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

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

Random number Value Frenquency Percentage44.005287018617 26 0 0.0%

36.3128785803921 28 0 0.0%37.5484787940045 30 2 1.0%36.3103882996003 32 5 2.5%

33.372543840421 34 19 9.5%42.1925553964045 36 22 11.0%44.6341421017851 38 24 12.0%

45.021531591692 40 26 13.0%28.9943876897529 42 32 16.0%33.4399538641563 44 33 16.5%42.4521768742791 46 18 9.0%40.7519320848807 48 12 6.0%39.4296166485296 50 4 2.0%33.5331635875876 52 3 1.5%44.2944150346837 54 0 0.0%43.9895725086873 56 0 0.0%40.2912237587526 20038.739413576011144.304327019540145.127900373936536.470216620143639.212202956152636.207299919705943.413993717052540.076989732188832.487915534354636.615054640361132.482661658237738.767034283857734.112497698678740.943856992996445.702080393262835.784522593066641.7738069167268

49.6298188557232.771850511971142.887289762014143.078123837598950.386824921930839.9613480175716

47.65981706117939.060509950152

41.570471616578542.700069943314943.424590210528836.373793683059140.9480510778864

46.421522427588539.136560693134133.8374900803674

43.28701236311335.987317339447633.2610992708397

41.71568352681449.080834070132336.647070625886333.8151652140623

37.65316061677437.561261003816342.972649488673141.2730099644281

37.28350753007447.545424359921633.9307622781551

36.68499758726638.0209003560329

40.54045456455741.198462386223347.384694794310834.794088291707936.547075435347634.533398784009742.798704018446647.035000168757235.814851806202641.409668690203334.687261004656730.749381345351445.356281192462740.859443196376628.651190982986541.356809150361935.125806171741434.2270790288789

40.77540457767238.060893754159850.219008581699340.851794348176834.551840318788745.8951266871345

39.91639474096442.054720308208540.523201907996240.872652005715144.8682358452754

35.92012376108838.1567010183097

36.952006585627242.0491135913019

46.13260658586342.6510881717864

42.47623904926544.355559343161145.279539778812535.564194229018636.620728586804347.069221980544742.104200359682940.514971117622946.410033991539144.105995662682641.577820924905342.214178004677440.5849705557873

43.49460606098940.305638587845838.407722036663640.667754475560741.237103604263538.974945034522550.829437961050242.076994656699634.384324828639243.919454880189532.190467056151147.7336638942278

38.96274347102237.131790368753630.159375863302637.183624407234937.077494682128638.382095581685639.727353085559436.553676276802444.096853426999434.866018603907734.959346618087333.690035842352739.141677442896633.2765994028442

44.13759791776543.034634387129238.552384504104738.129884955065633.444290199857945.162286164639647.6476661693066

43.165202984408843.638983172221635.817237168866138.805145802256536.080477568919843.7904007738014

43.70820452463240.59799293554143.195238313766

34.672706825003638.690033072763940.802603159778247.335872310635144.605171465888234.200698003095133.167788062573431.504687903403639.728253392678534.433624325381241.3242454399284

43.05296386399140.203742896047237.303847608756430.491992797817748.202161362536836.863564054047236.715190845877446.016281135154841.535133983058543.458415532332536.844847707286940.3324962563807

40.72482845633138.781746852172244.898897758667734.149448614562831.147028626967140.1887505233777

33.29549553073633.270345302530548.438673500052443.703394853073632.634545894414143.204271738653838.8957584701271

33.51289565299839.280146914379539.682865267042634.164544358550442.0078641733918

35.162381746926243.059670452185343.1977466043951

Harry's Auto Tire

Simulación

Datos Valor esperado

Categoría Valor Frequencia Probabilidad

0 Categoría 1 0 10 0.05 0.05

5 Categoría 2 1 20 0.1 0.15

15 Categoría 3 2 40 0.2 0.35

35 Categoría 4 3 60 0.3 0.65

65 Categoría 5 4 40 0.2 0.85

85 Categoría6 5 30 0.15 1

Total 200 Esperado

Ensayos de la Simulación

Pruebas Num. Aleatorios Valor

1 49.529422250742 3

2 0.0437701450929 0

3 81.530095081199 4

4 30.64616925423 2

5 39.339256861772 3

6 11.442829972163 1

7 56.578907000092 3

8 52.271100676003 3

9 30.904797585195 2

10 12.188684774877 1

11 74.29042520649 4

12 64.623404473052 3

13 27.789357454806 2

14 56.89029924114 3

15 56.003089124712 3

16 3.2791922306976 0

17 86.769422108663 5

18 69.51887602395 4

19 29.456558781278 2

20 0.5271041172875 0

21 95.765886041176 5

22 25.506300479305 2

23 32.665199944105 2

24 18.979633090459 2

25 10.006956521633 1

26 85.815295130378 5

27 71.203032588113 4

Números aleatorios

Probabilidad Acumulativa

28 1.7444040869338 0

29 92.484407783314 5

30 32.793667986497 2

31 8.3366010183628 1

32 26.586939365541 2

33 28.45246077851 2

34 23.431544598128 2

35 22.69692479162 2

36 83.730580622197 4

37 35.92865656954 3

38 65.570168551789 4

39 63.422058665867 3

40 62.645205409283 3

41 45.179084345489 3

42 48.850019297533 3

43 46.019022640284 3

44 81.461217913823 4

45 18.555840477593 2

46 30.744886103998 2

47 99.399136001025 5

48 99.691298141239 5

49 32.234627567576 2

50 79.002370156054 4

51 50.528876375532 3

52 67.681930993872 4

53 32.62374442531 2

54 46.083278668856 3

55 23.519351228789 2

56 78.552323951151 4

57 7.9709981118055 1

58 17.510914895689 2

59 9.065475973963 1

60 90.707723601657 5

61 3.1602390715738 0

62 39.118017556949 3

63 15.682885879464 2

64 87.552883345143 5

65 2.8413255984315 0

66 64.998187316887 3

67 65.983886600572 4

68 63.328387242879 3

69 84.793461821505 4

70 2.5722315449283 0

71 21.527979127498 2

72 32.572141560802 2

73 3.2005867519722 0

74 67.708082548088 4

75 88.346545529757 5

76 52.7490367475 3

77 38.377849094537 3

78 42.026137290614 3

79 88.347253454285 5

80 56.900640092463 3

81 98.758085566568 5

82 88.253419536385 5

83 56.149405449077 3

84 43.328959433217 3

85 2.743567954387 0

86 12.657691135851 1

87 10.602566329813 1

88 79.216647331106 4

89 93.185653275515 5

90 28.224334758371 2

91 35.55347861569 3

92 51.330203096391 3

93 90.243574665365 5

94 68.623451598572 4

95 60.946803824864 3

96 95.052340943847 5

97 23.411746189954 2

98 80.857862259004 4

99 18.146787554994 2

100 25.97456275422 2

101 75.163955494058 4

102 18.339043374533 2

103 99.161288084738 5

104 36.352575845796 3

105 32.292444816004 2

106 38.12787940461 3

107 31.850928583503 2

108 59.886241657049 3

109 45.569228103353 3

110 7.4535987928579 1

111 40.544950663474 3

112 11.907068556212 1

113 29.894261150546 2

114 82.654322967141 4

115 37.476787030141 3

116 94.563208528149 5

117 27.419226743977 2

118 77.622277924162 4

119 62.481714401288 3

120 99.76165636434 5

121 1.250703857742 0

122 3.6228463625444 0

123 52.929661338811 3

124 32.720513257063 2

125 14.283627200713 1

126 93.079437622584 5

127 96.615217855771 5

128 64.602969920414 3

129 74.711236856373 4

130 34.68995431129 2

131 30.739681799965 2

132 43.066800881755 3

133 35.917684076271 3

134 21.018418673047 2

135 55.166321923263 3

136 72.348231112429 4

137 5.2539213334044 1

138 73.973454381073 4

139 1.4203678896438 0

140 21.844801055794 2

141 2.9517877785083 0

142 36.354937369865 3

143 18.684919649218 2

144 42.201637488626 3

145 67.288495517377 4

146 22.722014899812 2

147 60.236489091962 3

148 90.341027244183 5

149 36.483109535816 3

150 78.410337681842 4

151 54.336685907635 3

152 44.42081022538 3

153 68.638324954188 4

154 60.083003391689 3

155 9.303351722103 1

156 31.937852487685 2

157 75.107417394989 4

158 94.541464013012 5

159 35.336173205918 3

160 82.98910221929 4

161 37.8639621919 3

162 52.228802708141 3

163 55.071613345562 3

164 15.781764579537 2

165 41.780580037247 3

166 33.675827908177 2

167 84.271817375179 4

168 28.742535986648 2

169 53.15261913423 3

170 22.013758708504 2

171 50.545037670331 3

172 6.9405076144144 1

173 59.802556498669 3

174 69.132600639547 4

175 89.132613756938 5

176 91.930190374348 5

177 28.661916678495 2

178 3.2855248964109 0

179 57.810779194675 3

180 43.460363308021 3

181 92.223294331288 5

182 43.090808031 3

183 90.020856518051 5

184 8.0414108716674 1

185 23.303452516774 2

186 3.9250867325628 0

187 45.829439610168 3

188 56.122319435542 3

189 41.004869371594 3

190 65.993414596012 4

191 87.182203748667 5

192 19.202720537421 2

193 31.059096806238 2

194 36.996376765244 3

195 82.911511721033 4

196 53.71048878482 3

197 91.979691689636 5

198 10.872350627545 1

199 60.914380107518 3

200 84.321630927431 4

Resultados de la simulación

Valor Porcentaje

0 0 15 0.075 0

20 1 16 0.08 16

80 2 46 0.23 92

180 3 63 0.315 189

160 4 32 0.16 128

150 5 28 0.14 140

Totals 200 1 565

Average 2.825

Valor * Frequencia

Ocurrencias de la Simulación

Ocurrencias* Valor

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

Day Arrivals Unloaded1 0 0.8216697 4 4 0.8405458 4 42 0 0.0928851 0 0 0.6517285 3 03 0 0.1244439 0 0 0.0312884 1 04 0 0.7987013 4 4 0.4019935 3 35 1 0.4880327 3 4 0.6034776 3 36 1 0.1022777 0 1 0.7461971 4 17 0 0.8265669 4 4 0.1122943 2 28 2 0.063667 0 2 0.3256637 3 29 0 0.0133063 0 0 0.3834851 3 0

10 0 0.4212555 2 2 0.9611529 5 2

Barge Arrivals Unloading ratesDemand 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 0.95 0.1 0.9 1 5

Previously delayed

Random number

Total to be unoaded

Random Number

Possibly unloaded


CumulativeUnloading0.05 1

0.2 20.7 30.9 4

1 5

Three Hills Power Company

Repair time1 0.1485 1.5 1.5 1.5 0.2086 12 0.4713 2 3.5 3.5 0.6328 23 0.1001 1 4.5 5.5 0.9410 34 0.9990 3 7.5 8.5 0.2287 15 0.8365 3 10.5 10.5 0.0446 16 0.4387 2 12.5 12.5 0.5189 27 0.6347 2.5 15 15 0.0240 18 0.0803 1 16 16 0.1667 19 0.0613 1 17 17 0.8813 3

10 0.7261 2.5 19.5 20 0.6120 2

Demand Table Repair times

Probability Lower Cumulative Demand Time0.5 0.05 0 0.05 0.5 11.0 0.06 0.05 0.11 1.0 21.5 0.16 0.11 0.27 1.5 32.0 0.33 0.27 0.6 2.02.5 0.21 0.6 0.81 2.53.0 0.19 0.81 1 3.0


Breakdown number

Random number

Time between breakdowns

Time of breakdowns

Time repairperson is free

Random Number

Time between

breakdowns

Repair ends2.55.58.59.5

11.514.516172022

Probability Lower Cumulative Lead time0.28 0.00 0.28 10.52 0.28 0.80 20.20 0.80 1.00 3


Three Grocery Example

State ProbabilitiesAmerican Food StFood Mart Atlas Foods

Time #1 #2 #3 Matrix of Transition Probabilities0 0.4 0.3 0.3 0.8 0.1 0.11 0.41 0.31 0.28 0.1 0.7 0.22 0.415 0.314 0.271 0.2 0.2 0.63 0.4176 0.3155 0.26694 0.41901 0.31599 0.2655 0.419807 0.316094 0.2640996 0.4202748 0.3160663 0.2636589

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 1.3793103 0.34482760.5172414 1.3793103

FA = 0.9655172 0.03448280.862069 0.137931

Box Filling Example

Quality Control x bar chart

Number of 1Sample siz 36

2

Data ResultsMean

Sample 1 16 x-bar valu 16Average 16 z value 3

Sigma x ba 0.333333

Upper cont 17Center lin 16Lower cont 15

Population standard deviation

Enter the population standard deviation then enter the data from each sample. Finally, you may change the number of standard deviations.

Super Cola Example

Quality Control x bar chart

Number of s 1Sample size 5

Data ResultsMean Range Xbar Range

Sample 1 16.01 0.25 x-bar value 16.01Average 16.01 0.25

R bar 0.25

Upper contro 16.15425 0.52875Center line 16.01 0.25

Table Lower contro 15.86575 0

2 1.88 3.268 03 1.023 2.574 04 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 0.28413 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 0.44324 0.157 1.548 0.45225 0.153 1.541 0.459

Sample size, n

Mean Factor, A2

Upper Range, D4

Lower Range, D3

Enter the mean and range from each sample.

ARCO

Quality Control p chart

Number of 20Sample size 100

Data Results# Defects % Defects Total Sampl 2000

Sample 1 6 0.06 Total Defec 80Sample 2 5 0.05 Percentage 0.04Sample 3 0 0 Std dev of 0.019596Sample 4 1 0.01 z value 3Sample 5 4 0.04Sample 6 2 0.02 Upper Contr0.098788Sample 7 5 0.05 Center Line 0.04Sample 8 3 0.03 Lower Contr 0Sample 9 3 0.03Sample 10 2 0.02Sample 11 6 0.06Sample 12 1 0.01Sample 13 8 0.08Sample 14 7 0.07Sample 15 5 0.05Sample 16 4 0.04Sample 17 11 0.11 Above UCLSample 18 3 0.03Sample 19 0 0Sample 20 4 0.04

Graph informationSample 1 0.06 0 0.04 0.098788Sample 2 0.05 0 0.04 0.098788Sample 3 0 0 0.04 0.098788Sample 4 0.01 0 0.04 0.098788Sample 5 0.04 0 0.04 0.098788Sample 6 0.02 0 0.04 0.098788Sample 7 0.05 0 0.04 0.098788Sample 8 0.03 0 0.04 0.098788Sample 9 0.03 0 0.04 0.098788Sample 10 0.02 0 0.04 0.098788Sample 11 0.06 0 0.04 0.098788Sample 12 0.01 0 0.04 0.098788Sample 13 0.08 0 0.04 0.098788Sample 14 0.07 0 0.04 0.098788

1 3 5 7 9 11 13 15 17 190

0.020.040.060.08

0.10.12

p-chart

Sample

Mea

n

Enter the sample size then enter the number of defects in each sample.

Sample 15 0.05 0 0.04 0.098788Sample 16 0.04 0 0.04 0.098788Sample 17 0.11 0 0.04 0.098788Sample 18 0.03 0 0.04 0.098788Sample 19 0 0 0.04 0.098788Sample 20 0.04 0 0.04 0.098788

1 3 5 7 9 11 13 15 17 190

0.020.040.060.08

0.10.12

p-chart

Sample

Mea

n

Red Top Cab Company

Quality Control c chart

Number of 9

Data Results# Defects Total unit 9

Sample 1 3 Total Defe 54Sample 2 0 6Sample 3 8 Standard d 2.44949Sample 4 9 z value 3Sample 5 6

Sample 6 7 Upper Cont13.34847Sample 7 4 Center Lin 6Sample 8 9 Lower Cont 0Sample 9 8

Graph informationSample 1 3 0 6 13.348469Sample 2 0 0 6 13.348469Sample 3 8 0 6 13.348469Sample 4 9 0 6 13.348469Sample 5 6 0 6 13.348469Sample 6 7 0 6 13.348469Sample 7 4 0 6 13.348469Sample 8 9 0 6 13.348469Sample 9 8 0 6 13.348469

Defect rate, l

1 2 3 4 5 6 7 8 90

4

8

12

16

c-chart

Sample

Mea

n

Enter the number of defects for each of the samples/items.

1 2 3 4 5 6 7 8 90

4

8

12

16

c-chart

Sample

Mea

n

AHP n= 3

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

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

Sys.2 0.33333 1 6 Sys.2 0.2308 0.2400 0.3750 0.2819 0.8602 3.0512

Sys.3 0.11111 0.16667 1 Sys.3 0.0769 0.0400 0.0625 0.0598 0.1799 3.0086

Column Total 1.44444 4.16667 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

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

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

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

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

Sys.3 0.16667 0.33333 1 Sys.3 0.0769 0.1429 0.1000 0.1066 0.3216 3.0172

Column Total 2.16667 2.33333 10

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

Hardware 1 0.125 0.33333 Hardware 0.0833 0.0857 0.0769 0.0820 0.2460 3.0004

Software 8 1 3 Software 0.6667 0.6857 0.6923 0.6816 2.0468 3.0031

Vendor 3 0.33333 1 Vendor 0.2500 0.2286 0.2308 0.2364 0.7096 3.0011

Column Total 12 1.45833 4.33333

n RI Hardware Software Vendor Priority

2 0.00 Sys.1 0.658 0.087 0.497 0.231

3 0.58 Sys.2 0.282 0.162 0.397 0.227

4 0.90 Sys.3 0.060 0.750 0.107 0.542

5 1.12

6 1.24

7 1.32

8 1.41

Consistency vector

Lambd 3.0541

CI 0.0270

CR 0.0466

Lambd3.00554307504178

CI 0.0028

CR 0.0048

Lambd 3.0539

CI 0.0269

CR 0.0464

Lambd 3.0015

CI 0.0008

CR 0.0013

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

xls qm simulacion

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