Program
1.3
1.4
2.1
2.2
2.3
2.4
2.5
2.6
3.1
3.5
4.1
4.2
4.3
4.4
4.5
4.6
4.8
5.1
5.2
5.3
5.4
5.5
5.6
5.7
6.1
6.2
6.3
6.4
7.2
7.4
7.6
7.7
8.1
8.2
8.3
8.4
8.5
8.6
8.5xx
8.7
8.8
8.9
8.10
9.1
9.2
9.3
9.4
9.5
9.1
9.2
10.2
10.4
Name
Pritchett Clock Repair Shop
Pritchett Clock Repair Shop
Expected Value and Variance
Source
Excel QM
Excel QM
Excel
Content
Breakeven Analysis
Goal Seek
Expected Value and Variance
Binomial Probabilities
Normal distribution
F Distribution
Exponential Distribution
Poisson distribution
Thompson Lumber
Bayes Theorem for Thompson Lumber Example
Triple A Construction Company Sales
Jenny Wilson Realty
Jenny Wilson Realty
MPG Data
MPG Data
Solved Problem 4-2
Triple A Construction Company Sales
Wallace Garden Supply Shed Sales
Port of Baltimore
Midwestern Manufacturing's Demand
Midwestern Manufacturing's Demand
Midwestern Manufacturing's Demand
Turner Industries
Turner Industries
Sumco Pump Company
Brown Manufacturing
Brass Department Store
Hinsdale Company Safety Stock
Flair Furniture
Holiday Meal Turkey Ranch
High note sound company
Flair Furniture
Win Big Gambling Club
Management Science Associates
Fifth Avenue Industries
Greenberg Motors
Labor Planning Example
ICT Portfolio Selection
Top Speed Bicycle Company
Goodman Shipping
Whole Foods Nutrition Problem
Low Knock Oil Company
Top Speed Bicycle Company
Transportation Example
Fix-It Shop
Frosty Machines Transshipment Problem
Transportation Problem - Birmingham
Fix-It Shop Assignment
Executive Furniture Company
Birmingham Plant
Harrison Electric IP Analysis
Bagwell Chemical Company
Excel
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Excel QM
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Excel
Excel
Binomial Probabilities
Normal distribution
F distribution probabilities
Exponential probabilities
Poisson probabilities
Decision Table
Bayes Theorem
Regression
Multiple Regression
Dummy Variables - Regression
Linear Regression
Nonlinear Regression
Regression
Regression
Weighted Moving Average
Exponential Smoothing
Expo. Smoothing with Trend
Trend Analysis
Trend Analysis
Multiplicative Decomposition
Multiple Regression
EOQ Model
Production Run Model
Quantity Discount Model
Safety Stock
Linear Programming
Linear Programming
Linear Programming
Linear Programming
Linear Programming
Linear Programming
Linear Programming
Linear Programming
Linear Programming
Linear Programming
Linear Programming
Linear Programming
Linear Programming
Linear Programming
Linear Programming
Linear Programming
Linear Programming
Linear Programming
Transportation
Assignment
Transportation
Transportation
Integer programming
Integer programming
10.5
10.6
10.7
10.9
10.10
10.11
10.12
10.13
12.1
12.2
12.extra
13.1
13.2
13.3
13.4
14.2
14.3
14.4
14.5
14.6
15.3
15.4
16.1
16.2
16.3
16.4
Module
M1.1
M5.1
Quemo Chemical Company
Sitka Manufacturing Company
Simkin, Simkin and Steinberg
Great Western Appliance
Hospicare Corp
Thermlock Gaskets
Solved Problem 10-1
Solved Problem 10-3
PERT - General Foundry Example
Crashing General Foundry Problem
Crashing General Foundry Problem
Arnold's Muffler Shop
Arnold's Muffler Shop
Golding Recycling, Inc.
Department of Commerce
Harry's Tire Shop
Generating Normal Random Numbers
Harry's Tire Shop
Port of New Orleans Barge Unloadings
Three Hills Power Company
Three Grocery Example
Accounts Receivable Example
Box Filling Example
Super Cola Example
ARCO
Red Top Cab Company
Excel
Excel
Excel
Excel
Excel
Excel
Excel
Excel
Excel QM
Excel
Excel QM
Excel QM
Excel QM
Excel QM
Excel QM
Excel
Excel
Excel QM
Excel
Excel
Excel
Excel
Excel QM
Excel QM
Excel QM
Excel QM
AHP
Matrix Multiplication
Excel
Excel
Integer programming
Integer programming
Integer programming
Nonlinear programming
Nonlinear programming
Nonlinear programming
0-1 programming
Nonlinear programming
Crashing
Crashing
Crashing
Single Server (M/M/1) system
Multi-Server (M/M/m) system
Constant Service Rate (M/D/1)
Finite population
Simulation (inventory)
Random #s and Frequency
Simulation (inventory)
Simulation (waiting line)
Maintenance Simulation
Markov Analysis
Fundamental Matrix & Absorbing States
Quality = x-bar chart
Quality = x-bar chart
p-Chart Analysis
c-Chart Analysis
- Regression
Rate (M/D/1)
ix & Absorbing States
Pritchett Clock Repair Shop
Breakeven Analysis
Enter
Enter the
the fixed
fixed and
and variable
variable costs
costs and
and the selling price in the data area.
Rebuilt Springs
1000
5
10
Fixed cost
Variable cost
Revenue
Results
Breakeven points
Units
Dollars $
Graph
Units
Cost-volume analysis
12
10
8
6
4
2
0
0
200
2,000.00
Costs
0
400
$
Data
Costs
Revenue
1000
3000
0
4000
2
4
Revenue
6
Units
8
10
12
Pritchett Clock Repair Shop
Breakeven Analysis
Enter
Enter the
the fixed
fixed and
and variable
variable costs
costs and
and the selling price in the data area.
Data
Fixed cost
Variable cost
Revenue
Volume (optional)
Rebuilt Springs
1000
5
10.71
250
Results
Breakeven points
Units
Dollars $
175
1,875.00
Volume Analysis@
Costs
Revenue
Profit
250
2,250.00
2,678.57
428.57
Graph
Units
$
$
$
Costs
0
350
Revenue
1000
2750
0
3750
X
5
4
3
2
1
P(X)
0.1
0.2
0.3
0.3
0.1
E(X) = ΣXP(X) =
XP(X)
0.5
0.8
0.9
0.6
0.1
2.9
(X - E(X))2P(X)
0.441
0.242
0.003
0.243
0.361
1.290
1.136
To see the formulas, hold down the CTRL key and press the ` (Grave accent) key
X))2P(X)
= Variance
= Standard deviation
press the ` (Grave accent) key
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 probabiliP(X < r) = 0.96875
Probability of exactlyP(X = r) = ###
X is a normal random variable
with mean, μ, and standard deviation, σ.
μ=
100
σ=
20
x=
P(X < x) =
P(X > x) =
75
0.10565
0.89435
F Distribution with df1 and df2 degrees of freedom
To find F given α
df1 =
5
df2 =
6
α=
F-value =
0.05
4.39
To find the probability to the right of a calculated value, f
df1 =
df2 =
f=
P(F > f) =
5
6
4.2
0.0548
Exponential distribution - the random variable (X) is time
Average number per time period = μ =
3 per hour
t=
0.5000 hours
P(X < t) =
0.7769
P(X > t) =
0.2231
Poisson distribution - the random variable is the number of occurrences per time period
λ=
x
0
1
2
2
P(X)
0.1353
0.2707
0.7293
P(X < x)
0.1353
0.4060
0.6767
urrences per time period
Thompson Lumber
Decision Tables
Enter
Enter the
the profits
profits or
or costs in the main body of the data table. Enter probabilities in the first row
if
you
want
to
compute
if you want to compute the
the expected
expected value.
value.
Data
Results
Favorable Unfavorable
Profit
Market
Market
EMV
Minimum Maximum
Hurwicz
Probability
0.5
0.5
coefficient
0.8
Large Plant
200000
-180000
10000 -180000
200000
124000
Small plant
100000
-20000
40000
-20000
100000
76000
Do nothing
0
0
0
0
0
Maximum
40000
0
200000
124000
Expected Value of Perfect Information
Column best
200000
0
100000 <-Expected value under certainty
40000 <-Best expected value
60000 <-Expected value of perfect information
Regret
Probability
Large Plant
Small plant
Do nothing
Favorable MUnfavorable Market
Expected Maximum
0.5
0.5
0
180000
90000
180000
100000
20000
60000
100000
200000
0
100000
200000
Minimum
60000
100000
Bayes Theorem for Thompson Lumber Example
Fill in cells B7, B8, and C7
Probability Revisions Given a Positive Survey
State
of
Posterior
Nature P(Sur.PosPrior Prob. Joint Pro Probability
FM
0.7
0.5
0.35
0.78
UM
0.2
0.5
0.1
0.22
P(Sur.pos.)
0.45
Probability
Revisions Given a Negative Survey
State
of
Posterior
Nature P(Sur.PosPrior Prob. Joint Pro Probability
FM
0.3
0.5
0.15
0.27
UM
0.8
0.5
0.4
0.73
P(Sur.neg.
0.55
Triple A Construction C
Sales (Y)Payroll (X)
6
3
8
4
9
6
5
4
4.5
2
9.5
5
SUMMARY OUTPUT
Regression Statistics
Multiple
0.8333
R Square 0.6944
Adjusted 0.6181
Standard 1.3110
Observat
6
ANOVA
df
SS
MS
Regressi
1 15.6250 15.6250
Residual
4
6.8750
Total
5
22.5
F
9.0909
1.7188
Coefficients
Standard 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
0.0989
6.8381 -2.8381
6.8381
2.4011
2.4011
0.0989
Jenny Wilson Realty
SELL PRICE
95000
119000
124800
135000
142800
145000
159000
165000
182000
183000
200000
211000
215000
219000
SF
1926
2069
1720
1396
1706
1847
1950
2323
2285
3752
2300
2525
3800
1740
AGE
30
40
30
15
32
38
27
30
26
35
18
17
40
12
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.8197
R Square
0.6719
Adjusted R Squa 0.6122
Standard Error
24313
Observations
14
ANOVA
df
Regression
Residual
Total
Intercept
SF
AGE
SS
2 1.3E+010
11 6.5E+009
13 2.0E+010
MS
F
Significance F
### 11.262 0.00217877
###
Coefficients
Standard Errort Stat
###
### 5.7543
43.819 10.2810 4.2622
-2899 796.5649 -3.6390
P-value Lower 95% Upper 95%
0.0001 90545.2073
###
0.0013
21.1911
66.4476
0.0039 -4651.9139 -1145.4586
Lower 95.0%Upper 95.0%
###
###
21.1911
66.4476
-4651.9139 -1145.4586
Jenny Wilson Realty
SELL PRICE
95000
119000
124800
135000
142800
145000
159000
165000
182000
183000
200000
211000
215000
219000
SF
1926
2069
1720
1396
1706
1847
1950
2323
2285
3752
2300
2525
3800
1740
AGE
30
40
30
15
32
38
27
30
26
35
18
17
40
12
X3 (ExcX4
0
1
1
0
0
0
0
1
0
0
0
0
1
0
(Mint Condition
0
Good
0
Excellent
0
Excellent
0
Good
1
Mint
1
Mint
1
Mint
0
Excellent
1
Mint
0
Good
0
Good
0
Good
0
Excellent
1
Mint
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.9476
R Square
0.8980
Adjusted R
0.8526
Standard Er
###
Observation
14
ANOVA
df
Regression
Residual
Total
Intercept
SF
AGE
X3 (Exc.)
X4 (Mint)
SS
MS
4 2E+010 4E+009
9 2E+009 2E+008
13 2E+010
Coefficients
Standard Errort Stat
###
###
6.981
56.43
6.95
8.122
-3962.82 596.03 -6.649
33162.65
###
2.723
47369.25
###
4.448
F Significance F
###
###
P-value Lower 95%
Upper 95%
Lower 95.0%
0.000
###
###
###
0.000
40.71
72.14
40.71
0.000
###
###
###
0.023 5610.43
### 5610.43
0.002
###
###
###
Upper 95.0%
###
72.14
###
###
###
Automobile Weight vs. MPG
MPG (Y) Weight (X1)
12
4.58
13
4.66
15
4.02
18
2.53
19
3.09
19
3.11
20
3.18
23
2.68
24
2.65
33
1.70
36
1.95
42
1.92
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.86288
R Square 0.74456
Adjusted R 0.71902
Standard E 5.00757
Observatio
12
ANOVA
df
Regression
Residual
Total
SS
MS
F
Significance F
1 730.909 730.909 29.14802 0.000302
10 250.7577 25.07577
11 981.6667
Coefficients
Standard Error t Stat
P-value Lower 95%
Intercept
47.6193 4.813151 9.89359 1.8E-006 36.89498
Weight (X1 -8.24597 1.527345 -5.398891 0.000302 -11.64911
Significance F
Upper 95%Lower 95.0%
Upper 95.0%
58.34371 36.89498 58.34371
-4.842833 -11.64911 -4.842833
Automobile Weight vs. MPG
MPG (Y) Weight (X1)
12
4.58
13
4.66
15
4.02
18
2.53
19
3.09
19
3.11
20
3.18
23
2.68
24
2.65
33
1.70
36
1.95
42
1.92
WeightSq.(X2)
20.98
21.72
16.16
6.40
9.55
9.67
10.11
7.18
7.02
2.89
3.80
3.69
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.9208
R Square
0.8478
Adjusted R
0.8140
Standard E
4.0745
Observatio
12
ANOVA
df
Regression
Residual
Total
SS
MS
2 832.2557 416.1278
9 149.411 16.60122
11 981.6667
Coefficients
Standard Error
Intercept
79.7888 13.5962
Weight (X1 -30.2224
8.9809
WeightSq.(
3.4124
1.3811
t Stat
5.8685
-3.3652
2.4708
F
25.0661
P-value
0.0002
0.0083
0.0355
Significance F
0.000209
Lower 95%Upper 95%Lower 95.0%
Upper 95.0%
49.0321 110.5454 49.0321 110.5454
-50.5386
-9.9062 -50.5386
-9.9062
0.2881
6.5367
0.2881
6.5367
Solved Problem 4-2
Advertising ($100) Y
11
6
10
6
12
Sales X
5
3
7
2
8
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.9014
0.8125
0.7500
1.4142
5
ANOVA
df
Regression
Residual
Total
Intercept
Sales X
SS
1
3
4
MS
26
6
32
F
26
2
Coefficients
Standard Error t Stat
4
1.5242
2.6244
1
0.2774
3.6056
Significance F
13 0.036618
P-value Lower 95%Upper 95%Lower 95.0%
0.0787
-0.8506
8.8506
-0.8506
0.0366
0.1173
1.8827
0.1173
Upper 95.0%
8.8506
1.8827
Triple A Construction
Forecasting
Regression/Trend analysis
IfIf this
this isis trend
trend analysis
analysis then
then simply
simply enter
enter the
the past
past demands
demands in
in the
the demand
demand
column.
column. IfIf this
this isis causal
causal regression
regression then
then enter
enter the
the y,x
y,x pairs
pairs with
with yy first
first and
and
enter
enter aa new
new value
value of
of xx at
at the
the bottom
bottom in
in order
order to
to forecast
forecast y.
y.
Data
Period
Period 1
Period 2
Period 3
Period 4
Period 5
Period 6
Intercept
Slope
Next period
Demand (y) Period(x)
6
3
8
4
9
6
5
4
4.5
2
9.5
5
2
1.25
10.75
Forecasts and Error Analysis
Forecast Error
Absolute
5.75
0.25
0.25
7
1
1
9.5
-0.5
0.5
7
-2
2
4.5
0
0
8.25
1.25
1.25
Total
0
5
Average
0 0.833333
Bias
MAD
SE
Squared Abs Pct Err
0.0625
04.17%
1
12.50%
0.25
05.56%
4
40.00%
0
00.00%
1.5625
13.16%
6.875
75.38%
1.145833
12.56%
MSE
MAPE
1.311011
7
Correlatio 0.833333
Wallace Garden Supply
Forecasting
Weighted moving averages - 3 period moving average
Enter
Enter the
the data
data in
in the
the shaded
shaded area.
area. Enter
Enter weights
weights in
in
INCREASING
INCREASING order
order from
from top
top to
to bottom.
bottom.
Data
Period
January
February
March
April
May
June
July
August
September
October
November
December
Demand
Forecasts and Error Analysis
Forecast Error
Absolute Squared
Weights
10
12
13
16
19
23
26
30
28
18
16
14
Next period 15.3333333
Abs Pct Err
1
2
3
12.1667
14.3333
17
20.5
23.8333
27.5
28.3333
23.3333
18.6667
Total
Average
3.8333
3.8333 14.6944
23.96%
4.6667
4.6667 21.7778
24.56%
6
6
36
26.09%
5.5
5.5
30.25
21.15%
6.1667
6.1667 38.0278
20.56%
0.5
0.5
0.25
01.79%
-10.3333 10.3333 106.7778
57.41%
-7.3333
7.3333 53.7778
45.83%
-4.6667
4.6667 21.7778
33.33%
4.3333 49.0000 323.3333
254.68%
0.4815
5.4444 35.9259
28.30%
Bias
MAD
MSE
MAPE
SE
6.79636
Port of Baltimore
Forecasting
Exponential smoothing
Enter
Enter alpha
alpha (between
(between 00 and
and 1),
1), enter
enter the
the past
past demands
demands in
in the
the shaded
shaded column
column then
then enter
enter aa starting
starting forecast.
forecast. IfIf the
the starting
starting
forecast
forecast isis not
not in
in the
the first
first period
period then
then delete
delete the
the error
error analysis
analysis for
for all
all rows
rows above
above the
the starting
starting forecast.
forecast.
Alpha
Data
Period
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Quarter 5
Quarter 6
Quarter 7
Quarter 8
0.1
Demand
180
168
159
175
190
205
180
182
Next period 178.595856
Forecasts and Error Analysis
Forecast Error
Absolute
175
5
5
175.5
-7.5
7.5
174.75
-15.75
15.75
173.175
1.825
1.825
173.3575 16.6425 16.6425
175.0218 29.97825 29.97825
178.0196 1.980425 1.980425
178.2176 3.782382 3.782382
Total 35.95856 82.45856
Average 4.49482 10.30732
Bias
MAD
SE
Squared Abs Pct Err
25
02.78%
56.25
04.46%
248.0625
09.91%
3.330625
01.04%
276.9728
08.76%
898.6955
14.62%
3.922083
01.10%
14.30642 0.02078232
1526.54
44.75%
190.8175
05.59%
MSE
MAPE
15.95065
t. IfIf the
st.
the starting
starting
Midwestern Manufacturing
Forecasting
Trend adjusted exponential smoothing
Enter
Enter alpha
alpha and
and beta
beta (between
(between 00 and
and 1),
1), enter
enter the
the past
past demands
demands in
in the
the shaded
shaded column
column then
then enter
enter aa
starting
starting forecast.
forecast. IfIf the
the starting
starting forecast
forecast isis not
not in
in the
the first
first period
period then
then delete
delete the
the error
error analysis
analysis for
for all
all
rows
rows above
above the
the starting
starting forecast.
forecast.
Alpha
Beta
Data
Period
Period 1
Period 2
Period 3
Period 4
Period 5
Period 6
Period 7
0.3
0.4
Forecasts and Error Analysis
Demand
74
79
80
90
105
142
122
Next period
Forecast
Smoothed
Including
Forecast, Smoothed Trend,
Ft
Trend, Tt FITt
Error
Absolute
74
74
0
0
74
0
74
5
5
75.5
0.6
76.1
4.5
4.5
77.27
1.068
78.338
12.73
12.73
81.8366 2.46744 84.30404 23.1634 23.1634
90.51283 4.950955 95.46378 51.48717 51.4872
109.4246 10.5353 119.9599 12.57535 12.5754
120.572 10.78011 131.3521
Total
109.4559 109.456
Average
15.63656 15.6366
Bias
MAD
SE
Squared
0
25
20.25
162.0529
536.5431
2650.929
158.1395
3552.914
507.5592
MSE
26.65676
Abs Pct
Err
00.00%
06.33%
05.63%
14.14%
22.06%
36.26%
0.103077
94.73%
13.53%
MAPE
Midwestern Manufacturing
Time (X)
1
2
3
4
5
6
7
Demand (Y)
74
79
80
90
105
142
122
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.89491
R Square 0.800863
Adjusted R 0.761036
Standard E 12.43239
Observatio
7
ANOVA
df
Regression
Residual
Total
Intercept
Time (X)
SS
MS
F
Significance F
1 3108.036 3108.036 20.10837 0.006493
5 772.8214 154.5643
6 3880.857
Coefficients
Standard Error t Stat
P-value Lower 95%Upper 95%Lower 95.0%
Upper 95.0%
56.71429 10.50729 5.397615 0.002948 29.70445 83.72412 29.70445 83.72412
10.53571 2.349501 4.484236 0.006493 4.496131 16.5753 4.496131 16.5753
Upper 95.0%
Midwestern Manufacturing
Forecasting
Regression/Trend analysis
IfIf this
this isis trend
trend analysis
analysis then
then simply
simply enter
enter the
the past
past demands
demands in
in the
the demand
demand column.
column. IfIf this
this isis
causal
causal regression
regression then
then enter
enter the
the y,x
y,x pairs
pairs with
with yy first
first and
and enter
enter aa new
new value
value of
of xx at
at the
the bottom
bottom in
in
order
order to
to forecast
forecast y.
y.
Data
Period
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Demand (y) Period(x)
74
1
79
2
80
3
90
4
105
5
142
6
122
7
Intercept
Slope
56.7142857
10.5357143
Next period
141
Forecasts and Error Analysis
Forecast Error
Absolute
67.25
6.75
6.75
77.7857
1.2143
1.2143
88.3214
-8.3214
8.3214
98.8571
-8.8571
8.8571
109.3929
-4.3929
4.3929
119.9286
22.0714
22.0714
130.4643
-8.4643
8.4643
Total
-4.263256E-014
60.0714
Average
-6.090366E-015
8.5816
Bias
MAD
SE
Squared
45.5625
1.4745
69.2462
78.4490
19.2972
487.1480
71.6441
772.8214
110.4031
MSE
12.43239
Correlatio
0.89491
8
Abs Pct Err
09.12%
01.54%
10.40%
09.84%
04.18%
15.54%
06.94%
57.57%
08.22%
MAPE
Turner Industries
Forecasting
4 seasons
Data
Period
Period 1
Period 2
Period 3
Period 4
Period 5
Period 6
Period 7
Period 8
Period 9
Period 10
Period 11
Period 12
Multiplicative decomposition
Enter
Enter past
past demands
demands in
in the
the data
data area.
area. Do
Do not
not change
change the
the time
time period
period
numbers!
numbers!
Demand (y) Time (x)
108
1
125
2
150
3
141
4
116
5
134
6
159
7
152
8
123
9
142
10
168
11
165
12
Average
131
133
135.25
137.5
140.25
142
144
146.25
149.5
132.000
134.125
136.375
138.875
141.125
143.000
145.125
147.875
Average
Ratios
Season 1
Average
0.8506
0.8475
0.8491
Season 2
Season 3 Season 4
1.1364
1.0513
0.9649
1.1267
1.0629
0.9603
0.9626
1.1315
1.0571
Forecasts
Period
Unadjusted Seasonal Adjusted
13
155.240
0.849
131.810
14
157.583
0.963
151.687
15
159.927
1.132
180.959
16
162.270
1.057
171.535
Ratio
1.136
1.051
0.851
0.965
1.127
1.063
0.848
0.960
Seasonal Smoothed
0.8491
127.1979
0.9626
129.8589
1.1315
132.5660
1.0571
133.3841
0.8491
136.6200
0.9626
139.2087
1.1315
140.5199
1.0571
143.7899
0.8491
144.8643
0.9626
147.5197
1.1315
148.4739
1.0571
156.0878
Intercept
Slope
124.7753
2.3434
Forecasts and Error Analysis
Unadjusted 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%
Bias
MAD
MSE
MAPE
SE
1.84397092
Year
Quarter
1
2
3
4
2
1
2
3
4
3
1
2
3
4
1
Sales X1 Time PeriodX2 Qtr 2 X3 Qtr 3 X4 Qtr 4
108
1
0
0
0
125
2
1
0
0
150
3
0
1
0
141
4
0
0
1
116
5
0
0
0
134
6
1
0
0
159
7
0
1
0
152
8
0
0
1
123
9
0
0
0
142
10
1
0
0
168
11
0
1
0
165
12
0
0
1
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.99718
R Square 0.99436
Adjusted R 0.99114
Standard E 1.83225
Observatio
12
ANOVA
df
Regression
Residual
Total
4
7
11
SS
MS
F
Significance F
4144.75 1036.188 308.6516 6.0E-008
23.5 3.357143
4168.25
Coefficients
Standard Error t Stat
Intercept
104.104 1.332194 78.14493
X1 Time Pe 2.3125 0.16195 14.27913
X2 Qtr 2
15.6875 1.504767 10.4252
X3 Qtr 3
38.7083 1.530688 25.28819
X4 Qtr 4
30.0625 1.572941 19.11228
P-value Lower 95%Upper 95%Lower 95.0%
Upper 95.0%
1.5E-011 100.954 107.2543 100.954 107.2543
2.0E-006 1.92955 2.69545 1.92955 2.69545
1.6E-005 12.12929 19.24571 12.12929 19.24571
3.9E-008 35.08883 42.32784 35.08883 42.32784
2.7E-007 26.34308 33.78192 26.34308 33.78192
Sumco Pump Company
Inventory
Economic Order Quantity Model
Enter
Enter the
the data
data in
in the
the shaded
shaded area
area
Data
Demand rate, D
Setup cost, S
Holding cost, H
Unit Price, P
1000
10
0.5 (fixed amount)
0
200
200
100
5
Cost ($)
Inventory: Cost vs Quantity
Results
Optimal Order Quantity, Q*
Maximum Inventory
Average Inventory
Number of Setups
12
10
8
Holding
cost
4
Total cost
Holding cost
Setup cost
$50.00
$50.00
6
Unit costs
Total cost, Tc
$0.00
2
$100.00
0
COST TABLE
Start at
25 Increment
Q
25
40
55
70
85
100
115
130
145
160
175
190
205
220
235
250
265
280
295
310
325
340
355
Setup cost
Order Quantity (Q)
15
Setup cost Holding cosTotal cost
400
6.25
406.25
250
10
260
181.8182
13.75 195.5682
142.8571
17.5 160.3571
117.6471
21.25 138.8971
100
25
125
86.95652
28.75 115.7065
76.92308
32.5 109.4231
68.96552
36.25 105.2155
62.5
40
102.5
57.14286
43.75 100.8929
52.63158
47.5 100.1316
48.78049
51.25 100.0305
45.45455
55 100.4545
42.55319
58.75 101.3032
40
62.5
102.5
37.73585
66.25 103.9858
35.71429
70 105.7143
33.89831
73.75 107.6483
32.25806
77.5 109.7581
30.76923
81.25 112.0192
29.41176
85 114.4118
28.16901
88.75 116.919
370 27.02703
92.5
119.527
Brown Manufacturing
Inventory
Production Order Quantity Model
Enter
Enter the
the data
data in
in the
the shaded
shaded area.
area. You
You may
may have
have to
to do
do some
some work
work to
to enter
enter the
the daily
daily production
production rate.
rate.
10000
100
0.5 (fixed amount)
80
60
0
12
10
Setup c
Holding
cost
Total co
8
6
Results
Optimal production quantity, Q*
Maximum Inventory
Average Inventory
Number of Setups
4000
1000
500
2.5
Holding cost
Setup cost
4
2
0
250
250
Unit costs
0
Total cost, Tc
COST TABLE
Inventory: Cost vs Quantity
Cost ($)
Data
Demand rate, D
Setup cost, S
Holding cost, H
Daily production rate, p
Daily demand rate, d
Unit price, P
500
Start at
Q
1000
1333.333
1666.667
2000
2333.333
2666.667
3000
3333.333
3666.667
4000
4333.333
4666.667
5000
5333.333
5666.667
6000
6333.333
6666.667
7000
7333.333
7666.667
8000
8333.333
8666.667
1000 Increment 333.3333
Setup cost Holding cosTotal cost
1000
62.5
1062.5
750 83.33333 833.3333
600 104.1667 704.1667
500
125
625
428.5714 145.8333 574.4048
375 166.6667 541.6667
333.3333
187.5 520.8333
300 208.3333 508.3333
272.7273 229.1667 501.8939
250
250
500
230.7692 270.8333 501.6026
214.2857 291.6667 505.9524
200
312.5
512.5
187.5 333.3333 520.8333
176.4706 354.1667 530.6373
166.6667
375 541.6667
157.8947 395.8333 553.7281
150 416.6667 566.6667
142.8571
437.5 580.3571
136.3636 458.3333 594.697
130.4348 479.1667 609.6014
125
500
625
120 520.8333 640.8333
115.3846 541.6667 657.0513
Order Quantity (Q)
aily
aily production
production rate.
rate.
ry: Cost vs Quantity
uantity (Q)
Setup cost
Holding
cost
Total cos t
Brass Department Store
Inventory
Quantity Discount Model
Data
Demand rate, D
Setup cost, S
Holding cost %, I
5000
49
20%
Range 1
Minimum quantity
Unit Price, P
Range 2
0
5
Range 3
1000
4.8
2000
4.75
Results
Range 1
Q* (Square root formula)
Order Quantity
Holding cost
Setup cost
Range 2
Range 3
700 714.4345083118 718.18484646
700
1000
2000
$350.00
$350.00
$480.00
$245.00
$950.00
$122.50
Unit costs
$25,000.00
$24,000.00
$23,750.00
Total cost, Tc
Optimal Order Quantity
$25,700.00
$24,725.00
1000
$24,822.50
minimum
=
$24,725.00
6.4
Inventory
Safety stock - Normal distribution
Select
aa model
and
then
the
data
inshaded
the
area.
The
onbottom
the
left
the
model
andenter
then enter
enter
thein
data
the shaded
shaded
area.
The model
model
the bottom
bottom
left represents
represents
the
Select
aa model
and
the
the
area.
on
left
the
SelectSelect
model
and then
then
enter
the data
data
in
thein
shaded
area. The
The model
model
on the
theon
bottom
left represents
represents
the 33 models
models described
described in
in the
the textbook
textbook under
under Other
Other Probabilistic
Probabilistic Models
Models
33 models
models described
described in
in the
the textbook
textbook under
under Other
Other Probabilistic
Probabilistic Models
Models
Model: Demand during leadtime and its standard deviation given
Data
Average demand during lead time, µ
Standard deviation of σdLT
Service level (% of demand met)
Results
Z-value
Safety stock
Model: Daily demand and its standard deviation are given
350
10
95.00%
1.64
16.45
Data
Average daily demand
Standard deviation of daily demand, σd
Lead time days
Service level (% of demand met)
Service level (% of demand met)
Results
Z-value
Average demand during lead time
Standard deviation of demand during lead time, σdLT
Safety stock
Reorder point
25
0 Enter 0 if demand is constant
6
3 Enter 0 if lead time is constant
98.00%
2.05
150
75.00
154.03
304.03
344787981.xls
3
4
97.00%
Results
Z-value
1.88
Average demand during lead time
60
Standard deviation of demand during lead time, σ 6.00
Safety stock
11.28
Reorder Point
71.28
Models: Either daily demand, lead time or both are variable
Data
Average daily demand
Standard deviation of daily demand
Average lead time (in days)
Standard deviation of lead time, σLT
15
Flair Furniture
Variables
T (Tables)C (Chairs)
Units Produced
30
40
Objective functi
70
50
Constraints
Carpentry
Painting
4
2
Profit
4100
LHS (Hours used)
3
240
<
1
100
<
RHS
240
100
Holiday Meal Turkey Ranch
Variables
Brand 1Brand 2
Units Produced 8.4
4.8
Objective functi 2
3
Constraints
Ingredient A
Ingredient B
Ingredient C
5
4
0.5
Cost
31.2
LHS (Amt. of Ing.)
10
90
>
3
48
>
0
4.2
>
RHS
90
48
1.5
High Note Sound Company
Variables
CD PlayerReceivers
Units Produced
0
20
Profit
Objective functi
2400
50
120
Constraints
LHS (Hrs. Used)
Electrician Hour
2
4
Audio Tech Hour
3
1
80
20
RHS
< ###
< ###
7.7
Enter
Enter the
the values
values in
in the
the shaded
shaded area.
area. Then
Then go
go to
to the
the DATA
DATATab
Tab on
on the
the ribbon,
ribbon, click
click on
on Solver
Solver in
in the
the Data
DataAnalysis
Analysis
Group
Group and
and then
then click
click SOLVE.
SOLVE.
IfIf SOLVER
SOLVER isis not
not on
on the
the Data
Data Tab
Tab then
then please
please see
see the
the Help
Help file
file (Solver)
(Solver) for
for instructions.
instructions.
Linear Programming
Signs
<
=
>
less than or equal to
equals (You need to enter an apostrophe first.)
greater than or equal to
x1
x2
Data
Objective
Constraint 1
Constraint 2
70
4
2
50 sign
3 <
1 <
Results
Variables
Objective
30
40
RHS
240
100
4100
Page 52
Results
LHS
Slack/Surplus
4100
240
0
100
0
A
1
B
C
D
E
er
X2
5
8500
Radio
30 sec.
X3
6.2069
2400
Radio
1 min.
X4
0
2800
Win Big Gambling Club
2
3
4
5
6
Variables
Solution
Audience per
ad
TV
X1
1.9688
5000
7
8
9
10
11
12
13
14
15
Constraints
Max. TV
Newspaper
radio
radio
Cost
Radio dollars
Radio spots
1
1
1
800
925
290
290
1
1
380
380
1
F
G
H
<
<
<
<
<
<
>
RHS
12
5
25
20
8000
1800
5
1
2
3
4
Total Audience
6
67240.3017
5
7
8
9
10
11
12
13
14
15
LHS
1.9688
5
6.2069
0
8000
1800
6.2069
A
1
B
C
D
E
F
G
H
I
J
>
>
>
>
<
RHS
2,300
1,000
600
0
0
Management Science Associates
2
3
4
5
Variable
Solution
Min. Cost
X1
0
7.5
X2
600
6.8
X3
X4
X5
X6
140 1000
0 560Total Cost
5.5
6.9 7.25
6.1
15166
6
Constraints
1
8 Total Househo
1
9 30 and Younge
0
10 31-50
11 Border States 0.85
12 51+ Border St
0
7
1
0
1
0.85
0
1
1
1
1
0
1
0
0
0
0
1
0
0.85 -0.15 -0.15 -0.15
0.8
0
0 -0.2
LHS
2300
1000
600
395
0
A
1
3
5
6
C
D
E
F
G
Fifth Avenue Industries
2
4
B
Variables
Values
Profit
All
silk
All
poly.
Blend 1
Blend 2
X1
5112
16.24
X2
14000
8.22
X3
16000
8.77
X4
8500
8.66
Total Profit
412028.88
7
8
9
10
11
12
13
14
15
16
17
18
19
Constraints
Silk available
0.125
available
available
1
Maximum silk
polyester
1
2
1
Minimum silk
polyester
1
Minimum blend
2
LHS
0.066
0.08
0.05
0.05
0.044
1
1
1
1
1
1
1200
1920
1174
5112
14000
16000
8500
5112
14000
16000
8500
<
<
<
<
<
<
<
>
>
>
>
20
21
22
23
Calculations to determine the profit per tie.
Polyes
Silk
ter
Blend 1 Blend 1
25 Selling Price per ti 19.24
8.7
9.52
10.64 Cost of material per yard
Yards of silk used
26
in tie
0.125
0
0
0.066
24
Yards of polyester
27
used in tie
0
0.08
0.05
0
6
24
Yards of cotton
used in tie
0
3
29 Material cost per t
30 Profit per tie
16.24
28
0
0.48
8.22
0.05
0.75
8.77
0.044
1.98
8.66
9
H
I
J
K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
RHS
1200
3000
1600
7000
14000
16000
8500
5000
10000
13000
5000
20
21
22
23
24
f material25per yard
26
27
28
29
30
Slack/Surplus
0
1080
426
1888
0
0
0
112
4000
3000
3500
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
Greenberg Motors
Variable
Solution
Min. Cost
A1
A2
A3
A4
B1
B2
B3 B4 IA1 IA2 IA3 IA4 IB1
IB2
IB3 IB4
### 223.1 ### 792.3 ### ### 77.8 ### ### 0 ### 450
0
###
0
300
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 Constraints
Jan. GM3A
1
Feb. GM3A
1
Mar. GM3A
Apr. GM3A
Jan. GM3B
Feb. GM3B
Mar. GM3B
Apr. GM3B
Inv.GM3A Apr.
Inv.GM3B Apr.
Labor Hour Constraints
Hrs Min. Jan. 1.3
Hrs Min. Feb.
1.3
Hrs Min. Mar.
Hrs Min. Apr.
Hrs Max. Jan. 1.3
Hrs Max. Feb.
1.3
Hrs Max.Mar.
Hrs Max. Apr.
Storage Constraints
Jan. Inv. Limit
Feb. Inv. Limit
Mar. Inv. Limit
Apr. Inv. Limit
-1
1
1
-1
1
1
-1
1
-1
1
-1
1
1
1
-1
1
1
-1
1
-1
1
1
0.9
0.9
1.3
0.9
1.3
0.9
0.9
0.9
1.3
0.9
1.3
0.9
1
1
1
1
1
1
1
1
A
B
C
D
E
33
34
35
36
37
38
39
GM3A Units
GMBA Units
GM3A Inven
GM3B Inven
Labor Hours
Jan
Feb
Mar
Apr
### 223.1 ### 792.3
### ### 77.8 ###
476.9
0.0 757.7 450.0
0.0 ###
0.0 300.0
### ### ### ###
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
1
2
3
4 Total Cost
###
5
6
7
8
9
10
11
12
13
14
15
16
17
LHS SignRHS
800 = 800
700 = 700
1000 = ###
1100 = ###
1000 = ###
1200 = ###
1400 = ###
1400 = ###
450 = 450
300 = 300
18
19
20
21
22
23
24
25
26
2560
2560
2355
2560
2560
2560
2355
2560
>
>
>
>
<
<
<
<
###
###
###
###
###
###
###
###
476.92
1322.22
757.69
750
<
<
<
<
###
###
###
###
27
28
29
30
31
32
Slack/Surplus
320
320
115
320
0
0
205
0
R
33
34
35
36
37
38
39
S
T
U
V
W
A
1
B
C
D
E
F
G
H
P3
2
32
P4
5
32
P5
0
32
Total Cost
1448
I
J
Labor Planning Example
2
3
4
5
6
Variables
Values
Cost
F
10
100
P1
0
32
P2
7
32
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Constraints
9 a.m. - 10 a 1
10 a.m. - 11
1
11 a.m. - noo 0.5
noon - 1 p.m. 0.5
1 p.m. - 2 p.m 1
2 p.m. - 3 p.m 1
3 p.m. - 4 p.m 1
4 p.m. - 5 p.m 1
Max. Full tim 1
Total PT hours
1
1
1
1
4
1
1
1
1
4
1
1
1
1
4
1
1
1
1
4
1
1
1
1
4
LHS
10
17
14
19
24
17
15
10
10
56
Sign RHS
>
10
>
12
>
14
>
16
>
18
>
17
>
15
>
10
<
12
<
56
K
L
M
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Slack/Surplus
0
5
0
3
6
0
0
0
2
0
N
O
A
1
B
C
D
E
F
G
H
<
<
<
<
>
>
<
RHS
###
###
###
###
0
0
5000000
ICT Portfolio Selection
2
3
4
5
Variable
X1
X2
X3
X4
Solution
750000 950000 2E+006 2E+006Total Return
Max. Return
0.07
0.11
0.19
0.15 712000
6
7
8
9
10
11
12
13
14
Trade
Bonds
Gold
Construction
Min. Gold+Con
Min. Trade
Total Investe
1
1
1
-0.55
0.85
1
-0.55
-0.15
1
0.45
-0.15
1
1
0.45
-0.15
1
LHS
750000
950000
1500000
1800000
550000
0
5000000
Goodman Shipping
Variables
X1
X2
X3
Values
0.333
1
0
Load Value 22500 24000 8000
Constraints
Total weigh 7500
% Item 1
1
% Item 2
% Item 3
% Item 4
% Item 5
% Item 6
7500
3000
X4
X5
X6
0
0
0 Total Value
9500 11500 9750
31500
3500
4000
1
1
1
1
LHS
Sign RHS
3500 10000
< 10000
0.333333 <
1
1
<
1
0
<
1
0
<
1
0
<
1
1
0
<
1
A
1
B
C
D
E
F
G
Sign
>
>
>
>
=
RHS
3
2
1
0.425
0.125
Whole Foods Nutrition Problem
2
3
4
5
6
Variable
Solution
Minimize
Grain AGrain BGrain C
Xa
Xb
Xc
0.025
0.05
0.05
0.33
0.47
0.38
Total Cost
0.05075
7
8
9
10
11
12
13
Constraints
Protein
22
Riboflavin
16
Phosphoru 8
Magnesiu
5
Total Weig
1
28
14
7
0
1
21
25
9
6
1
LHS
3
2.35
1
0.425
0.125
H
I
J
1
2
3
4
5
6
7
8
9
10
11
12
13
Slack/Surplus
0
0.35
0
0
0
Low Knock Oil Company
Variable
Solution
Cost
X100 ReX100 EcoX220 ReX220 Econ
X1
X2
X3
X4
15000 26666.67 10000 5333.33
Total Cost
30
30
34.8
34.8
1783600
Constraints
Demand Regula 1
Demand Economy
Ing. A in Regul -0.1
Ing. B in Economy
1
1
1
0.15
0.05
-0.25
LHS
25000
32000
0
0
Sign
>
>
>
<
RHS
25000
32000
0
0
Slack/Surplus
0
0
0
0
Top Speed Bicycle Company
N.O. to N.O. to N.O. to Omaha to Omaha to Omaha to
NY
Chicago
LA
NY
Chicago
LA
Variables
Values
Cost
Constraints
NY Demand
Chi. Demand
LA Demand
N.O. Supply
Omaha Supply
X11
10000
2
X12
0
3
X13
8000
5
1
X21
0
3
X23
7000 Total Cost
4
96000
1
1
1
X22
8000
1
1
1
1
1
1
1
1
1
LHS
10000
8000
15000
18000
15000
otal Cost
Sign
=
=
=
<
<
RHS
10000
8000
15000
20000
15000
Shipping Cost Per Unit
From\ToAlbuquerque
Boston
Cleveland
Des Moines
5
4
3
Evansville
8
4
3
Fort Lauderdal
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 Lauderdal
200
0
100
300
300
Total receive
300
200
200
Demand
300
200
200
Total cost =
3900
Cost for Assignments
erson\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 pSupply
Adams
0
0
1
1
1
Brown
0
1
0
1
1
Cooper
1
0
0
1
1
Total assigne
1
1
1
Total workers
1
1
1
Total cost =
25
Frosty Machines Transshipment Problem
From\To
Toronto
Detroit
Chicago
Buffalo
Shipping Cost Per Unit
Chicago
Buffalo NYC
Phil. St.Louis
4
7
5
7
6
4
5
2
3
4
Toronto
Detroit
Chicago
Buffalo
Total receiv
Demand
Solution - Number of
Chicago
Buffalo NYC
650
150
0
300
0
450
650
450
450
450
Total cost =
9550
units shipped
Phil. St.Louis
Total shipped
Supply
800
800
300
700
350
300
650
0
0
450
350
300
350
300
9.4
Birmingham
Transportation
Enter
Enter the
the transportation
transportation data
data in
in the
the shaded
shaded area.
area. Then
Then go
go to
to the
the DATA
DATATab
Tab on
on the
the ribbon,
ribbon, click
click on
on Solver
Solver in
in the
the Data
DataAnalysis
Analysis
Group
Group and
and then
then click
click SOLVE.
SOLVE.
IfIf SOLVER
SOLVER isis not
not on
on the
the Data
Data Tab
Tab then
then please
please see
see the
the Help
Help file
file (Solver)
(Solver) for
for instructions.
instructions.
Data
COSTS
Origin 1
Origin 2
Origin 3
Origin 4
Demand
Shipments
Shipments
Origin 1
Origin 2
Origin 3
Origin 4
Column Total
Total Cost
Dest 1
73
85
88
84
10000
Dest 2
Dest 3
Dest 4
Supply
103
88
108
15000
80
100
90
6000
97
78
118
14000
79
90
99
11000
12000
15000
9000 46000 \ 46000
Dest 1
Dest 2
Dest 3
Dest 4
Row Total
10000
0
1000
4000
15000
0
1000
0
5000
6000
0
0
14000
0
14000
0
11000
0
0
11000
10000
12000
15000
9000 46000 \ 46000
3741000
Page 75
9.4
lver in
olver
in the
the Data
DataAnalysis
Analysis
Page 76
9.5
A
1
B
C
D
E
F
Fix-It Shop Assignment
2
3
4
5
6
7
Assignment
Enter
Enter the
the assignment
assignment costs
costs in
in the
the shaded
shaded area.
area. Then
Then go
go to
to the
the DATA
DATATab
Tab on
on the
the ribbon,
ribbon, click
click on
on
Solver
Solver in
in the
the Data
DataAnalysis
Analysis Group
Group and
and then
then click
click SOLVE.
SOLVE.
IfIf SOLVER
SOLVER isis not
not on
on the
the Data
Data Tab
Tab then
then please
please see
see the
the Help
Help file
file (Solver)
(Solver) for
for instructions.
instructions.
Data
9 COSTS
10 Adams
11 Brown
12 Cooper
8
Project 1 Project 2 Project 3
11
14
6
8
10
11
9
12
7
13
14
15
16
17
18
19
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
20
21
Total Cost
25
22
Page 77
G
Harrison Electric Integer Programming Analysis
Variables
Values
Profit
Chandeliers Fans
X1
X2
5
0
7
6
Constraints
Wiring hours
Assembly hours
2
6
3
5
Total Profit
35
LHS
10
30
Sign
<
<
RHS
12
30
Bagwell Chemical Company
Xyline (bags)Hexall (lbs)
Variables
X
Y
Values
44
20
Total Profit
Profit
85
1.5
3770
Constraints
Ingredient A
Ingredient B
Ingredient C
30
18
2
0.5
0.4
0.1
LHS
1330
800
90
sign
<
<
<
RHS
2000
800
200
Quemo Chemical Company
Catalytic Conv.
Variables
X1
Values
1
Net Present Val
25000
Constraints
Year 1
Year 2
8000
7000
Software
X2
0
18000
6000
4000
Warehouse Expan.
X3
1
NPV
32000
57000
12000
8000
LHS
20000
15000
sign
<
<
RHS
20000
16000
Sitka Manufacturing Company
Baytown
Variables
X1
Values
0
Cost
340000
Constraints
Minimum capacity
Maximum in Baytown
Maximum in L. C.
Maximum in Mobile
Lake Charles
X2
1
270000
Mobile
X3
1
290000
Baytown units
X4
0
32
1
1
-21000
-20000
-19000
L. Charles units
Mobile units
X5
X6
19000
19000
33
30
1
1
1
1
Cost
1757000
LHS
38000
0
-1000
0
Sign RHS
>
38000
<
0
<
0
<
0
`
Simkin, Simkin and Steinberg
Variables
X1
Values
0
Return ($1,000s) 50
Constraints
Texas
1
Foreigh Oil
California
$3 Million
480
X2
0
80
1
540
X3
1
90
X4
1
120
X5
1
110
1
1
X6
1
40
X7
0
75
1
680 1000
700
1
510
1
900
Return
360
LHS
2
1
1
2890
Sign
>
<
=
<
RHS
2
1
1
3000
Great Western Appliance
Variables
Values
MicroSelf-Clean
X1
X2
0
1000
Terms
X1
Calculated Values 0
Profit
28
Constraints
Capacity
1
Hours Available 0.5
X2
1000
21
1
0.4
X22
###
0.25
Profit
271000
LHS
1000
400
Sign RHS
< 1000
<
500
Hospicare Corp
Variables
Values
X1
###
Terms
X1
Calculated Values###
Profit
Constraints
Nursing
X-Ray
Budget
13
X2
###
X12 X1*X2 X2
X23
1/X2
###
0
###
### Total Profit
1
###
2
1
8
###
6
###
5
4
1
-2
LHS
90.00
75.00
40.33
Sign RHS
< 90
< 75
< 61
Thermlock Gaskets
Variables
Values
Cost
Value
Constraints
Hardness
Tensile Stre
Elasticity
X1
3.325
5
X2
14.672 Total Cost
7
119.333
X1
X12
X13
X2
X22
3.325
11.058
36.771
14.672
215.276
3
13
0.7
0.25
4
1
1
0.3
LHS Sign
###
>
80
>
17
>
RHS
125
80
17
Solved Problem 10-1
Variables
Values
Maximize
Constraints
Constraint 1
Constraint 2
Constraint 3
Constraint 4
X1
1
50
19
22
1
1
X2
1
45
27
13
1
-1
X3
0
48
Total
95
34
12
1
0
LHS Sign RHS
46
<
80
35
<
40
2
<
2
0
<
0
Forecasting - Exponential Smoothing
Ft+1 = Ft + α(Yt-Ft)
Time Period (t)Demand (Yt) Forecast (Ft) Error = Yt - F |error|
α = 0.3478
1
2
3
4
5
6
7
8
110
156
126
138
124
125
160
110
110
125.999999781
125.9999998571
130.1739128932
128.0264649597
126.9737815099
138.461161697
0
46.000
0.000
12.000
-6.174
-3.026
33.026
MAD=
46.000
0.000
12.000
6.174
3.026
33.026
16.704
F1 is assumed to be a perfect forecast.
MAD is based on time periods 2 through 7
`
General Foundry
Project Management
Precedences; 3 time estimates
Enter
Enter the
the times
times in
in the
the appropriate
appropriate column(s).
column(s). Enter
Enter the
the precedences,
precedences, one
one per
per column.
column. (Do
(Do not
not try
try to
to use
use
commas).
commas).
Data
Activity
Optimistic Likely
Pessimistic
Mean
A
1
2
3
B
2
3
4
C
1
2
3
D
2
4
6
E
1
4
7
F
1
2
9
G
3
4
11
H
1
2
3
Precedences
Immediate Predecessors (1 per column)
Activity
Time
Pred 1
Pred 2
A
2
B
3
C
2
A
D
4
B
E
4
C
F
3
C
G
5
D
E
H
2
F
G
2
3
2
4
4
3
5
2
A
Std dev
Variance
B
0.333333 0.111111
0.333333 C 0.111111
0.333333 0.111111
D
0.666667 0.444444
1 E
1
1.333333 1.777778
F
1.333333 1.777778
0.333333 G 0.111111
H
0
2
4
6
Slack
Early
Start
Early
Finish
0
0
2
0
4
4
8
13
Project
Early start computations
A
B
C
D
E
F
G
H
Late finish computations
A
B
A
15
B
15
C
2
D
15
E
15
Late
Start
Late
Finish
2
3
4
4
8
7
13
15
15
0
12
2
4
4
10
8
13
0
0
2
0
4
4
4
7
0
0
0
0
0
0
8
13
Variance
0.111111
0
12
0
4
0
6
0
0
0.111111
1
Project
Std.dev
C
15
15
15
15
15
Slack
2
15
4
8
8
13
13
15
D
15
15
15
15
4
E
15
15
15
15
15
F
15
15
15
15
15
G
15
15
15
15
15
1.777778
0.111111
3.111111
1.763834
H
15
15
15
15
15
8
Time
Noncritical Activity
Results
Activity
A
B
C
D
E
F
G
H
Gantt Chart
15
15
15
15
15
1
C
F
G
H
Graph
A
B
C
D
E
F
G
H
15
15
15
2
0
0
2
0
4
4
8
13
15
15
15
15
10
15
15
4
15
8
15
8
15
8
15
8
Critical Act Noncritical Slack
2
0
0
0
3
12
2
0
0
0
4
4
4
0
0
0
3
6
5
0
0
2
0
0
9
8
7
6
5
4
3
2
1
15
15
13
13
Graph
H
G
F
E
D
C
B
A
15
15
13
13
15
15
15
15
13
8
4
4
0
2
0
0
Critical Acti
2
5
0
4
0
2
0
2
t try
ot
try to
to use
use
Gantt Chart
2
6
lack
4
8
Time
Noncritical Activity
10
12
Critical Activity
14
16
Noncritical Slack
0
0
3
0
4
0
3
0
0
0
6
0
4
0
12
0
Crashing
A
3
4
5
B
C
Project Management
8
E
F
G
H
I
J
K
L
M
Crashing
Enter
Enter the
the data
data in
in the
the shaded
shaded area.
area. Then
Then go
go to
to the
the DATA
DATATab
Tab on
on the
the ribbon,
ribbon, click
click on
on Solver
Solver in
in the
the Data
DataAnalysis
Analysis Group
Group and
and then
then click
click SOLVE.
SOLVE.
IfIf SOLVER
SOLVER isis not
not on
on the
the Data
DataTab
Tab then
then please
please see
see the
the Help
Help file
file (Solver)
(Solver) for
for instructions.
instructions.
6
7
D
Data
Project goal
12
Results
Normal time
Minimum time
15
7
Minimum crash cost to meet project goal $
Project time
5,000.00
12
9
Immediate Predecessors (1 per column)
10
11
12
13
14
15
16
17
18
19
Activity
A
B
C
D
E
F
G
H
Normal Normal
Time
Cost
2
###
3
###
2
###
4
###
4
###
3
###
5
###
2
###
Crash
Time
1
1
1
3
2
2
2
1
Crash
Cost
$23,000
$34,000
$27,000
$49,000
$58,000
$30,500
$86,000
$19,000
Pred 1 Pred 2
A
B
C
C
D
F
E
G
20
344787981.xls
Pred 3
Pred 4
Crash
days
0
0
0
0
1
0
2
0
0
Intermediate
Computations
Crash
cost/da
y
Crash limit
1000
1
2000
2
1000
1
1000
1
1000
2
500
1
2000
3
3000
1
0
0
Crashing
N
3
4
5
6
7
8
9
Computations
10
11
12
13
14
15
16
17
18
19
20
344787981.xls
Crashing General Foundry Problem
Values
Minimize cost
A crash max.
B crash max.
C crash max.
D crash max.
E crash max.
F crash max.
G crash max.
H crash max.
Due date
Start
A constraint
B constraint
C constraint
D constraint
E constraint
F constraint
G constraint 1
G constraint 2
H constraint 1
H constraint 2
Finish constraint
YA YB YC YD YE YF YG YH XST XA XB XC XD XE XF XG
0
0
1
0
0
0
2
0
0
2
3
3
7
7
6 10
1000 2000 1000 1000 1000 500 2000 3000
1
1
1
1
1
1
1
1
1
-1
-1
1
1
1
1
1
-1
1
1
-1
1
1
-1
-1
1
1
1
1
1
-1
1
1
-1
1
1
-1
-1
XH
12
XFIN
12
1
1
1
-1
1
Totals
5000
0
0
1
0
0
0
2
0
12
0
2
3
2
4
4
3
5
5
6
2
0
<
<
<
<
<
<
<
<
<
=
>
>
>
>
>
>
>
>
>
>
>
1
2
1
1
2
1
3
1
12
0
2
3
2
4
4
3
5
5
2
2
0
Arnold's Muffler Shop
Waiting Lines
M/M/1 (Single Server Model)
The
RATE
and
service
RATE
both
rates
and
use
same
Given
aa time
The
arrival
RATE
and
service
RATE
both
must
rates
and
use
the
same
time
unit.
The arrival
arrival
RATE
and
service
RATE
both must
must
be
ratesbe
and
use the
the
same
time
unit.
Given
time
The
arrival
RATE
and
service
RATE
bothbe
must
be
rates
and
usetime
theunit.
same
time
unit. Given
Given aa
such
10
convert
to
66 per
hour.
such as
as
10 minutes,
minutes,
convert ititconvert
to aa rate
rate such
such
as
persuch
hour.as
time
such
as
it
a
time
such
as 10
10 minutes,
minutes,
convert
it to
toas
a rate
rate
such
as 66 per
per hour.
hour.
Data
Results
Arrival rate ()
Average server utilization()
2
0.66667
Average
number
of
customers
in
the
queue(L
Service rate ()
3
1.33333
Average number of customers in the system(L
2
Average waiting time in the queue(Wq 0.66667
Average time in the system(Ws)
1
Probability (% of time) system is empty
(P
0.33333
Probabilities
Number
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Probabi
lity
###
###
###
###
###
###
###
###
###
###
###
###
###
###
###
###
###
###
###
###
###
e
Probabilit
y
0.333333
0.555556
0.703704
0.802469
0.868313
0.912209
0.941472
0.960982
0.973988
0.982658
0.988439
0.992293
0.994862
0.996575
0.997716
0.998478
0.998985
0.999323
0.999549
0.999699
0.999800
unit.
unit. Given
Given aa
Arnold's Muffler Shop
Waiting Lines
M/M/s
The
The arrival
arrival RATE
RATE and
and service
service RATE
RATE both
both must
must be
be rates
rates and
and use
use the
the same
same time
time unit.
unit. Given
Given
aa time
such
as
10
minutes,
convert
it
to
a
rate
such
as
6
per
hour.
time such as 10 minutes, convert it to a rate such as 6 per hour.
Data
Results
Arrival rate ()
Average server utilization()
2
0.33333
Average number of customers in the queue(L q) 0.08333
Service rate ()
3
Number of servers(s)
Probabilities
Number
2
Average number of customers in the system(L)
0.75
Average waiting time in the queue(W q)
0.04167
Average time in the system(W)
0.375
Probability (% of time) system is empty (P 0)
0.5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Probability
0.500000
0.333333
0.111111
0.037037
0.012346
0.004115
0.001372
0.000457
0.000152
0.000051
0.000017
0.000006
0.000002
0.000001
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
(lam/mu)^nCumsum(n-term2
1
0.666667
1
0.222222 1.666667
0.049383 1.888889
0.00823 1.938272
0.001097 1.946502
0.000122 1.947599
1.2E-005 1.947721
9.7E-007 1.947733
7.2E-008 1.947734
4.8E-009 1.947734
2.9E-010 1.947734
1.6E-011 1.947734
8.3E-013 1.947734
3.9E-014 1.947734
Computations
n or s
Cumulative Probability
0.500000
0.833333
0.944444
0.981481
0.993827
0.997942
0.999314
0.999771
0.999924
0.999975
0.999992
0.999997
0.999999
1.000000
1.000000
1.000000
1.000000
1.000000
1.000000
1.000000
1.000000
P0(s)
2
0.3333333333
0.0634920635
0.0098765432
0.0012662235
0.0001371742
0.000012835
1.05569378546059E-006
7.74175442671098E-008
5.12020795417393E-009
3.08313597240581E-010
1.70369367459144E-011
8.69753527569206E-013
4.12575391282828E-014
0.33333
0.5
0.5122
0.51331
0.51341
0.51342
0.51342
0.51342
0.51342
0.51342
0.51342
0.51342
0.51342
0.51342
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
1.7E-015
7.3E-017
2.9E-018
1.1E-019
3.7E-021
1.2E-022
3.9E-024
1.2E-025
1.947734
1.947734
1.947734
1.947734
1.947734
1.947734
1.947734
1.947734
1.82757648408783E-015
7.59282983727312E-017
2.96998446015785E-018
1.09750556974159E-019
3.84311714656988E-021
1.27871411410371E-022
4.05275511573853E-024
1.22628006974231E-025
0.51342
0.51342
0.51342
0.51342
0.51342
0.51342
0.51342
0.51342
Rho(s)
0.666667
0.333333
0.222222
0.166667
0.133333
0.111111
0.095238
0.083333
0.074074
0.066667
0.060606
0.055556
0.051282
0.047619
Lq(s)
1.333333
0.083333
0.009292
0.001014
0.0001
8.8E-006
6.9E-007
4.9E-008
3.2E-009
1.9E-010
1.0E-011
5.1E-013
2.4E-014
1.1E-015
L(s)
2
0.75
0.675958
0.667681
0.666767
0.666675
0.666667
0.666667
0.666667
0.666667
0.666667
0.666667
0.666667
0.666667
Wq(s)
0.666667
0.041667
0.004646
0.000507
5.0E-005
4.4E-006
3.5E-007
2.5E-008
1.6E-009
9.4E-011
5.1E-012
2.6E-013
1.2E-014
5.3E-016
W(S)
1
0.375
0.337979
0.33384
0.333383
0.333338
0.333334
0.333333
0.333333
0.333333
0.333333
0.333333
0.333333
0.333333
0.044444
0.041667
0.039216
0.037037
0.035088
0.033333
0.031746
0.030303
4.4E-017
1.7E-018
6.2E-020
2.2E-021
7.2E-023
2.3E-024
6.8E-026
2.0E-027
0.666667
0.666667
0.666667
0.666667
0.666667
0.666667
0.666667
0.666667
2.2E-017
8.5E-019
3.1E-020
1.1E-021
3.6E-023
1.1E-024
3.4E-026
9.8E-028
0.333333
0.333333
0.333333
0.333333
0.333333
0.333333
0.333333
0.333333
Garcia-Golding Recycling
Waiting Lines
M/D/1 (Constant Service Times)
The
RATE
and
service
RATE
both
rates
and
use
same
Given
aa time
The
arrival
RATE
and
service
RATE
both
must
rates
and
use
the
same
time
unit.
The
arrival
RATE
and
service
RATE
bothbe
must
be
rates
and
usetime
theunit.
same
time
unit. Given
Given
The arrival
arrival
RATE
and
service
RATE
both must
must
be
ratesbe
and
use the
the
same
time
unit.
Given
time
such
as
10
itit to
aa rate
as
per
a
time
as 10convert
minutes,
it to
such as 6 per hour.
assuch
10 minutes,
minutes,
convert
toconvert
rate such
such
asa66rate
per hour.
hour.
asuch
Data
Arrival rate ()
8
Service rate ()
12
Results
Average server utilization()
0.667
Average number of customers in the
queue(L
0.667
Average number of customers in the
system(L
1.333
Average waiting time in the queue(W
0.083
Average time in the system(Ws)
0.167
Probability (% of time) system is empty
0.333(P
Department of Commerce
Waiting Lines
M/M/s with a finite population
The
The
arrival
rate
is
for
each
member
of
the
population.
they
go
for
service
every
20
minutes
then enter
enter 33 (per
(per
The arrival
arrival rate
rate is
is for
for each
each member
member of
of the
the population.
population. IfIfIf they
they go
go for
for service
service every
every 20
20 minutes
minutes then
then
hour).
hour).
then enter
enter 33 (per
(per hour).
hour).
Data
Results
Arrival rate () per
customer
Service rate ()
0.05
0.5
Number of servers
1
Population size (N)
5
Average server utilization()
0.436
Average number of customers in the
queue(L
0.2035
Average number of customers in the
system(L
0.6395
Average waiting time in the queue(W
0.9333
Average time in the system(Ws) 2.9333
Probability (% of time) system is empty
0.564(P
Effective arrival rate
0.218
Probabilities
Number, n
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Probability,
P(n)
0.5639522
0.2819761
0.1127904
0.0338371
0.0067674
0.0006767
Cumulative
Probability Number waiting
0.56395218
0.84592827
0.9587187
0.99255583
0.99932326
1
0
0
1
2
3
4
Arrival
rate(n)
0.25
0.2
0.15
0.1
0.05
0
31
Term 1
Sum term
1
Term 2
1
1
1
0.5
1.5
0.5
0.2
0.06
0.012
0.0012
1.7732
Sum term Decum
2
term 2
P0(s)
1
0.7732
1.5
0.2732 0.563952
1.7
0.0732
1.76
0.0132
1.772
0.0012
1.7732
0
Harry's Tire Shop
Probability
0.05
0.1
0.2
0.3
0.2
0.15
NOTE: The random numbers appearing here may not be the same as the ones in th
Probability
Range
(Lower)
0
0.05
0.15
0.35
0.65
0.85
Cumulative Tires
Probability Demand
0.05
0
0.15
1
0.35
2
0.65
3
0.85
4
1
5
Results (Frequency table)
Tires
Demanded Frequency Percentage Cum %
0
0
0%
0%
1
2
20%
20%
2
1
10%
30%
3
2
20%
50%
4
3
30%
80%
5
2
20%
100%
10
Day
1
2
3
4
5
6
7
8
9
10
Random Simulated
Number
Demand
0.449176
3
0.572293
3
0.338668
2
0.881313
5
0.787202
4
0.077921
1
0.700836
4
0.081046
1
0.923639
5
0.783819
4
Average
3.2
not be the same as the ones in the book, but the formulas are the same.
Generating Normal Random Numbers
Random number
35.66217706
43.4541210475
30.9997808372
39.9841791973
33.9599191774
38.0507262478
39.4126226815
41.6584858903
35.3366608808
38.3847299047
45.7094588485
43.0334214104
43.4415082129
39.2490803259
43.1336798745
38.3049433749
42.5800331792
41.7288995074
40.6773544585
41.8763848974
40.8345128271
45.1887589042
43.6570248457
44.2625120011
42.9724933155
36.5383682642
26.2505138431
31.2225714125
38.1135966805
37.9581972212
39.8997401042
36.4921817379
38.7180210312
38.3623987397
34.8027000158
46.6073142417
41.6343524839
54.1012330859
39.1086150687
42.5744691587
39.2129381568
43.2118977598
42.353608553
46.2890184771
43.0296486927
42.4460874494
52.3155323844
NOTE: The random numbers appearing here may not be the same as the
Value
26
28
30
32
34
36
38
40
42
44
46
48
50
52
54
56
Frenquency Percentage
0
0.0%
2
1.0%
3
1.5%
9
4.5%
9
4.5%
12
6.0%
24
12.0%
31
15.5%
36
18.0%
29
14.5%
19
9.5%
11
5.5%
8
4.0%
2
1.0%
2
1.0%
3
1.5%
200
35.5923846141
34.9932454573
37.1689602802
29.6145236177
41.1177530643
36.3092534493
40.5170367891
39.1796352761
33.9545351361
30.8584053987
38.415004549
32.7954472803
37.1403855814
46.3594106276
49.2193389159
41.2899619769
38.0816743249
54.8581024177
50.0418283515
36.8188921655
30.8735303765
35.7582161763
36.6767120171
38.0121050781
34.3666147531
29.5810750591
40.4374777304
48.3660368738
45.6292837245
35.8088828152
39.2633515927
39.7306688246
39.2341007536
31.5738994359
42.3997806629
45.2499887843
41.5171822923
33.2874514651
39.0765634783
30.094892767
36.8958895142
40.9014310506
45.6729809924
42.1224653374
37.4920543039
31.4109352909
41.285195843
42.602684259
43.4748279927
32.4683215
40.5806186595
42.4786300634
39.0472866491
45.651830371
48.7841820432
42.4312503067
40.1865630393
41.9683261549
43.8482496906
47.0771658999
38.6028206609
41.8630447419
37.6025940189
41.6283737496
45.5281081134
40.9280745546
40.7726313266
39.8234645921
45.1943822201
49.2426216956
35.3124112917
33.9936590816
41.1265867744
49.1292858781
45.0868178565
39.738677419
38.5557929013
46.3600971566
46.4383018845
40.2577030067
38.3859498488
43.9387537922
36.2960875488
33.8285064034
31.6075871977
27.3843298459
46.7638188995
39.4173314397
44.8242463459
28.1929171102
48.1738825527
31.0741621374
45.8710376998
40.1986664824
45.559721804
42.343034699
47.8401692327
46.7182708109
37.2917470546
36.1064605769
42.7435790251
41.8541329641
37.554476295
44.3046112576
42.3946592738
36.6802059419
40.2710462285
41.3794589387
51.1166284813
32.0686330505
41.7848287758
36.3232268837
35.7626995839
40.0657947913
42.2607490588
34.8478840083
44.0981643574
42.5652300974
36.1927075118
44.3196810757
41.0868619387
46.3011533903
47.2267852579
36.7188017193
38.8519132653
36.1934612567
49.6029103598
41.334447226
40.6266067372
49.4014768024
44.2172741182
38.9060442782
42.751476354
40.6263771405
53.9016501819
42.8697492759
36.6298976656
44.9862230482
42.5213835647
34.0155427788
37.6638640275
43.7070881191
37.1967743087
37.8872884314
40.2536279818
39.3881045531
41.2544234875
40.736369335
54.239675664
44.5716652578
40.6530315606
39.3338354007
33.0779366473
ay not be the same as the ones in the book, but the formulas are the same.
Harry's Auto Tire
Enter
you
Enter the
the values
values and
and the
the requencies
requencies in
in the
the top
top table.
table. Press
Press F9
F9 to
to run
run another
another simulation.
simulation. IfIf you
you like,
like, you
may
enter
the
random
numbers
in
the
column
labeled
"Random
number".
you
may
enter
the
random
numbers
in
the
column
labeled
"Random
number".
may
enter
the
random
numbers
in
the
column
labeled
"Random
number".
you may enter the random numbers in the column labeled "Random number".
Simulation
Data
Random Number
Sorter
Category name
0 Category 1
5 Category 2
15 Category 3
35 Category 4
65 Category 5
Expected Value
Value
85 Category 6
Total
Simulation trials
Trial
Random Number Value
1 22.8900237009
2 70.3702027211
3 71.4120813878
4
90.894848574
5
56.255218084
6 14.3627001438
7 49.3072967511
8 40.8398482716
9 86.3991524791
10
6.0743131209
11 80.7928047841
12
44.799211924
13 93.8955886755
14 18.9728558296
15 97.3265731707
16 18.8319931272
17 72.5881911581
18
23.485507234
19 88.9919940149
20 17.0039511984
21 91.8881825637
22
74.69147956
23 99.4226894109
24 73.5060438048
25 19.0859120572
26 77.1607221104
27 58.6619689828
28 78.8606178248
0
1
2
3
4
5
2
4
4
5
3
1
3
3
5
1
4
3
5
2
5
2
4
2
5
2
5
4
5
4
2
4
3
4
Frequency
10
20
40
60
40
30
200
Cumulative Value *
Probability Probability Frequency
0.05
0.05
0
0.1
0.15
20
0.2
0.35
80
0.3
0.65
180
0.2
0.85
160
0.15
1
Expected
150
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
68.5886266408
17.9254049901
18.8293419313
38.1274621701
22.8036499582
15.7862418797
61.2161038909
15.201445506
13.7213571463
3.0067386106
86.8577451911
33.4866090911
19.7712074034
25.6976653123
95.5655977828
74.9597870279
1.2430545408
52.9916756554
55.4621624062
73.0321761221
48.59406834
88.2621139754
54.0364086162
67.1644056216
26.2794302776
95.1684745261
29.157937807
65.1450897101
37.4737669248
8.8827905478
2.8544727713
84.9805137375
99.5820469456
81.1015354702
99.182711821
32.3291743174
34.8162844079
86.8591265054
57.7946602833
73.5104673542
87.2502506012
39.9015814066
65.2849586448
89.7253899369
80.1764891483
19.1533505684
4
2
2
3
2
2
3
2
1
0
5
2
2
2
5
4
0
3
3
4
3
5
3
4
2
5
2
4
3
1
0
4
5
4
5
2
2
5
3
4
5
3
4
5
4
2
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
52.2505224217
44.1956240917
45.5989846028
93.2668151567
46.8185584294
23.8823801512
98.3112802263
64.2099103425
32.2139839409
20.4450122546
34.5314383507
74.3251680396
0.0500658061
95.2479100088
31.2648780411
8.964074566
10.7813088223
64.4238760928
0.3198517254
22.6206715684
32.5894006295
7.6591262361
65.2365585091
95.4842021922
93.5619320953
72.5847069873
54.0295996936
83.7285606889
11.0218179412
52.2487533046
43.5149635887
95.5267214682
76.4233416179
92.0931770001
87.9557676846
20.0083405711
0.5574464565
75.9208671981
50.528338179
78.1940029236
35.7695176499
1.2391780969
64.0809280099
72.4709199509
74.2071215529
87.4271171167
3
3
3
5
3
2
5
3
2
2
2
4
0
5
2
1
1
3
0
2
2
1
4
5
5
4
3
4
1
3
3
5
4
5
5
2
0
4
3
4
3
0
3
4
4
5
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
20.8654625108
42.2588814981
90.4488344444
17.6485036965
52.4875628529
39.9065654725
24.1868208628
55.2028777543
46.4802255621
40.8364770701
57.3154730257
10.7205542503
38.6630218709
22.76611696
60.5356013402
69.6791257244
66.9041987276
97.4071971374
35.7183869695
57.4116867268
72.1197341802
65.8680128632
99.0398705238
85.2428071899
95.7474360941
38.2660532836
33.7398207048
72.6344193798
70.3811890678
75.4429384368
33.2980142441
61.2077435711
86.4855042426
46.6657841345
19.2036100896
50.6395783741
20.0543286512
56.6374006914
84.4483341323
48.938318342
91.15736268
7.9124493757
45.0878832024
98.9690010669
15.5556295533
87.5270802993
2
3
5
2
3
3
2
3
3
3
3
1
3
2
3
4
4
5
3
3
4
4
5
5
5
3
2
4
4
4
2
3
5
3
2
3
2
3
4
3
5
1
3
5
2
5
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
24.4515901199
17.4784969771
29.7331007896
9.1989770066
30.9250849765
53.784429864
15.9133591224
4.3543504085
2.7481737547
39.6302024135
27.888119407
67.983404221
98.6363616539
32.6203250326
44.498590799
20.231256634
84.8455259111
76.5323361149
88.2226668298
50.4917829297
39.0589143848
73.4208649723
52.2085150238
60.2563095512
65.4621685157
17.909296602
52.6507224888
42.3929086421
18.2651501615
60.7217872282
38.268987136
11.1037781695
95.6373346271
2
2
2
1
2
3
2
0
0
3
2
4
5
2
3
2
4
4
5
3
3
4
3
3
4
2
3
3
2
3
3
1
5
200
97.6083526621
5
other
you
other simulation.
simulation. IfIf you
you like,
like, you
".
mber".
".
mber".
Simulation results
Simulation
Occurrences
Value
Totals
0
1
2
3
4
9
12
46
55
40
5
38
200
Occurences *
Percentage Value
0.045
0
0.06
12
0.23
92
0.275
165
0.2
160
0.19
1
Average
190
619
3.095
Port of New Orleans Barge Unloadings
Day
1
2
3
4
5
6
7
8
9
10
Previously
delayed
0
0
0
0
0
0
1
1
0
0
Total to
Random
be
number
Arrivals
unoaded
0.40506
2
2
0.012574
0
0
0.310235
2
2
0.06141
0
0
0.398153
2
2
0.762375
4
4
0.732746
4
5
0.3762
2
3
0.708391
4
4
0.692791
3
3
Barge Arrivals
Demand Probability Lower
CumulativeDemand
0
0.13
0
0.13
0
1
0.17
0.13
0.3
1
2
0.15
0.3
0.45
2
3
0.25
0.45
0.7
3
4
0.2
0.7
0.9
4
5
0.1
0.9
1
5
NOTE: The random numbers appearing here may not
Random Possibly
Number unloaded Unloaded
0.772695
4
2
0.314004
3
0
0.100185
2
2
0.942721
5
0
0.440008
3
2
0.272945
3
3
0.895601
4
4
0.933073
5
3
0.813173
4
4
0.935232
5
3
Unloading rates
Number Probability Lower
1
0.05
0
2
0.15
0.05
3
0.5
0.2
4
0.2
0.7
5
0.1
0.9
numbers appearing here may not be the same as the ones in the book, but the formulas are the same.
CumulativeUnloading
0.05
1
0.2
2
0.7
3
0.9
4
1
5
Three Hills Power Company
Breakdow
n number
1
2
3
4
5
6
7
8
9
10
Random
number
0.1752
0.4306
0.0822
0.5608
0.5267
0.3154
0.4012
0.8527
0.8936
0.3312
Demand
Time Table
between
breakdow
ns
Probability
0.5
0.05
1.0
0.06
1.5
0.16
2.0
0.33
2.5
0.21
3.0
0.19
Time
Time of
Time
between
breakdown repairperson is
breakdowns
s
free
1.5
1.5
1.5
2
3.5
4.5
1
4.5
5.5
2
6.5
6.5
2
8.5
8.5
2
10.5
11.5
2
12.5
13.5
3
15.5
15.5
3
18.5
18.5
2
20.5
20.5
Random
Number
0.9045
0.2455
0.1960
0.0326
0.9869
0.7180
0.1775
0.9581
0.4937
0.1613
Repair
time
3
1
1
1
3
2
1
3
2
1
Repair times
Lower
0
0.05
0.11
0.27
0.6
0.81
Cumulative
0.05
0.11
0.27
0.6
0.81
1
Demand
0.5
1
1.5
2
2.5
3
Time
1
2
3
NOTE: The random numbers appearing here may not be the same as the ones in the book, but the formulas
Repair
ends
4.5
5.5
6.5
7.5
11.5
13.5
14.5
18.5
20.5
21.5
Repair times
Probability Lower CumulativeLead time
0.28
0.00
0.28
1
0.52
0.28
0.80
2
0.20
0.80
1.00
3
in the book, but the formulas are the same.
Three Grocery Example
Time
0
1
2
3
4
5
6
State Probabilities
American Food S Food Mart
Atlas Foods
#1
#2
#3
Matrix of Transition Probabilities
0.4
0.3
0.3
0.8
0.1
0.1
0.41
0.31
0.28
0.1
0.7
0.2
0.415
0.314
0.271
0.2
0.2
0.6
0.4176
0.3155
0.2669
0.41901
0.31599
0.265
0.419807
0.316094
0.264099
0.4202748
0.3160663
0.2636589
Accounts Receivable Example
P=
I:0
A:B
=
I-B=
1
0
0.6
0.4
0
1
0
0.1
0.8
-0.3
-0.2
0.8
F = (I - B) inverse
1.37931 0.344828
0.517241 1.37931
FA =
0.965517 0.034483
0.862069 0.137931
0
0
0.2
0.3
0
0
0.2
0.2
Box Filling Example
Quality Controlx bar chart
Enter
Enter the
the population
population standard
standard deviation
deviation
then
then enter
enter the
the data
data from
from each
each sample.
sample.
Finally,you
you may
may change
change the
the number
number of
of
1 Finally,
standard
deviations.
standard
deviations.
36
Number of
Sample siz
Populatio
n
standard
deviation
2
Data
Results
Mean
Sample 1
16
Average
16
x-bar va
16
z value
3
Sigma x 0.3333
Upper c
Center
Lower c
17
16
15
Super Cola Example
Quality Controlx bar chart
Number of
Sample si
1
5
Enter
Enter the
the mean
mean and
and range
range from
from
each
each sample.
sample.
Data
Results
Mean
Range
Sample 1
16.01
0.25
Average
16.01
0.25
Xbar
Range
x-bar valu
16.01
R bar
0.25
Upper con
16.1543 0.52875
Center li
16.01
0.25
Lower con
15.8658
0
Table
Sample
size, n
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Upper
Lower
Mean
Range,
Range,
Factor, A2 D4
D3
1.88
3.268
0
1.023
2.574
0
0.729
2.282
0
0.577
2.115
0
0.483
2.004
0
0.419
1.924
0.076
0.373
1.864
0.136
0.337
1.816
0.184
0.308
1.777
0.223
0.285
1.744
0.256
0.266
1.716
0.284
0.249
1.692
0.308
0.235
1.671
0.329
0.223
1.652
0.348
0.212
1.636
0.364
0.203
1.621
0.379
0.194
1.608
0.392
0.187
1.596
0.404
0.18
1.586
0.414
0.173
1.575
0.425
0.167
1.566
0.434
0.162
1.557
0.443
0.157
1.548
0.452
0.153
1.541
0.459
ARCO
Quality Control p chart
Number o
Sample s
20
100
Enter
Enter the
the sample
sample size
size then
then enter
enter the
the number
number of
of defects
defects in
in each
each sample.
sample.
Data
# Defects
1
6
2
5
3
0
4
1
5
4
6
2
7
5
8
3
9
3
1
2
1
6
1
1
1
8
1
7
1
5
1
4
1
11
1
3
1
0
2
4
Graph information
Sample 1
0.06
Sample 2
0.05
Sample 3
0
Sample 4
0.01
Sample 5
0.04
Sample 6
0.02
Sample 7
0.05
Sample 8
0.03
Sample 9
0.03
Sample 1
0.02
Sample 1
0.06
Sample 1
0.01
Sample 1
0.08
Sample 1
0.07
% Defects
0.06
0.05
0
0.01
0.04
0.02
Upper Co
0.05
Center L
0.03
Lower Co
0.03
0.02
0.06
0.01
0.08
0.07
0.05
0.04
0.11 Above UCL
0.03
0
0.04
Mean
Sample
Sample
Sample
Sample
Sample
Sample
Sample
Sample
Sample
Sample
Sample
Sample
Sample
Sample
Sample
Sample
Sample
Sample
Sample
Sample
Results
Total Sam
Total Def
Percenta
Std dev o
z value
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.09879
0.09879
0.09879
0.09879
0.09879
0.09879
0.09879
0.09879
0.09879
0.09879
0.09879
0.09879
0.09879
0.09879
2000
80
0.04
###
3
###
0.04
0
p-chart
0.12
0.1
0.08
0.06
0.04
0.02
0
Sample
Sample
Sample
Sample
Sample
Sample
Sample
1
1
1
1
1
2
0.05
0.04
0.11
0.03
0
0.04
0
0
0
0
0
0
0.04
0.04
0.04
0.04
0.04
0.04
0.09879
0.09879
0.09879
0.09879
0.09879
0.09879
chart
Sample
Quality Controlc chart
Number of
9
Enter
Enter the
the number
number of
of defects
defects for
for each
each of
of the
the
samples/items.
samples/items.
Data
Results
Total un
9
Total De
54
Defect rate, 6
Standard2.4495
z value
3
# Defects
Sample 1
3
Sample 2
0
Sample 3
8
Sample 4
9
Sample 5
6
Sample 6
7
Sample 7
4
Sample 8
9
Sample 9
8
Graph information
Sample 1
Sample 2
Sample 3
Sample 4
Sample 5
Sample 6
Sample 7
Sample 8
Sample 9
3
0
8
9
6
7
4
9
8
Upper C 13.35
Center
6
Lower C
0
0
0
0
0
0
0
0
0
0
6
6
6
6
6
6
6
6
6
13.34847
13.34847
13.34847
13.34847
13.34847
13.34847
13.34847
13.34847
13.34847
Mean
Red Top Cab Company
c-chart
15
10
5
0
1
2
3
4
5
Sam
c-chart
5
0
5
0
1
2
3
4
5
6
Sample
7
8
9
AHP
n=
3
Sys.1
Sys.2
Sys.3
Sys.1
Sys.2
Sys.3
Priority
Sys.1
1
3
9
Sys.1
0.6923
0.7200
0.5625
0.6583
2.0423
3.1025
Sys.2
0.3333
1
6
Sys.2
0.2308
0.2400
0.3750
0.2819
0.8602
3.0512
Sys.3
0.1111
0.1667
1
Sys.3
0.0769
0.0400
0.0625
0.0598
0.1799
3.0086
Column Total 1.4444 4.1667
16
Hardware
Software
Wt. sum vector Consistency vector
Sys.1
Sys.2
Sys.3
Sys.1
Sys.2
Sys.3
Priority
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
Wt. sum vector
Sys.1
Sys.2
Sys.3
Sys.1
Sys.2
Sys.3
Priority
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
0.1667 0.3333
1
Sys.3
0.0769
0.1429
0.1000
0.1066
0.3216
3.0172
Column Total 2.1667 2.3333
10
Sys.3
Factor
Wt. sum vector
Hard.
Soft.
Vendor
Hardware
Software
Vendor
Priority
Hardware
1
0.125
0.3333
Hardware
0.0833
0.0857
0.0769
0.0820
Wt. sum vector
0.2460
3.0004
Software
8
1
3
Software
0.6667
0.6857
0.6923
0.6816
2.0468
3.0031
Vendor
3
0.3333
1
Vendor
0.2500
0.2286
0.2308
0.2364
0.7096
3.0011
Column Total
12
1.4583 4.3333
n
RI
Hardware
Software
Vendor
Priority
2
0.00
Sys.1
0.658
0.087
0.497
0.231
3
0.58
Sys.2
0.282
0.162
0.397
0.227
4
0.90
Sys.3
0.060
0.750
0.107
0.542
5
1.12
6
1.24
7
1.32
8
1.41
Consistency vector
Lambd
3.0541
CI
0.0270
CR
0.0466
Lambd
3.005543075
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
1
2
2
3
0
B=
AxB =
2
1
3
1
1
2
13
4
9
3
-0.5
1
Matrix Inverse
A=
2
4
1
3
A-inverse=
1.5
-2
4
2
det(A)=
-10
Matrix Determinant
A=
3
4