project for management science

PROJECT SCHEDULING WITH PERT/CPM

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*** PROJECT ACTIVITY LIST ***

IMMEDIATE OPTIMISTIC MOST PROBABLE PESSIMISTIC

ACTIVITY PREDECESSORS TIME TIME TIME

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A - 1.0 5.0 12.0

B - 1.0 1.5 5.0

C A 2.0 3.0 4.0

D A 3.0 4.0 11.0

E A 2.0 3.0 4.0

F C 1.5 2.0 2.5

G D 1.5 3.0 4.5

H B,E 2.5 3.5 7.5

I H 1.5 2.0 2.5

J F,G,I 1.0 2.0 3.0

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EXPECTED TIMES AND VARIANCES FOR ACTIVITIES

ACTIVITY EXPECTED TIME VARIANCE

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A 5.5 3.36

B 2.0 0.44

C 3.0 0.11

D 5.0 1.78

E 3.0 0.11

F 2.0 0.03

G 3.0 0.25

H 4.0 0.69

I 2.0 0.03

J 2.0 0.11

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*** ACTIVITY SCHEDULE ***

EARLIEST LATEST EARLIEST LATEST CRITICAL

ACTIVITY START START FINISH FINISH SLACK ACTIVITY

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A 0.0 0.0 5.5 5.5 0.0 YES

B 0.0 6.5 2.0 8.5 6.5

C 5.5 9.5 8.5 12.5 4.0

D 5.5 6.5 10.5 11.5 1.0

E 5.5 5.5 8.5 8.5 0.0 YES

F 8.5 12.5 10.5 14.5 4.0

G 10.5 11.5 13.5 14.5 1.0

H 8.5 8.5 12.5 12.5 0.0 YES

I 12.5 12.5 14.5 14.5 0.0 YES

J 14.5 14.5 16.5 16.5 0.0 YES

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CRITICAL PATH: A-E-H-I-J

EXPECTED PROJECT COMPLETION TIME = 16.5

VARIANCE OF PROJECT COMPLETION TIME = 4.31

A Project Map is NOT required

LINEAR PROGRAMMING PROBLEM

MAX 65X1+90X2+40X3+60X4+20X5

S.T.

1) 1X1<15

2) 1X2<10

3) 1X3<25

4) 1X4<4

5) 1X5<30

6) 1500X1+3000X2+400X3+1000X4+100X5<30000

7) 1X1+1X2>10

8) 1500X1+3000X2<18000

9) 1000X1+2000X2+1500X3+2500X4+3000X5>50000

OPTIMAL SOLUTION

Objective Function Value = 2370.000

Variable Value Reduced Costs

-------------- --------------- ------------------

X1 10.000 0.000

X2 0.000 65.000

X3 25.000 0.000

X4 2.000 0.000

X5 30.000 0.000

Constraint Slack/Surplus Dual Prices

-------------- --------------- ------------------

1 5.000 0.000

2 10.000 0.000

3 0.000 16.000

4 2.000 0.000

5 0.000 14.000

6 0.000 0.060

7 0.000 -25.000

8 3000.000 0.000

9 92500.000 0.000

OBJECTIVE COEFFICIENT RANGES

Variable Lower Limit Current Value Upper Limit

------------ --------------- --------------- ---------------

X1 0.000 65.000 90.000

X2 No Lower Limit 90.000 155.000

X3 24.000 40.000 No Upper Limit

X4 43.333 60.000 100.000

X5 6.000 20.000 No Upper Limit

RIGHT HAND SIDE RANGES

Constraint Lower Limit Current Value Upper Limit

------------ --------------- --------------- ---------------

1 10.000 15.000 No Upper Limit

2 0.000 10.000 No Upper Limit

3 20.000 25.000 30.000

4 2.000 4.000 No Upper Limit

5 10.000 30.000 50.000

6 28000.000 30000.000 32000.000

7 8.667 10.000 11.333

8 15000.000 18000.000 No Upper Limit

9 No Lower Limit 50000.000 142500.000

FORECASTING WITH MOVING AVERAGE

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TIME PERIOD TIME SERIES VALUE FORECAST FORECAST ERROR

=========== ================= ======== ==============

1 17

2 21 17.00 4.00

3 19 21.00 2.00

4 23 19.00 4.00

5 18 23.00 -5.00

6 16 18.00 -2.00

7 20 16.00 4.00

8 18 20.00 -3.00

9 22 18.00 4.00

10 20 22.00 -2.00

11 15 20.00 -5.00

12 22 15.00 7.00

THE MEAN SQUARE ERROR 16.73

THE FORECAST FOR PERIOD 13 22.00

FORECASTING WITH LINEAR TREND

*****************************

THE LINEAR TREND EQUATION:

T = 20.4 + 1.1 t

where T = trend value of the time series in period t

TIME PERIOD TIME SERIES VALUE FORECAST FORECAST ERROR

=========== ================= ======== ==============

1 21.6 21.50 0.10

2 22.9 22.60 0.30

3 25.5 23.70 1.80

4 21.9 24.80 -2.90

5 23.9 25.90 -2.00

6 27.5 27.00 0.50

7 31.5 28.10 3.40

8 29.7 29.20 0.50

9 28.6 30.30 -1.70

10 31.4 31.40 0.00

THE MEAN SQUARE ERROR 3.07

THE FORECAST FOR PERIOD 11 32.50

Regression

Store # Population

x

Sales

y Forecast Error Error

2

1 2 58 70 -12 144

2 6 105 90 15 225

3 8 88 100 -12 144

4 8 118 100 18 324

5 12 117 120 -3 9

6 16 137 140 -3 9

7 20 157 160 -3 9

8 20 169 160 9 81

9 22 149 170 -21 441

10 26 202 190 12 144

Slope 5

MSE 153

y-int 60

r 0.950123

Trend Line 60 + 5x Forecast 16

140(,000)

OR

Store # Population

(1,000s) x

Sales y

1 2 58

2 6 105

3 8 88

4 8 118

5 12 117

6 16 137

7 20 157

8 20 169

9 22 149

10 26 202

b1 = 5

b0 = 60

16 140

SUMMARY OUTPUT

Regression Statistics Multiple R 0.950 R Square 0.903 Adjusted R Square 0.891 Standard Error 13.829 Observations 10

ANOVA df SS MS F Sig F

Regression 1 14200 14200 74.248 0.000 Residual 8 1530 191.25 MSE Approx imate

Total 9 15730

Coefficients Standard

Error t Stat P-

value Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept 60 9.226 6.503 0.000 38.725 81.275 38.725 81.275 Population (1,000s) 5 0.580 8.617 0.000 3.662 6.338 3.662 6.338

Population

(1,000s) Sales

Population (1,000s) 1

Sales 0.950 1