project for management science

PROJECT SCHEDULING WITH PERT/CPM ******************************** *** PROJECT ACTIVITY LIST *** IMMEDIATE OPTIMISTIC MOST PROBABLE PESSIMISTIC ACTIVITY PREDECESSORS TIME TIME TIME ----------------------------------------- ------------------------------- 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 ----------------------------------------- ------------------------------- EXPECTED TIMES AND VARIANCES FOR ACTIVITIES ACTIVITY EXPECTED TIME VARIANCE ------------------------------------------- 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 ------------------------------------------- *** ACTIVITY SCHEDULE *** EARLIEST LATEST EAR LIEST LATEST CRITICAL ACTIVITY START START FI NISH FINISH SLACK ACTIVITY ------------------------------------------------------------------------ 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 ----------------------- ------------------------------------------------- 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 OBJE CTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit ------------ --------------- --------------- --------------- X1 0.000 65.000 90.000 X2 No Lower Li mit 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 28 000.000 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 ************************************** 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 S QUARE ERROR 16 .73 THE FORE CAST 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