Chapter 3 Methodology
4.5 Sensitive analysis
4.5.1 Available budget ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 59
4.5 Sensitive analysis
This chapter constructs the sensitive analysis of this bi-level programming model.
And further defines the results of the sensitive analysis to do the strategy management.
To identify the effect of corresponding parameters to the optimal budget allocation plan, sensitivity analyses on some key parameters of the AG model are conducted.
4.5.1 Available budget
This section presents the optimal budget allocation plan under various amounts of available budget, as Table 4.6 and from Figure 4.2 to Figure 4.4 following below.
Figure 4.2 and Figure 4.3 reveal the truth about increasing budget will make ecological footprint decrease but quality of life increase. As this result, increasing the budget which doesn’t consider other elements any more, we could foresee that the percentage of the private car using will transfer to public transit mode.
500
Figure 4.2 footprint under various amounts of available budget.
60 Figure 4.3 QOL under various amounts of available budget.
0%
Figure 4.4 Optimal budget allocation plan under various amounts of available budget.
Figure 4.4 presents the optimal budget allocation plan under various amounts of available budget. Most of budget goes to the fare discount subsidy to attract more people use public transportation, which is also the reason why quality of life increases.
Table 4.6 presents the result of the sensitive analysis, set 100 million dollars as the bench mark, increase (and decrease) 10%, 20%, 30% and 40% to realize the influence among public transit subsidy, quality of life and ecological footprint under various amount of available budget.
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Table 4.6 The result of the sensitive analysis under various amounts of available budget.
Budget x
(NT dollars)
y (Frequency)
z (hectare)
Budget (NT dollars) Market Share Footprint (ha.) Price
discount
Deficit subsidy
Green
land Private Public Total
Utility Private Public Total 60 16 10 231 46% 28% 23% 51% 49% -6715 388.39 296.28 684.67
70 21 9 195 60% 21% 17% 43% 57% -5833 343.72 296.28 640.00
80 22 9 181 66% 18% 14% 37% 63% -5332 300.20 296.28 596.48
90 22 9 171 67% 17% 11% 33% 67% -5377 272.03 338.60 610.63
100 28 10 126 70% 18% 12% 28% 72% -2528 70.27 423.25 493.52 110 32 8 134 76% 13% 7% 25% 75% -3445 206.88 296.28 503.16 120 33 8 130 73% 12% 7% 24% 76% -3466 184.36 338.60 522.96 130 33 8 126 68% 11% 6% 24% 76% -3397 162.67 338.60 501.28 140 34 8 126 66% 11% 5% 22% 78% -3385 142.89 338.60 481.49
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4.5.2 Various values of α associated with in-vehicle travel time
This section presents the optimal budget allocation plan under various values of α associated with in-vehicle travel time. Figure reveals the truth about increasing α will make ecological footprint increase but quality of life decrease, as Table 4.7 and from Figure 4.5 to Figure 4.6 following below.. That is because if the value of α increase, it means the weight of the in-vehicle travel time increase. Therefore, some users will transfer from public transportation into private car using to decrease their time wasting.
However, in this situation, public transportation has to satisfy the needs of the users, frequency still not change any more. Therefore, ecological footprint will increase because of the private car using increasing.
520
0.03 0.04 0.05 0.11 0.22 0.43 0.86 1.30 1.73
Footprint (ha.)
Total Utility
α QOL Footprint
Figure 4.5 QOL and footprint under various values of α
63 0%
10%
20%
30%
40%
50%
60%
70%
80%
0.03 0.04 0.05 0.11 0.22 0.43 0.86 1.30 1.73
Budget allocation (%)
α
x y z
Figure 4.6 Optimal budget allocation plan under various values of α
Figure 4.6 presents the optimal budget allocation plan under various values of α.
Most of budget goes to the fare discount subsidy. We could find out the truth about the most amount of budget allocation into price discount, and the remained budget into deficit subsidy and green land acquired. And we also could figure out if the weight of in-vehicle travel time increases will make more people choice private car using. It results in quality of life and bus frequency decreases.
Table 4.7 presents the result of the sensitive analysis, set α = 0.216 as the bench mark, times (and divided by) 2, 4, 6 and 8 to realize the influence among public transit subsidy, quality of life and ecological footprint under various amount of available budget.
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Table 4.7 The results of the sensitive analysis under various amounts of α
α x
(NT dollars)
y (Frequency)
z (hectare)
Budget (NT dollars) Market Share Footprint (ha.) Price
discount
Deficit subsidy
Green
land Private Public Total
Utility Private Public Total 0.027 26 13 168 65% 25% 10% 29% 71% -1690 110.27 550.23 660.50 0.036 26 13 168 65% 25% 10% 29% 71% -1730 130.27 550.23 660.50 0.054 26 13 168 65% 25% 10% 29% 71% -1810 150.27 550.23 660.50 0.108 28 10 126 70% 18% 12% 28% 72% -2047 170.27 423.25 533.53 0.216 28 10 126 70% 18% 12% 28% 72% -2528 70.27 423.25 493.52 0.432 29 9 112 73% 16% 11% 28% 72% -3488 210.27 380.93 491.20 0.864 29 9 112 73% 16% 11% 28% 72% -5414 230.27 380.93 491.20 1.296 29 9 112 73% 16% 11% 28% 72% -7339 250.27 380.93 491.20 1.728 29 9 112 73% 16% 11% 28% 72% -9265 270.27 380.93 491.20
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4.5.3 Various values of β associated with out-of-vehicle travel time
This section presents the optimal budget allocation plan under various values of β associated with out-of-vehicle travel time. Figure reveals the truth about increasing β will make ecological footprint increase but quality of life decrease, as Table 4.8 and from Figure 4.7 to Figure 4.8 following below. That is because if the value of β increases, it means the weight of the out-of-vehicle travel time increase. Therefore, bus frequency will increase in order to decrease user’s time wasting. On the other side, ecological footprint will increase which depends on the frequency of bus change.
0
0.03 0.04 0.05 0.11 0.22 0.43 0.86 1.30 1.73
Footprint (ha.)
Total Utility
β
QOL Footprint
Figure 4.7 QOL and footprint under various values of β
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0%
20%
40%
60%
80%
100%
Budget allocation (%)
x y
Figure 4.8 Optimal budget allocation plan under various values of β
Figure 4.8 presents the optimal budget allocation plan under various values of β.
Most of budget goes to the fare discount subsidy; however, it also decreases gradually depending on the weight of out-of-vehicle travel time increases. We could find out that the budget allocation transfer from price discount to increase bus frequency, that is also the reason why ecological footprint increases but quality of life decreases.
Table 4.8 presents the result of the sensitive analysis, set β = 0.216 as the bench mark, times (and divided by) 2, 4, 6 and 8 to realize the influence among public transit subsidy, quality of life and ecological footprint under various amount of available budget.
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Table 4.8 The results of the sensitive analysis under various amounts of β
β x
(NT dollars)
y (Frequency)
z (hectare)
Budget (NT dollars) Market Share Footprint (ha.) Price
discount
Deficit subsidy
Green
land Private Public Total
Utility Private Public Total 0.027 34 3 28 94% 2% 4% 21% 79% ‐1617 110.27 126.98 237.25 0.036 31 6 70 83% 9% 8% 23% 77% ‐1705 100.27 253.95 354.22 0.054 30 8 98 80% 13% 7% 24% 76% ‐1800 90.27 338.60 428.87 0.108 30 8 98 78% 14% 8% 26% 74% ‐2043 80.27 338.60 418.87
0.216 28 10 126 70% 18% 12% 28% 72% -2528 70.27 423.25 493.52 0.432 28 11 140 70% 21% 9% 28% 72% ‐3395 70.27 465.58 535.85
0.864 21 16 210 53% 30% 16% 27% 73% ‐5108 70.27 677.20 747.47 1.296 20 17 224 55% 31% 14% 22% 78% ‐6722 65.27 719.53 784.80 1.728 11 25 336 33% 46% 21% 14% 86% ‐8225 55.27 1058.13 1113.40
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4.5.4 Various values of γ associated with travel cost
This section presents the optimal budget allocation plan under various values of γ associated with travel cost. Figures reveal the truth about increasing γ will make ecological footprint increase but quality of life decrease, as Table 4.9 and from Figure 4.9 to Figure 4.10 following below. That is because if the value of γ increases, it means the weight of the travel cost increase. Therefore, government will increase the percentage of price discount in order to attract more people use public transportation.
However, quality of life and bus frequency are both decrease.
0
0.01 0.01 0.02 0.04 0.08 0.16 0.32 0.48 0.64
Footprint (ha.)
Total Utility
γ
QOL Footprint
Figure 4.9 QOL and footprint under various values of γ
69 0%
20%
40%
60%
80%
100%
0.01 0.01 0.02 0.04 0.08 0.16 0.32 0.48 0.64
Budget allocation (%)
γ
x y z
Figure 4.10 Optimal budget allocation plans under various values of γ
Figure 4.10 presents the optimal budget allocation plan under various values of γ.
Most of budget goes to the fare discount subsidy in order to attract more people use public transportation. However, bus frequency decreasing results in the quality of life and ecological footprint decreases.
Table 4.9 presents the result of the sensitive analysis, set γ = 0.0803 as the bench mark, times (and divided by) 2, 4, 6 and 8 to realize the influence among public transit subsidy, quality of life and ecological footprint under various amount of available budget.
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Table 4.9 The results of the sensitive analysis under various amounts of γ
γ x
(NT dollars)
y (Frequency)
z (hectare)
Budget (NT dollars) Market Share Footprint (ha.) Price
discount
Deficit subsidy
Green
land Private Public Total
Utility Private Public Total 0.010038 30 14 182 58% 31% 11% 35% 65% -1902 110.27 592.55 702.83 0.013383 31 13 168 61% 28% 11% 32% 68% -1935 100.27 550.23 650.50 0.020075 33 11 140 66% 24% 10% 30% 70% -2001 90.27 465.58 555.85 0.04015 32 10 126 71% 20% 8% 29% 71% -2168 80.27 423.25 503.53
0.0803 28 10 126 70% 18% 12% 28% 72% -2528 70.27 423.25 493.52
0.1606 29 6 70 86% 7% 7% 26% 74% -3183 60.27 253.95 314.23
0.3212 27 6 70 91% 5% 4% 24% 76% -4409 50.27 253.95 304.23
0.4818 26 6 70 90% 4% 6% 24% 76% -5728 40.27 253.95 294.23
0.6424 26 6 70 91% 4% 6% 23% 77% -6936 30.27 253.95 284.23
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Chapter 5 Conclusion and Suggestion
5.1 Conclusion
This paper develops two bi-level programming models – the SG model and the AG model -- to maximize total utility (a proxy of social welfare) under constraints of budget, capacity of transport system and ecological footprint. Three policy measures are considered here: bus fare discount, bus frequency increase, and green land acquisition. The former two measures aim to increase the attractiveness of bus, while the last one is simply to accommodate the excess footprint. To investigate the applicability of the model, a case study on an exemplified network is conducted.
Results of the SG model show that the measure of bus fare discount and the measure of bus frequency increase can both attract remarkable percentage of bus usage and achieve almost the same social welfare, however, the latter will generate much larger footprint than that of bus fare discount due to the high emission characteristic of buses.
The results of the AG model show that the optimal decision of the contemporary generation will compromise its total utility with that of the next generation by intentionally leaving part of budget to the next generation.
(1) The results in the SG model, government allocates 82% budget into price discount for the users of the public transportation, 10% budget into deficit subsidy and 8%
budget into green land acquired. The percentage of private and public transportation mode using are separately 29.02% and 70.98%.
(2) The results in the AG model, in contemporary generation, government allocates 47% budget into price discount, 17% budget into deficit subsidy 12% budget into