The main contribution of this study is to develop a non-linear programming approach for simultaneously assessing the achievement level as well as the transport diversity of the satisfactions of urban public transit stakeholder needs. If maximizing the total achievement level of satisfaction, i.e. minimizing the summation of the normalized gaps between the targets and the present values, for stakeholder needs is considered as the single objective, the finite resource may be allocated inequitably. The inequitable allocation leads to the neglect of some needs with which transportation stakeholders certainly live without deficiencies. On the other hand, an equitably but inefficiently resource allocation may reduce the total quality of urban public transit system if the achievements of stakeholder needs sink to an even low level.
Therefore, the proposed multi-objectives model helps decision-makers allocate resources equitably and efficiently.
To further demonstrate the applicability of the constructed model, an experimental analysis from public transit system of the Taipei metropolitan area is conducted. Along with the consentaneous influence functions provided by expert discussion (as shown in appendix B), the actual data, such as population, length of operation lines, average income, headway, and so on, are taken in this analysis according to the annual reports published by Ministry of Transportation and Communications. Table 4-4 reveals the results of the baseline alternative considering actual data nowadays without resource allocation policies. The goal values denoting the expected target of sustainable development and the threshold value referring to the basic level of needs maintaining quality of life are set by government to monitor system.
TABLE 4-4 Results of the baseline (no-action) alternative
Indicator Present
Value Goal Value Threshold
Value
m
in
i =∑
i i i
i n
P n
MRT Accessibility 0.7565 0.85 0.60 0.37 0.63 0.13
MRT Affordability 0.0811 0.05 0.15 0.31 0.69 0.14
MRT Operator Profit 65.3247 20.00 150.00 0.35 0.65 0.13
Bus Accessibility 0.6867 0.85 0.60 0.65 0.35 0.07
Bus Affordability 0.0508 0.03 0.10 0.30 0.70 0.14
Bus Operator Profit 140.4401 200.00 50.00 0.40 0.60 0.12
Bus Mobility 0.5794 0.80 0.40 0.55 0.45 0.09
Bus Reliability 0.7300 0.85 0.65 0.60 0.40 0.08
Energy Consumption 35.8534 20.00 45.00 0.63 0.37 0.07
Emission 28.1338 15.00 30.00 0.88 0.12 0.03
∑
mi = 5.04 H =−∑
PilnPi =2.2274.3.1 Single Objective Problem - Minimizing Gap
The optimal allocation corresponding to seven policies are determined by the proposed constraints with a single objective to minimize the summation of normalized gaps. The analytical results are indicated in Table 4-5. The summation of normalized gap declines from 5.04 to 3.89, a 22.96% improvement, due to the significant improvements of MRT affordability, bus affordability and bus mobility. The investment policies include subsidizing the fares of public transit and constructing bus exclusive lanes. However, the affordability of each public transit system has been reached relatively high satisfaction level in the baseline alternative. The variation between achievements of different stakeholder needs is enlarged from 0.04 (in the baseline alternative) to 0.09 due to the inequitable allocation. Accordingly, the transport diversity diminishes by 47.98% to 2.190 because the values of energy consumption and emission are calculated by the trips distributed around modal trips, namely the modal share, increasing the modal share of public transit is an effective strategy to mitigate the environmental impact. For the same purpose of transferring trips from private vehicles to public transit, the resources could be allocated to the infrastructures related to those needs with lower satisfaction, such as accessibility and reliability, prior to affordability.
TABLE 4-5 Solution to the allocation model under a minimum gap objective
Indicator Present
Value Goal Value Threshold
Value
m
in
i =∑
i i i
i n
P n
MRT Accessibility 0.7565 0.85 0.60 0.37 0.63 0.10
MRT Affordability 0.0500 0.05 0.15 0.00 1 0.16
MRT Operator Profit 66.3379 20.00 150.00 0.36 0.64 0.11
Bus Accessibility 0.6867 0.85 0.60 0.65 0.35 0.06
Bus Affordability 0.0300 0.03 0.10 0.00 1 0.16
Bus Operator Profit 148.2754 200.00 50.00 0.34 0.66 0.11
Bus Mobility 0.7645 0.80 0.40 0.09 0.91 0.15
Bus Reliability 0.7301 0.85 0.65 0.60 0.40 0.07
Energy Consumption 35.3783 20.00 45.00 0.62 0.38 0.06
Emission 27.7931 15.00 30.00 0.85 0.15 0.02
∑
mi = 3.89 H =−∑
PilnPi =2.1904.3.2 Single Objective Problem - Maximizing Transport Diversity
Secondly, the analytical results of maximizing transport diversity problem are expressed in Table 4-6. The summation of normalized gap decreases by 5.96% whereas the transport diversity increases to 2.2429 due to the investments, such as constructing bus exclusive lanes, extending bus operation routes, and reducing the bus headway. The satisfactions of bus accessibility, mobility and reliability are thus improved obviously because reducing average bus headway costing dearly improves the bus mobility and reliability simultaneously. Since the achievements of stakeholder needs distributed uniformly in the baseline alternative, restricted budgets allocated to raise equity become less efficient. Particularly, the achievement of bus operator profit performs poorly in comparison to the baseline alternative. Moreover, the need satisfactions derived from the most equitable resource allocation are inferior to that from the most efficient allocation except bus accessibility and bus reliability.
TABLE 4-6 Solution to the allocation model under a maximum diversity objective
Indicator Present
Value Goal Value Threshold
Value
m
in
i =∑
i i i
i n
P n
MRT Accessibility 0.7565 0.85 0.60 0.37 0.63 0.12
MRT Affordability 0.0811 0.05 0.15 0.31 0.69 0.13
MRT Operator Profit 65.3247 20.00 150.00 0.35 0.65 0.12
Bus Accessibility 0.7075 0.85 0.60 0.57 0.43 0.08
Bus Affordability 0.0508 0.03 0.10 0.30 0.70 0.13
Bus Operator Profit 133.6368 200.00 50.00 0.44 0.56 0.11
Bus Mobility 0.6288 0.80 0.40 0.43 0.57 0.11
Bus Reliability 0.7513 0.85 0.65 0.49 0.51 0.10
Energy Consumption 35.5842 20.00 45.00 0.62 0.38 0.07
Emission 27.9494 15.00 30.00 0.86 0.14 0.03
∑
mi = 4.74 H =−∑
PilnPi =2.2434.3.3 Multi-Objective Problem
Traditionally, goal programming is often employed to solve problems with conflicting objectives such that an optimized solution may not exist. The principle idea is to convert the original multi-objectives into a single combined goal, and then to seek a compromised solution based on the relative importance of each objective. In fact, both proposed objectives in this study, normalized gap and transport diversity, simultaneously consider the setting and weighting of each goal, fuzzy multi-objectives programming is thus utilized.
According to the solution of each single objective shown in Table 4-5 and Table 4-6, the ideal and anti-ideal solution set refer to
I
* ={3.89,2.243} andI
# ={4.75,2.190} , respectively. The multi-objectives problem can be transformed into a single objective problem maximizing λ using the ideal and anti-ideal solution set. Along with the equations mentioned in Section 3.4, the following two more constraints are added into the model.)
Table 4-7 reveals the analytical results of fuzzy multi-objectives programming in which the maximized compromise-grade generated within membership function equals to 0.4810.
The optimal allocation indicates that all policy variables are variously invested except extending MRT lines and reducing average bus headway. Since manufacturing new infrastructures of MRT is costly, MRT accessibility is improved via extending feeder buses routes rather than lengthening MRT lines. Along with slightly raising bus mobility and reliability, building bus exclusive lanes avoids the severely negative impacts of reducing average bus headways on government finance and bus operator profit.
TABLE 4-7 Compromised solution to the fuzzy allocation model
Indicator Present
Value Goal Value Threshold
Value
m
in
i =∑
MRT Accessibility 0.7716 0.85 0.60 0.31 0.69 0.12
MRT Affordability 0.0745 0.05 0.15 0.24 0.76 0.13
MRT Operator Profit 65.8027 20.00 150.00 0.35 0.65 0.11
Bus Accessibility 0.6969 0.85 0.60 0.61 0.39 0.07
Bus Affordability 0.0474 0.03 0.10 0.25 0.75 0.13
Bus Operator Profit 148.2331 200.00 50.00 0.35 0.65 0.12
Bus Mobility 0.7111 0.80 0.40 0.22 0.78 0.14
Bus Reliability 0.7462 0.85 0.65 0.52 0.48 0.08
Energy Consumption 35.4217 20.00 45.00 0.62 0.38 0.07
Emission 27.8308 15.00 30.00 0.86 0.14 0.03
∑
mi = 4.33 H =−∑
PilnPi =2.230The ideal transport diversity under the given 10 indicators values at 2.30 if the achievements of stakeholder needs follows a uniform distribution. Transport diversity in present situation reaching 2.268 confirms that the Taipei metropolitan area performed well under equitably satisfying public transit stakeholder needs. Accordingly, resources utilized to bridge 75% gaps in stakeholder needs bring transport diversity a mere 21.23% improvement.
The compromised allocation elevates the satisfactions of stakeholder needs including MRT
accessibility, MRT affordability, bus affordability, bus mobility and bus reliability to a remarkably high level. Besides, energy consumption and emissions are mitigated due to the increment of public transit trips.
After comparing the proposed Pareto based model to single objective strategies, most need achievements of the compromised model lie between single objective models excluding MRT accessibility. This manifests that investments allocated to improve MRT accessibility are favorable for the trade-off consideration between efficiency and equity but might be harmful to each single target. Additionally, with the exception of affordability achieving advantaged levels in present situation, satisfactions incline to better performance of each need.
The Pareto based allocation contributes to a 14.14% improvement in normalized gaps in stakeholder needs, as well as to a 4.25% improvement in transport diversity. Consequently, the Pareto based approach evades inefficient and inequitable resource allocation.
C
HAPTER5 D
ISCUSSIONThe purpose of this chapter is to discuss the issues related to the definition of transport diversity proposed in Chapter 2, the methodologies presented in Chapter 3 and the empirical findings demonstrated in Chapter 4. The connections among sustainability, quality of life and transport diversity are discussed in Section 5.1. The determination of stakeholder needs and the spatiotemporal development of transport diversity are shown in Section 5.2 and Section 5.3, respectively. The confounding effects are presented in Section 5.4, followed by the issues of resource allocation.