中 華 大 學

中 華 大 學 博 士 論 文

雙占市場上補貼差異與路線選擇之 競爭策略研究:需求反應運輸服務之應用 Competitive Strategies of Subsidy Differentiation

and Routing Choices in Duopoly Markets:

Application of Demand Responsive Transport Services

系 所 別 ： 科技管理博士學位學程 學 號 姓 名 ： D 0 9 8 0 3 0 0 8 陳 立 峰

指 導 教 授 ： 張 建 彥 博 士

中 華 民 國 102 年 6 月

摘 要

透過運輸使得人口聚集所帶來的經濟成長對於國家發展至關重要。副大眾運輸之一 即隨招隨停(Jitney)的運輸方式大約在1914年美國各大城市開始展露頭角且以定期租用 往返為主要交通路線。之後，隨招隨停公車成功實施於美國各大城市，不僅媲美有軌電 車(Streetcar)也相較於其他運具上占有優勢地位。然而，由於隨招隨停的運輸形式受到管 制，縮小和削減不受約束隨招隨停公車業者，主要路線以有軌電車所取代。

歐洲從西元1996年至1997年提出SAMPO/SAMPLUS與需求反應運輸服務(Demand Responsive Transport Service, DRTS)計畫。其中一項是將無線通訊技術應用於都市或農村 的運輸需求中。由此計畫結果得知，DRTS的效率和可行性是顯而易見。由於近年來老 年人口增加，他們健康照護的議題受到矚目，尤其是可及性與易行性。之後，副大眾運 輸成為全世界所矚目的焦點。

現今副大眾運輸系統推廣較多的運輸形式之一為DRTS。DRTS在台灣是以復康巴士 運輸服務(Fu-Kang bus transport service)形式呈現。藉由復康巴士從起點移動至迄點的運 輸形式以增加身障者的可及性與易行性。但是必要面對一些棘手的問題。首先，政府財 源於社會福利支出是受到限制。第二，復康巴士車輛明顯不足，即使運輸公司每天排班 運行。第三，副大眾運輸市場的經濟前景未明，而且關於複雜的身障者運輸政策是由內 政部規劃與交通部執行，以至於私人運輸公司對於資本投資抱持著疑慮的態度。最後，

在整體副大眾運輸市場上公私立運輸公司扮演著重要的角色，可是運輸公司在復康巴士 運行上處於混亂競爭的狀態。

基於這些問題所建構之模型是歸於政治經濟問題模型，以分析下列議題。第一，政 府管理者所擁有的資源如何達成最佳化。第二，政府考慮如何決定公私營運輸公司之間 的補貼率。最後，為了達到政府經營在經濟上平衡的狀態，公私營運輸公司如何選擇他 們運輸路線，例如:補貼限制下，服務結構( Service Configuration)如何配置。

本論文的目的是以台灣復康巴士採用DRTS形式為研究對象，透過賽局理論與最佳 化控制加以分析與討論補貼差異與路徑選擇。另外，以此研究成果建議副大眾運輸的競 爭策略以彌補社會福利政策對於財政決策上之不足處。台灣大眾運輸與副大眾運輸補貼 做法相同。本論文之貢獻在於透過理論模型訂出副大眾運輸的策略明確地制定補貼政策 以提供公私營運輸企業如何制定本身之營運目標，透過補貼機制能夠讓乘客可以選擇自 己適當的乘車型式。以這篇論文為研究基礎，延伸性的研究即是對於台灣長期照護系統

對於身障者運輸補貼差異與公私營長期照護管理中心選址之間的關係。

關鍵詞:路線形式、經驗累積、微分賽局、研究與發展、合營企業。

ABSTRACT

The economic growth of human agglomerations through transportation has crucial to the development of a national future. The jitney was a kind of paratransit appeared in many cities around 1914 in the United States and plied the main traffic routes for hire. Afterward, the jitney buses prospered in many American cities, competing not only with streetcars but also among themselves. However, due to regulation of jitney, reducing or eliminating the uncontrolled jitney bus operations on major routes served by streetcars.

The SAMPO/SAMPLUS project of European Union from 1996 to 1997 is a Demand Responsive Transport Service (DRTS) project which applied the wireless communication technology to transportation demands in urban or villages. According to the results from the project, the efficiency and feasibility of DRTS is obvious. Due to the increase in the population of eldery people, the issues of their health care has been gradually emphasized in particular accessibility and mobility. Afterward, paratransit is the focus of attention around the world.

Nowadays, DRTS in Taiwan is defined as Fu-Kang bus transport service. Due to the increase of accessibility and mobility, disabled persons who move from an orginal point to a destinate point through Fu-Kang bus. However, some thorny problems are faced. Firstly, the government fiscal resources with respect to social welfare are restricted. Secondly, the quantities of Fu-Kang bus are not sufficient even through the public transport firms operate regularly. Thirdly, the economic prospect of paratransit market is not unclear; furthermore, the complex decision making of transport policy with disabled persons must be integrated between Ministry of the Interior (MOI) and Ministry of Transportation and Communication (MOTC), the private transport firms hesitate to invest sufficient capital.

Finally, the public and the private transport firms have significant role in a paratransit market; however, the state of Fu-Kang bus operation is competing chaotically each other.

The problems underlying these models are political economy problems to analysis these issues in the following. Firstly, the government administrates how to optimize their limited resources. Secondly, the government considers how to determine the rate of subsidy between the public and private bus firm. Finally, due to a state of economic equilibrium the government, the public and private bus firms must consider how to choose their routing profiles, i.e. service configurations under constricted subsidy.

The purpose of this dissertation I attempt to establish competitive spatial model through game theory and optimal control to analysis and discuss between subsidy

differentiation and routing choices; furthermore, I provide a competitive strategy of a paratransit transport policy to complement the lack of social welfare policy with respect to finance. The contribution of this dissertation is to suggest a paratransit guidance through models so that precisely establish subsidy policies; furthermore, provide a guidance to the public and the private transport firm and they know how to determine their operation aim.

Our further research is based on this dissertation, that is, I consider the relationship between transportation of the subsidy differentiation with respect to disabled persons on the medical health care system in Taiwan and location of the public or the private medical care organization.

Keywords: Routing Types; Experience Accumulation; Differential Game; Research and Development; Joint Venture.

Acknowledgement

Four years ago, in the autumn of 2009, I attended an entrance examination of a Ph.D program of technology management in Chung Hua University. I deeply appreciated my advisors who gave me many rewards, encouraged me to write journal papers and assisted me in accomplishing my dissertation step by step. My study progresses with them are described in the following.

My first advisor, Cho, Y. J., gave me a recent research direction with respect to transportation, i.e. Demand Responsive Transport Service (DRTS). I followed him to interview the Tainan County Government’s Bureau of Social Affairs in order to assist them in solving the executive transportation problem of the Fu-Kang bus. I was able to understand the practical application of DRTS through this interview.

The second advisor, Chang, C. Y., gave me the first suggestion that it is necessary for writing paper promptly even though writing technique is not very well. He said “you must write first and then I shall support your writing.” Afterward, he revised my writing when I have submitted it to him. Because of his incentive, my writings are accomplished as soon as possible.

Third advisor, Lee, Y. H., gave me a few research methods that includes simple and sophisticate. Furthermore, he guided me to entrance his professional studying fields step by step so that I could combine my study idea with his providing research method. He also has patience to explain it again and again when I do not understand some mathematical meanings.

Finally, I want to thank my family. My father, Chen, M. D., gives me financial supports. My mother, Chen-Shu, U. L., takes care of my daughters in the day. My wife, Yang, Y. S., takes care of my daughters in the night. My two daughters, Jinger and Jinnger are quiet when I am writing papers.

Table of Contents

摘 要 ... I ABSTRACT ... III ACKNOWLEDGEMENT ... V TABLE OF CONTENTS ... VI

1. INTRODUCTION ... 1

1.1BACKGROUND ... 1

1.2PURPOSES ... 4

1.3RESEARCH SCOPE ... 4

1.4PLAN OF THE DISSERTATION ... 4

2. LITERATURE REVIEW ... 5

2.1PARATRANSIT ... 5

2.1.1 Background and Classifications ... 5

2.1.2 Applied to Paratransit ... 6

2.2DEMAND RESPONSIVE TRANSPORT SERVICE (DRTS) ... 7

2.2.1 History ... 7

2.2.2 Development ... 8

2.3MICROECONOMIC PERSPECTIVE... 21

2.3.1 Markets of DRTS ... 21

2.3.2 Monopolistic Competition ... 22

2.3.3 Product Differentiation ... 22

2.3.4 Oligopoly ... 23

2.3.5 Duopoly ... 23

2.3.6 Price Discrimination ... 24

2.4PRICING OF TRANSIT ... 25

2.4.1 Fare Structure ... 25

2.4.2 Subsidy ... 26

2.4.3 Fare and Subsidy of Fu-kang bus ... 27

2.4.4 Political Consideration ... 28

2.4.5 Transportation Problems and Game Theory ... 29

3. ECONOMIC MODELING ... 30

3.1INTRODUCTION ... 30

3.2HOTELLING MODEL ... 30

3.3GAME THEORY... 31

3.4DUOPOLY MODEL ... 33

3.5OPTIMAL CONTROL... 33

3.6DIFFERENTIAL GAMES ... 34

4. DISCUSSION ... 35

4.1THE FLEXIBLE CHOICES OF ROUTING TYPES ... 35

4.1.1 The Routing Profiles ... 35

4.1.2 Adapted Rider Service Quality ... 35

4.1.3 Revenues ... 35

4.1.4 Riders ... 35

4.1.5 The Games ... 36

4.1.6 Competitions ... 36

4.1.7 A Brief Summary of Flexible Choice ... 39

4.2THE FIXED CHOICES OF ROUTING TYPES ... 40

4.2.1 Service Configuration ... 40

4.2.2 Quality of Service ... 41

4.2.3 Firm’s Revenues ... 41

4.2.4 Riders preferences ... 41

4.2.5 Competition between Both firms ... 42

4.2.6 The Social Optimum ... 48

4.2.7 A Brief Summary ... 55

4.3COMPATIBILITY ... 55

4.3.1 The Routing Profiles ... 57

4.3.2 Network Effects ... 57

4.3.3 Partial Compatibility ... 58

4.3.4 The Competition Perspective ... 59

4.3.5 Subsidy and Partial Compatibility of Routing Profiles ... 61

4.3.6 Effects of Partial Compatibility, degree of compatibility and subsidy ... 62 4.3.7 Difference of Partial Compatibility, degree of compatibility and subsidy . 64

4.3.8 Numeral Experiments ... 65

4.3.9 A Brief Summary ... 69

4.4OPTIMAL CONTROL... 70

4.4.1 Open-Loop Nash Equilibrium (OLNE) ... 74

4.4.2 Closed-Loop Nash Equilibrium (CLNE) ... 79

4.4.3 A Brief Summary ... 86

5. CONCLUSIONS AND RECOMMENDATIONS ... 87

REFERENCES ... 89

APPENDIX A ... 101

APPENDIX B ... 104

APPENDIX C ... 105

APPENDIX D ... 108

APPENDIX E ... 111

APPENDIX F ... 112

APPENDIX G ... 115

List of Tables

TABLE 1 FORECASTING THE POPULATION OVER THE AGE OF 65 IN TAIWAN ... 11

TABLE 2 THE OPERATION STATUS OF THE FU-KANG BUS AT 2013 IN TAIWAN ... 17

TABLE 3 THE SCALE VALUE OF



TABLE 4 THE SCALE VALUE OF,AND SOCIAL WELFARE (Ⅱ) ... 53

TABLE 5









TABLE 6









TABLE 7 THE FARE TABLE OF SHUTTLE BUS WITH RESPECT TO MILD OR MODERATE COGNITIVE ELDERLY IMPAIRMENT (TAIPEI CITY GOVERNMENT DEPARTMENT OF SOCIAL WELFARE AUTHORIZED) ... 101

TABLE 8 WHEN S→0, THE VALUE OF EQUATION (112) AND (113) UNDER 0.01< <0.99 AND 1.01<<1.99. ... 105

TABLE 9 WHEN S→^, THE VALUE OF EQUATION (112) AND (113) UNDER 0.01< <0.99 AND 1.01<<1.99. ... 108

TABLE 10WHEN S→0, THE VALUE OF EQUATION (131) AND (132) UNDER 0.01< <0.99 AND 1.01<<1.50. ... 112

TABLE 11WHEN S→^, THE VALUE OF EQUATION (135) AND (136) UNDER 0.01< <0.99 AND 1.01<<1.50. ... 115

List of Figures

FIGURE 1.THE DISABLED POPULATION FROM 1997 TO 2011 IN TAIWAN ... 15

FIGURE 2.ECONOMIC MODEL. ... 30

FIGURE 3.HOTELLING’S “MAIN STREET” ... 31

FIGURE 4.THE CURVE SHOWS ... 38

FIGURE 5.THE CURVE SHOWS ... 38

FIGURE 6.RIDERS’ PREFERENCE WITH TWO FIRMS ... 42

FIGURE 7.   ... 46

FIGURE 8.



FIGURE 9.



FIGURE 10.  ;  ... 51

FIGURE 11.



FIGURE 12.



FIGURE 13.  ;  ... 52

FIGURE 14.



FIGURE 15.



FIGURE 16.  ;  ... 54

FIGURE 17.



FIGURE 18.



FIGURE 19.THE RIDERS’ DISTRIBUTION OF CHOICES ... 56

FIGURE 20. ¹



P ... 60





P

FIGURE 22.THE SUBSIDY RANGE: 12







FIGURE 23.THE SUBSIDY RANGE: 12







FIGURE 24. THE VALUE OF ¹,







FIGURE 25. 0

n

n

n

n









n

n

n

n

THE VALUES OF

E

AND

Q

ARE OBTAINMENT. ... 77 FIGURE 29.SETTING RANGES ARE BETWEEN  AND ^ ,

THE VALUES OF

E

AND

Q

ARE OBTAINMENT. ... 78 FIGURE 30.SETTING RANGE ARE BETWEEN  AND  ,

THE VALUES OF

E

AND

Q

ARE OBTAINMENT. ... 78 FIGURE 31.SETTING RANGE ARE BETWEEN  AND  ,

THE VALUES OF

E

AND

Q

ARE OBTAINMENT. ... 79 FIGURE 32.SETTING RANGES ARE BETWEEN  AND  ,

THE VALUES OF

Z

AND

P

ARE OBTAINMENT. ... 84 FIGURE 33.SETTING RANGES ARE BETWEEN  AND 

THE VALUES OF

Z

AND

P

ARE OBTAINMENT. ... 84 FIGURE 34.SETTING RANGES ARE BETWEEN  AND ^

THE VALUES OF

Z

AND

Z

ARE OBTAINMENT. ... 85 FIGURE 35.SETTING RANGES ARE BETWEEN  AND ^ ,

THE VALUES OF

P

AND

P

ARE OBTAINMENT. ... 86

1. Introduction

1.1 Background

As time goes on, the nature of transit service will be changed. From the historical opinion, a predecessor of analogous paratransit service is jitney. The appearance of jitneys in many cities about 1914 gave a further incentive to motorbus in the United States. The jitney ware private automobiles plying the main transport route for hire. Furthermore, they have no official regulation and they threaten to the profitability of streetcar systems.

Afterward, the jitney buses flourished in many American cities, competing with streetcars.

Unfortunately, regulation of jitney and bus transportation was introduced during 1920’s, the merits of bus transportation service were underlined and the capabilities of jitney service were neglected (Vuchic, 2007).

Since 1960’s, the economic growth is gradually increased, the migration of population is from countries to metropolis. Most public transportation services are concentrated in central business districts (CBD) of the cities and they are usually fixed route services.

However, the public transportation services of the poorer countries are not sufficient and the significance of flexible route services is gradually appeared. ‘paratransit’ is the term that Kirby, Bhatt, Kemp, McGillivray, and Wohl (1974) vitalized before-mentioned older idea and newer variations on them. That is automobiles and buses demand-responsive, transit-type services on existing streets. Afterwards, the applications of paratransit include not only taxi, jitney, dial-a-ride, and subscription commuting services but also car rentals and carpools.

Nowadays, according to demographics data between 1980 and 2000 from Wang, Lo, Fan, and Chao (2009), the proportion of the population age 65 and older increased slightly in seven of the eight countries, only Japan was doubled increased. Between 2000 and 2020, the proportion of age 65 and older increases rapidly in all countries. The United Kingdom is the smallest rise that is from 16.0 to 19.8 percent and the Japan is the largest rise that is from 17.1 to 26.2 percent. In Taiwan, between 2008 and 2018, the proportion of the elderly person age 65 increases from 10.4 to 14.7 percent. The significant of elderly persons with respect to accessibility and mobility is appeared again. Furthermore, in Taiwan, between 1999 and 2010, the population of the impaired persons increases from 64 million to 107 million. However, the functional design of public transportation with respect to facility, vehicle and timetable fits in with most citizens. The groups of lone elderly and impaired

people are easily neglected due to an influence of social exclusion.

Public transportation is essential to the economy development of a country. In Taiwan, the public transportation services are concentrated in metropolitan areas, especially the bus services. From 1946, the bus service has played a prominent role with the economy growth in Taiwan. In 1996, the Taipei Mass Rapid Transit (MRT) started operation. It is a big milestone for the development of public transportation services in Taiwan. Moreover, the Kaohsiung Mass Rapid Transit started operation in 2008. It indicated that the public transportation services in metropolitans are much more convenient than before. Nowadays the single and simple transportation mode is changed into multiple transportation modes.

In addition, the public transportation service has been changed from only bus service into multiple services including MRT, Light Rail Transit (LRT), and bus. In metropolitan areas, buses and MRT services are both fixed route transportation services. Therefore, the MRT services are easily replaced the bus services and become a major public transportation services because of their high mobility. The role of bus services should be reconsidered and their accessibilities need to be enhanced to promote their contributions to the transportation systems.

Disabled persons are classified minority groups. According to the viewpoint of market economy, transport firms hesitate to operate the transport markets of disabled persons.

Nevertheless, the concept of globalization via the borderless world was spread around many nations (Ohmae, 1990); futhermore, in 1990, democratization trend was sprawled around the world and the notion of residual welfare state was transformed into the notion of citizen’s welfare state (George & Miller, 1994).

The political and economical situation of Taiwan was affected by globalization and democratization. In 1990, the reformation of Taiwan Congress was happened and the League of Welfare Organizations for the Disabled was registered. Afterward, this league endeavors to improve welfare benefits of disabled persons through promotion of legislations. According to the legislations, the government must make social welfare policies with respect to disabled persons to support them. Providing Fu-Kang bus service is one kind of support of delivery when disabled persons move to hospitals or clinic centers.

Due to publicly-owned budgets in the initial stage of promotion, the government can simultaneously nominate the publicly-managed transport operation or the privately-managed transport operation to serve the medical transport market. Unfortunately, the expenditure of the other department with respect to social welfare was insufficient in

order to serve the transport of disabled persons in the paratransit market. Afterward, the government trends to the publicly-managed transport operation. For instance, the Ministry of the Interior (MOI) promulgated the “Senior Citizens Welfare Act (SCWA)” on 2009 (President order Hua-Tzon(1)Yi/Tze No. 09800166511 on July 8, 2009).The Act was declared that the services are to be cooperated with private institutions under allowance, commission if necessary. As a result of this trend, the delivery method of “Purchase of Service Contracting, POSC” was appeared (Kettner & Martin, 1987).

After the “People with Disabilities Rights Protection Act (PDRPA)” was announced in 2009 (President Order Hua-Tzon(1)Yi/Tze No. 09800015921, 2009), the public and the private firms launched into paratransit, in particular, the barrier-free transportation services.

Nowadays, existing public transportation services whose accessibility and mobility with respect to disabled persons were neglected, and therefore the government administrator must consider an additional transport method to support them. Due to specific character of transportation, paratransit services are respected again; furthermore, the new paratransit industry market needs to be established immediately in order to the public transport utility of impaired persons as well as most citizens. Demand Responsive Transport Service (DRTS) is a kind of paratrasit service around the world. DRTS in Taiwan is defined as Fu-Kang bus transport service. Disabled persons who move from an original point to a destination point by Fu-Kang bus. However, some thorny problems are faced. Firstly, the government fiscal resources with respect to social welfare are restricted, i.e. the government reduces in expenditure as small as possible because the government fiscal revenues are not sufficient. Secondly, the quantities of Fu-Kang bus are not adequate even through the public transport firms operate regularly. Thirdly, the economic prospect of paratransit market is not unclear; furthermore, the complex decision making of transport policy with disabled persons must be integrated between Ministry of the Interior (MOI) and Ministry of Transportation and Communication (MOTC), the private transport firms hesitate to invest sufficient capital. Finally, the public and the private transport firms have significant role in a paratransit market; however, the state of Fu-Kang bus operation is competing chaotically each other.

The problems underlying these models are political economy problems to analysis these issues in the following. Firstly, the government administrates how to optimize their limited resources. Secondly, the government considers how to determine the rate of subsidy between the public and private bus firm. Finally, due to a state of economic

equilibrium the government the public and private bus firms must consider how to choose their routing profiles, i.e. configuration service under constricted subsidy.

1.2 Purposes

Above-mentioned the constructed problems, I plan to solve and accomplish them through four models in the following. Firstly, I analysis and discuss between the subsidy differentiation and routing choices when the public and private transport firms could choose concurrently the routing types from the configuration service of DRTS under incomplete information. Secondly, I also analysis and discuss the subsidy differentiation and routing choices when the public and private transport firms could choose concurrently the routing types from the configuration service of DRTS under complete information.

Thirdly, I consider the compatibility level of configuration service between the public and the private firm. Fourthly, I attempt to find a saddle point.

Finally, I suggest a competitive strategy of a paratransit transport policy to complement the lack of social welfare policy with respect to finance.

1.3 Research Scope

I describe the research scopes in the following.

Firstly, due to specific characteristics of Fu-kang bus transport service I assume the possibility of Fu-kang bus operation toward the economical behavior in the dissertation;

however, the firms use the existing method of fare calculation.

Secondly, there are many the service configurations of DRTS; however, I do not discuss which types of service configurations appropriate for the Fu-kang transport service in the dissertation.

Finally, I only discuss and emphasize the importance of carpool through service configuration and subsidy method.

1.4 Plan of the Dissertation

I construct our dissertation in the following. Chapter 1 introduces the background, our purpose and plan of the dissertation. Chapter 2 introduces the literature review with respect to paratransit, DRTS, economical perspective and pricing of transit. Chapter 3 introduces the economic modeling with respect to game theory and optimal control. Chapter 4 is the result of economic modeling by game theory and optimal control. Chapter 5 is my conclusions and recommendations.

2. Literature Review

Our literature review is split into three parts. The first part traces in relation to paratransit, in particular, DRTS. I also trance their background, classification and development of its service in many nations and future research. The second part explores applied possibility of DRTS through microeconomic perspective. The third part seeks pricing of transit. Due to sustainable transport operation of a firm, the firms must obtain revenue. I need to gather literature with respect to pricing of transit.

2.1 Paratransit

In order to establish our model with respect to disabled persons who are carried from original point to destination point I need to transport type. Disabled persons are minority groups; furthermore, their accessibility and mobility are inconvenient. For example, the action of impair people is clumsy. They have no idea when they desire to move to a hospital for taking medical treatment. Moreover, even though government promotes the barrier-free policy, most public transportation could not directly help them move to a hospital. They firstly move to bus stop station or main transport station by themselves.

However, their accessibility and mobility could be solved by paratransit service. Paratransit is roughly defined as the representing modes of public and semipublic transport. According to basic characteristics of paratransit modes, pratransit includes not only taxi, jitney, dial-a-ride, and subscription commuting services but also carpools, DRTS. The last one, in particular, was broadly applied to Fu-Kang bus service. In this section, I review literature with respect to paratransit and DRTS in the following.

2.1.1 Background and Classifications

Generally speaking, transit and private transportation are assigned according to passenger transport modes. Transit is the conventional transport mode. Due to the general carrier type of passenger transport, it is also referred to as public transport, mass transportation. These characteristics of transport system are fixed routes and schedules, available for use by people who pay the regulated fare. Private transportations are another conventional transport mode. Most of private transportations that are privately owned vehicles operated by owned for their own use, for instance, automobile, motorcycle, bicycle and walking (Vuchic, 2007).

Paratransit is between transit and private transportations. Before the early 1960’s, U.S.

transportation planners forced on conventional transport mode planning. Most of families

used linear trolley systems for communication and used taxis or jitneys for their trip.

Jitneys were in competitive with trolleys in big cities but their comparative advantage in flexible service was neglected. After that, because of economical environment, for instance, unfavorable trends in inflation, energy use, capital and pollution costs, few planners try to find another transport mode. Kirby, et al. (1974) collected these older ideas and develop the newer variations: paratransit is between automobiles and buses of varying sizes that provide demand-responsive, transit-type service.

There are classifications about paratransit. Orski (1975) brought up that paratransit (the prefix”para“ means “closely resembling” or “ akin to”) is the innovative types of transportation known under such as public automobile service, jitneys, dial-a-ride, community transit, subscription bus, vanpool, shared taxi, pre-arranged taxipool and auto rapid transit. Cervero (1997) summarized paratransit services that are included commercial services, employer-sponsored and developer-sponsored services. Commercial service includes shared-ride taxis, dial-a-ride (divide into two parts, specialized and airport shuttles), jitneys (divide into three parts, circulators, transit feeders and area wide) and commuter vans, employer-sponsored and developer-sponsored services include shuttles, vanpools and bus-pools. Service types of shraed-ride taxis and dial-a-ride are “on demand, hail request”or“on demand, phone request”. Service types of jitneys are “regular route, fixed stops ”or“regular route, hail request”or“semi-regular route, hail request ”. Service types of commuter vans are “pre-arranged, scheduled ”. Service types of shuttles, vanpools and buspools are “pre-arranged, regular route ”, “pre-arranged, scheduled ”and

“pre-arranged, schedules ”. Service configuration of paratransit services included that

“many-to-many ”, “many-to-one ”, “few-to-one ”, “fixed route/loop ”, “one-to-one ”.

Vuchic (2007) divided paratransit into semipublic paratransit and public paratransit.

Semipublic paratrasnit includes vanpools, subscription bus and car sharing. Public paratransit includes taxis, jitneys, dial-a-ride and hybrid services.

2.1.2 Applied to Paratransit

Paratransit is a branch of urban transit and its transportable function of passenger capacity is limit and it is able to only supplement of regular transit service. In the recent several decade, paratransit play an important role that can provide personal and flexible transport services (Kirby, 1976). In practice, Lave and Mathias (2000) addressed that paratransit comprise two areas. One is the Americans with Disabilities Act of 1990 (ADA),

called ADA complementary paratrasnit services and the other is demand-responsive services. Stern (1993) established a choice model to measure transportation demand by elderly and disabled persons. The prominent results show as follows. Firstly, paratransit systems support them door-to-door service well. Secondly, when subsidized, taxis are probably a potential alternative. Thirdly, buses are poor alternative in rural area. Finally, Demand is price inelastic as well as the research result of Nguyen-Hoang and Yeung (2010). Fitzgerald, Shaunesey, and Stern (2000) utilized econometric methods to reduce the number of door-to-door trips and utilized the education program to slightly affect paratransit demand of disabled persons. Bearse, Gurmu, Rapaport, and Stern (2004) used a National Transit Database (NTD) data and standart time series techniques to establish a aggregate demand model. The result show that the moderate sized American cities have a phnomenal growth in demand for paratransit. The growth is due to increased participation of disabled persons. Nguyen-Hoang and Yeung (2010) also used a NTD to conduct the benefit-cost analysis and institute demand and cost models for paratransit services. This article evidence that paratransit services impact on the complete level of transit service and fleet size is correlate with the number of passenger trips.

2.2 Demand Responsive Transport Service (DRTS)

2.2.1 History

The SAMPO project of European Union from 1996 to 1997 is a DRTS project which applied the wireless communication technology to transportation demands in urban or villages. According to the results from the project, the efficiency and feasibility of DRTS is obvious. The study scope of this research includes six countries, Belgium, Finland, Ireland, Italy, Sweden, and Britain. The SAMPO project has some meanings described from Ambrosino, et al. (2000): (1) Expanding the bus routes and bus stops, allow more passengers to ride bus; (2) The improvement of accessibility of terminals and rural areas;

(3) The improvement of accessibility and mobility for elderly and mobility impaired persons; (4) The improvement of accessibility and service for students who live in a area with low density of population and housewives having no driver licenses; (5) Increasing utilization ratio of public transportation systems by promotion of service levels; (6) The promotion of economic activity in the region.

Castex, Clavel, and Josselin (2008) indicated that if communication technology collocate with flexible demand responsive transportation, then the efficacy will be good.

The function of DRTS is to provide a public transportation service to mobility impaired persons and people who live in low density areas. Moreover, the service routes and schedules of transportation service need to be flexible.

Chen, Gross, Pecheux, and Jovan (2005) studied whether Advanced Technology Transport Service (ATTS) and Advanced Transport Information System (ATIS) could improve the mobility of elderly and mobility impaired persons. Results of the study showed that usage percentage of public transportation system will increase if the Advanced Transport Information System has been utilized. In addition, the in-home Advanced Transport Information System interests’ elderly and mobility impaired people, especially via telephone service.

2.2.2 Development

Paratransit consists of demand-responsive modes and provides shared rides. The development of DRTS emphasized the research of door-to-door services and dial-a-ride communication techniques. The general prototype is that the transportation operators carrier the riders from door of person origin point to an exact destination point according to request or demand of the rider by phone or some communication tools. Daganzo (1978) established a deterministic model of many-to-many dial-a-bus systems that it possible to predict quickly and accurately average total time in the system. Ferna´ndez, De Cea, and Malbran (2008) defined the Public Network Design Problem (PTNDP) as a multilevel programming problem and the application of this methodology to the Santiago transit system. There are two conclusions. One conclusion is that the private opearting costs and the social costs are considerably lower than the costs of the current system. The other one is that the these cost reductions permit government authorities to lauch an important measures without subsidies and fare increases. Horn (2004) designed the journey-planning procedures and reduction techniques that are used to obtain acceptable computational performance. Use the simulation to exam the procedures that are well suited for use in a real-time traveller information system. Brake, Mulley, Nelson, and Wright (2007) discussed that most of DRTS is applied to elderly persons, persons with disabilities and try to set up a new scheme, Flexible Transport Service (FTS), a border appreciation of ‘public transport’ and a more integrated approach to provision.

2.2.2.1 The United State

Higgins (1976) indicated that the dial-a-ride services could support the poor and elderly. Yim and Khattak (2000) used two research methods that are focus group and

Computer Aided Telephone Interview(CATI) technique to survey customers needs. The results was accordant and indicate that the Personalized Demand Responsive Transit(PDRT) service may appeal to commuters as well as non-commuters. The most prominent is a rationally priced PDRT service that is dependable and meets customer expectations(of transportation cost, travel time and wait time) can be successful in the long duration. Kurt , Dessouky, and Abdelmaguid (2004) established the DRT systems design of the benchmarking to improve the efficiency of the service, the DRT systems consist of dial-a-ride programs that transit agencies use for point-to-point pick-up and delivery of the elderly and disabled persons. The results that the use of paratransit computer aided dispatching (CAD) system and agency service delivery provide a productivity benefit and the use of advanced communication technology has a beneficial impact on opearting cost.

2.2.2.2 European Unit

During the 1960s and early 1970s, analogous DRTS in United Kingdom(UK), Black Taxibus services in Belfast and Londonderry,Northern Ireland, are emerged. However, this transport type is illegal. Since then, the 1985 Act has legalized the approach, but this has only been applied in a few towns and cities (Enoch, Potter, Parkhurst, & Smith, 2004).

DRTS scheme can be expandable in European Unit (EU) through EC-funded R&D projects such as System for Advanced Management of Public Transport Operations (SAMPO) and System for Advanced Management of Public Transport operations Plus (SAMPLUS). Successful experieces from Europe shows that DRT is more strategically simple and understandable to complete in more regulated enviorment as there is less contest with other public transport modes. Thus DRTS has progressed more swiftly on the continent than in the UK(Mageean & Nelson, 2003).The oveall SAMPLUS aim is to demonstrate and evluate DRTS in EU using telematica technologies. SAMPLUS includes five test sites in four different EU member states(Belguim, Finland, Italy, and Sweden), and feasibility studies in two UK sites(Irish and Finnish). This project shows a set of DRT technologies and operations fully demonstrated on urban and rural test sites across Europe and ready for market.(University of Newcastle upon Tyne, 1999). Brake, Nelson, and Wright (2004) studies about UK experience with telematics-based DRTS in rural areas.

Telematics-based DRTS services have the extent to produce public transport nearer to the flexibility and convenience of private transport.

2.2.2.3 Japan

DRTS is especial named “Demand Bus” in Japan. Demand Bus orginated in Japan

from early 1970s. Since then, the numbers of paivate car and labor costs were increased due to rapid economic growth. Furthermore, because the Japanese government must hold down the inflation, the public utility charges need to be restricted and the people migrated from the village to the urban city, the overall bus enterprises were decreased. Suzuki (2009) described the Hankyu Bus Company,Limited tried to reverse the inferior situation and upgrated the bus operating efficiency in an sparsely area that is located on Nose town, Osaka prefecture. This company brought DRTS into the bus opeation in 1972. The protoype of DRTS is that the riders use the telephone in the bus stop to convay the call center and the call center confirms the situation of operating bus, convay an optimum routing to riders by the telephone and to the bus driver by the radio.

The Japan government, Ministry of Land, Infrastructure, Transport and Tourism (2009) formulates an activation of regional public transportation policy due to promotion of secure, sustained and improved regional public transporation. There are more than one hundred approved case studies by the Japan government. The case studies are divided into seven transport modes that are a community bus mode, a routing bus mode, a carpool taxi mode, a railroad mode, a shipped passenger mode, a multiple transport mode and other mode. Most of commnity bus mode, routing bus mode and carpool taxi mode include the DRTS.

DRTS in Japan with respect to survey literature. Nakashma and Kawakami (2006) establish the model area of bus routing and simulate this model. The valuation of this model is used by Osaka prefecture. Usami, Motoda, Kurauchi, and Nakamura (2007) use the questionnaire to survey DRTS with respect to operation modes, for example riders need to make an appointment or bus operating time-table beforehand when riders use the DRTS.

The fare of DRTS, for example, the transport operators need to establish the flat fare, zone fare or regional fare. The revenue source of DRTS, for example, the revenues are from operating revenues or subsidy. The results of survey that firstly, the riders hope the bus operating time-table when riders use the DRTS. Secondly, the transport operators are 59.6 percent to choose the flat fare. Finally, the subsidy makes up 59 percent of opearting revenues.

2.2.2.4 Taiwan

Public transportation is essential to the economic development of a country. From 1946, the bus service has played a prominent role in economic growth of Taiwan. However, Wang, et al. (2009) illustrated the population of elderly persons (more than 65 years old) in Taiwan

is estimated to be 2 million in 2018(see Table 1). Furthermore, in recent years, the accessibility and mobility of transport of impaired persons are gradually emphasized in the society of Taiwan, this is because elderly and impaired people require a barrier-free transport in Taiwan.

Table 1

Forecasting the population over the age of 65 in Taiwan

Year Over the age of 65

The structure of 65 age (%) Over the age of 65(thousand)

The age of 65-74

Over the age of 75

The age of 65-74

Over the age of 75

2008 10.4 56.9 43.1 1,365 1,032

2013 11.6 54.6 45.4 1,478 1,231

2018 14.7 58.3 41.7 2,028 1,452

2023 18.5 62.7 37.3 2,758 1,644

2028 22.5 58.7 41.3 3,147 2,215

2031 27.9 50.0 50.0 3,271 3,271

2041 34.0 45.3 54.7 3,399 4,111

2051 37.5 40.3 59.7 3,069 4,547

Source: Wang, L., Lo, Y. M., Fan, S. C., & Chao, W. T. (2009).

As a result of the announcement of the Act of People with Disabilities Rights Protection in 2009, the public and the private bus firms have put efforts to setup a system of Demand Responsive Transport Services (DRTS) in Taiwan. DRTS, also named dial-a-ride, flexible transportation or special transportation system, presents multi-applied transport service mode of paratransit (Kirby, et al., 1974). Cervero (1997) sorted the service configuration of DRTS into the following four routing profiles: many-to-many, many-to-few/few-to-many, few-to-few, and many-to-one/few-to-one. Many-to-many routing profile means that a provider places no constraints on the type of trips it handles;

i.e. the origins and destinations are random and can happen anywhere. Many-to-few routing profile means that a provider has random origins and only regular destinations (hospitals, sightseeing places, etc.). The Control Yuan R.O.C. (2009) investigated that the passengers transport stopped problems of remote districts; furthermore, the report is

suggested that the government must innovate the novel transport service (i.e. DRTS) to improve the transportation with respect to remote districts.

DRTS in Taiwan, also named Fu-Kang bus Service (i.e., medical transportation), usually makes use of few-to-few or few-to-one routing profile carrying impaired people to hospitals. The origin and destination points of impaired people are usually from home to hospitals or the clinic centers. Kittelson, Quade, and Hunter-Zaworski (2004) stated that DRTS services are able to be explained and defined in terms of both “modes of firm” and

“types of markets.”

In recent years, the studies of Fu-Kang bus and taxi services have focused on the routing planning characteristics and optimized solutions analysis used to improve the operational efficiency of vehicle fleets for bus firms and the service qualities for users.

Huang (2001), Huang and Hsu (2009), and Shyr, et al. (2009) studied the optimization of operational cost, service quality, riders demand and efficiency under the carpool condition.

In addition, Chang (2004) analyzed the integration of the Fu-Kang bus service and Mass Rapid Transit (MRT) service. Moreover, the political economy and behavior choice were also discussed in the above issue. For instance, Chang (2009) used the DEMATEL and the cluster analysis models to explain the taxi market policies. Lin (2005) and Gi (2010) studied the vehicle choice of the elderly people and analyzed the transport demand of DRTS. Chang and Chu (2008)discussed the relationship between the choice behavior of riders who are willing to pay fee and the operational cost of taxi.

According to the Act of People with Disabilities Right Protection, Ministry of Transportation and Communications (MOTC) is giving new impetus to promote a perfect barrier-free transport service and a door-to-door service in order to benefit the accessibility and mobility of impaired people. For some reasons there are some difficulties still needed to be overcome. Firstly, impaired people are the social exclusion groups, government usually does not support them sufficient social welfare budgets. Secondly, impaired people are a minority group; i.e., they have no “economics of agglomeration” effect, the transport providers do not want to enter this poor market. Thirdly, most of costs of Fu-Kang bus are supported by the social welfare budgets and the patronage of the social welfare organization, the riders or policy makers easily neglect the fact such as how to use vehicle resources efficiently and how to optimize these vehicle resources. In addition, according to the Law of People with Disabilities Having a Discount Rate to Ride the Public Transport Vehicle, people with disabilities are favor a 50% discount rate to ride a

domestic transport vehicle and a discount rate of one way trip based on regulated taxi rate from 50% to 66.7% to ride a Fu-Kang bus, however, the operational incentive of the providers is still needed to be increased.

I observe that product and transport service compatibility have the analogous structure in differentiated industry. Farrell and Saloner (1987) indicated that compatibility has significantly studied in industrial economics. For instance, in the industrial revolution period, the use of interchangeable parts of railroad gauges was an essential step. Nowadays, a rapid growth of the information technology, academic economists has well noticed the importance of product compatibility. Chou and Shy (1993) defined compatibility with other brands varies among brands in the same industry. For example, some Apple machines are able to read DOS diskettes but DOS machines cannot read the Apple format.

Economides (1996) analyzed the economic features of networks. He illustrated the structure of a network that many components of a network are demanded for the provision of a representative service. Moreover, he gave an example of information superhighway network to explain that services demanded by consumers are consists of many complementary components.

In next section, I establish a model for the DRTS with the partial compatibility and supporting service (e.g., Chou & Shy, 1993) in a duopoly transport market, in particular, for vanpool taxi and the Fu-Kang bus service. This both services provide a differentiated routing profile. In addition, the accessibility and mobility of the riders with routing profiles and subsidy are considered. Moreover, I assume the riders that are same total budgets spend on a vehicle and routing profile of DRTS for the sake of simplicity. By doing this, I are able to analyze the issue mentioned above.

I use the concept of partial compatibility that includes the element of differentiated subsidy and routing profiles to present the relations between the partial compatibility of routing profiles, degree of compatibility and subsidy. In addition, I use sub-game prefect equilibrium method to solve the problem. Relationships and implications in subsidy, partial compatibility of routing profiles and degree of compatibility are discussed in Section 3. The major findings and suggestions are concluded in Section 4.

Since enactments of the People with Disabilities Rights Protection Act (PDRPA) were announced in 2009, the public and the private firms launched into DRTS services in Taiwan, in particular, the barrier-free transportation service. Moreover, impaired people whose accessibility the government needs to consider. Thus MOI makes policies with

respect to impaired people. The most important policy is “White Paper of People with Disabilities Right Protection Act (WPPDRPA)”. According to this policy, MOI award municipal authorities social welfare funds. Afterward, municipal authorizes entrust the social welfare organization to operate the bus transport services which the impaired people desire to carry them to the hospitals or the clinic centers, i.e. door-to-door service. In addition, Ministry of Transportation and Communications (MOTC) gives renewed impetus to the barrier-free bus transportation service. Therefore, the bus firms obtain proportional subsidies from the municipal authorities. The goal is that current existing buses are phased out and lower floor buses are gradually joined the bus transportation market. On the other hand, impaired people have a financial burden for accessibility as they are the vulnerable group in our society. The government attempts to provide them wider and low-priced to utilize the transport facilities in order to lighten their burden. According to the “Law of People with Disabilities Having a Discount Rate to Use the Public Transportation Service”, people with disabilities are given a discount of 50% when they ride a domestic public transports. Furthermore, the Fu-Kang bus is one type of paratransit that is only utilized by impaired people. They are given a discount of between 50 and 66.7 per cent taxi- based fare for riding a Fu-Kang bus.

According to Statistical Yearbook of Interior (Ministry of Transportation and Communication R.O.C. [MOTC], 2011), the black bold trend line of the disabled population is illustrated as Fig. 1. It is implied that the market shares of transport service with respect to impaired people are gradually increasing. However, the government, the public and the private bus firms are in a predicament. Although the public bus firm had a superiority of vehicle facilities and human resource over the private one, the public transport department had a rough transport planning for Demand Responsive Transport Service (DRTS). The result of performance was that many of impaired people cannot obtain DRTS service (MOTC, 2011). On the other hand, most of the private bus firm considers the demographic and geographic factors so that they always invest their facilities and operate their transport business in central business districts (CBD) of the cities. They would rather serve citizens dwelling in the CBD then metropolitan outskirts or outlying communities. Due to development of sustainable transportation in Taiwan (Chang, et al., 2002), government must tackle the problem that relates with impaired people whose accessibility. Furthermore, enactments were established, white paper was written and researches were done considerable, government should actually integrate and wisely use these

resources. Most important is that the government ought to establish a fiscal policy belong to barrier-free transport so that the public and private firms will know how to obtain themselves superiority for medical service quality and subsidy in a paratransit duopoly market.

Our paper considers the routing choice of Origin-Destination (OD) points of riders either the public firm or the private firm and determines the effect of the subsidy differentiation in terms of medical service quality, government’s fiscal budget, and social welfare. To do so, in this paper, I assume to establish a spatial competition model with respect to paratransit duopoly market, especially for vanpool taxi service and Fu-Kang bus service between the public and the private firm. The purpose of this paper, therefore, is to analyze riders’ choice of routing and decisions about subsidy differentiation under an asymmetric paratransit duopoly market that comprise both the public firm and the private firm, and I examine the changes in terms of quality of service(QOS), profits, and social welfare.

Remaining sections of the paper are organized. The “Related literature” section introduces the definition and applications of DRTS and gives an overview of related literature.

In “Model” section, I present the model of a paratransit duopoly market in which each bus firm have one type of service configurations. In “Competition between both firms” section, I solve the public and private firms with respect to riders’ expenses, subsidies and quality of service and equilibrium findings. In “Social optimum” I investigate the firm’s profits and social welfare when the public firm receives the subsidies from government and provides the one type of service configurations. In “Concluding remarks” section presents the conclusion and discussion.

0 200000 400000 600000 800000 1000000 1200000 1400000

Disabled Population (Persons)

years persons

Source: MOI, 2011

Figure 1

Most of DRTS applications used in Taiwan is in medical transport. Accessibility and mobility of impaired people are harder than any other citizens when they move to the hospitals or rehabilitation centers.

(Ministry of The Interior [MOI], 2009) enacted the Law of “People with Disabilities Rights Protection Act” and this Law was announced in 2009. The transport vehicle is called the ‘Fu-Kang’ bus. The meaning of ‘Fu-Kang’ word is rehabilitation. According to the previous studies in Fu-Kang bus services, the routing planning characteristics and heuristics optimized solutions were analyzed by dynamic and real time dispatching method to improve the operational efficiency of vehicle fleets for operators and the service qualities for users (Hsin, 2005; Wei, Wang, Tsai, & Hsin, 2007). Huang, et al. (2006) established the integration and demonstration planning of dial-a-ride bus operational management to improve the operational efficiency of Fu-Kang bus and to match the users’

demand. Chang (2004) used analytic efficiency model to study the integration of the Fu-kang bus service and Mass Rapid Transit (MRT) service in Taipei. As a result, 25%

trips of Fu-Kang bus could be diminished, impaired people could be increased 50% and the revenues could be increased 14% for the operators. Gi (2010) used the Nested Multinomial Logit Model (NMNL) to study the vehicle choice of the elderly people who are conducting medical transportation trips and analyzed the transportation demand of DRTS. As a result, physical characteristics and active ability could significant impact the vehicle choice. Chen, Hsu, Lu, and Kao (2009) used questionnaires survey with respect to elderly people who are willing to take a DRTS bus for their medical trips.

Lin (2005) established the vehicle choice behavior model to analyze the factors of DRTS. As a result, the factors of DRTS are included safety, comfortable, make an appointment and auxiliary.

Chang, Wu, and Chen (2009) used the DEMATEL and the cluster analysis models to analyze the taxi market policies and to improve the factors relationship of between cause and effect. As a result, the key factors of the improvement policy of taxi industry are that the stable operating income could be ensured, the integrity as a taxi industry policy could be accepted.

Huang and Hsu (2009) established the operating profit model to discuss the operating cost between carpool taxi and dial-a-ride taxi services. As a result, according to the riders demand, the authors used this model to analyze which service types could be practicable.

Shyr, Tao, and Hsu (2009) established the heuristic paired algorithm to provide the dynamic paired carpool taxi service in a real time based on the commercial vehicle operation system platform of Intelligent Transportation System (ITS) technology. As a result, authors found the optimization of operational cost, service quality, demand and

efficiency under the carpool condition. Furthermore, Lin (2011) established a bee colony optimization algorithm for improving the transport efficiency with respect to the dial-a-ride problem by numerical examples.

Chang and Chu (2008) aimed at the social welfare maximum and found a solution to optimal vacancy rate and fare for a cruising taxi market under the consideration of maximum willingness-to-pay.

Cho, Chen, and Gao (2009) developed a general the framework for designing the operational model of DRTS. The authors generalized the elements of design, vehicle, stop, route and schedule. In addition, the authors concluded several basic types of DRTS service to provide a guideline for the service provider and planner.

2.2.2.5 Fu-Kang bus in Taiwan

In this section, I attempt to show the entire operations of Fu-kang bus in Taiwan.

Table 2 shows the operation status of the Fu-kang bus at present.

Table 2

The operation status of the Fu-kang bus at 2013 in Taiwan

City/Count y

disabled people

Fare calculations

Numbe rs of Fu-Kan

g bus

Numbe rs of lower

floor bus

Publi cly-o wned

Aut hori zed

Numbers of transport

operation or social welfare

parties

Bus Sizes L/M/

S

derive benefits per person-time

2008

Keelung 26,131 NA

14

8  1 S 4,220

Taipei City

147,742

General fare:

one-third of taxi fare Carpool fare:

34 off discount

225

1,264  7 L/S 324,308

New Taipei City

192,370

General fare:

one of second of taxi fare Carpool fare:

34 off discount

222

628  2 S 22,746

Taoyuan County

100,576

General fare:

one of second of taxi fare Carpool fare:

30 off discount

73

60  1 S 60,260

