Applied Science and Innovative Research ISSN 2474-4972 (Print) ISSN 2474-4980 (Online) Vol. 8, No. 3, 2024 www.scholink.org/ojs/index.php/asir 189 Original Paper Planning for Introducing Electric Buses Based on Ecological and Financial Impacts Hengrui Song, Zhiyuan Zhang, Yang Zhao, Xiaole Zou Chengdu Shude Middle School International Department, 610000, China Received: July 18, 2024 Accepted: August 19, 2024 Online Published: August 28, 2024 doi:10.22158/asir.v8n3p189 URL: http://doi.org/10.22158/asir.v8n3p189 Abstract The transition from fossil fuel-powered buses to electric buses has emerged as a central concern in recent years. Governments worldwide are urging this shift in major urban centers as a strategic response to ecological challenges, particularly issues related to pollution and carbon emissions. The primary impediment to the electrification transition lies in real-world financial constraints. Consequently, comprehending both the ecological benefits and financial intricacies of transitioning bus fleets is paramount. In the initial section of this paper, we formulate a mathematical model to assess the reduction in carbon emissions and pollution resulting from a complete transition of the bus fleet. This model is then applied to the city of Sendai, Japan. By comparing the carbon dioxide and emission gases released by conventional buses with those emitted by electric buses, we can discern the impact of employing electric buses on the urban ecological environment. Moving on to the second section, we present a mathematical model delineating the financial aspects of the transition. We use Sendai as a real-world exemplar for our model. The economic model is categorized into expenditures and revenues. Expenditures encompass the acquisition of electric buses, maintenance costs, and carbon taxes. On the income side, we consider bus fares, revenue from bus advertising, the budget of the bus company, and government subsidies. By subtracting expenditures from revenues, we can ascertain the financial ramifications of transitioning to electric buses. Following the evaluation from both ecological and financial perspectives of the bus fleet's electric transition, a third model is constructed mathematically to address the optimal planning solution for a city aiming to fully electrify its bus fleet within a decade. The objective is to achieve cost-efficiency: to be the most economical while meeting ecological goals. Finally, the cities of Sendai, Kunshan, and Nashville serve as subjects for our model, each providing a tailored solution to the transition planning. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 190 Published by SCHOLINK INC. Keywords Electric buses, Carbon emissions, Financial ramifications, Cost-efficiency 1. Introduction Nowadays, air pollution and climate change have inflicted serious harm on the world. For instance, according to the World Health Organization, air pollution contributes to up to 7 million premature deaths annually. Simultaneously, climate change poses similar health risks. Furthermore, climate change is anticipated to bring about food security challenges, leading to reduced crop yields of staples like rice, wheat, and maize. There are additional adverse effects that won't be elaborated on here. The emergence of these issues has finally sparked intense public concern about air pollution and climate change. One viable solution to address these problems is the gradual replacement of diesel buses with electric buses. This strategy could mitigate the impacts of climate change and air pollution by reducing emissions of carbon dioxide, PM2.5, nitrogen dioxide, and sulfur dioxide. For instance, examining China as a system for evaluation and analysis, traditional oil vehicles emit 1146kg of air pollutants per year, whereas pure electric vehicles emit only 279kg, marking a 75% reduction in gas pollutant emissions. Additionally, pure electric buses solely produce CO2 emissions during the power generation stage, in contrast to diesel vehicles and plug-in buses, whose CO2 emissions are predominantly concentrated during the driving stage. Analyzing the results further, the CO2 emission per kilometer of a 12-meter bus, with a fuel consumption of 38L/100km under China IV standards, is 1103g. In comparison, the CO2 emission per kilometer of a pure electric bus, with a power consumption of 120kWh, is 943g. Electrification leads to a 15%-20% reduction in CO2 emissions compared to diesel vehicles. However, electric vehicles encounter financial challenges. Firstly, the cost of electric buses is high—approximately 2-3 times that of traditional fuel vehicles—raising the operational threshold for enterprises. Secondly, the development of charging infrastructure lags behind. Insufficient dedicated charging stations and slow charging speeds significantly diminish operational efficiency. Urban areas often lack an adequate number of charging points, placing additional pressure on enterprises when driving distances are substantial and necessitate recharging. Considering these factors, comprehensive planning is not only essential but also urgent. 1.1 Question Restatement The problem we are addressing involves a series of steps, which can be outlined as follows: 1. City Selection and Ecological Impact Assessment: - Identify a city with a population of at least 500,000 that currently lacks an all-electric bus fleet. - Develop a model and input the city's data and current situation to comprehend the ecological consequences of transitioning to an all-electric bus fleet, including aspects such as pollution gases and carbon dioxide emissions. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 191 Published by SCHOLINK INC. 2. Financial Implications Model: - Recognizing the financial challenges associated with electric buses, establish a second model. - This model should specifically concentrate on the financial implications linked to the transition to electric buses. - Apply this financial model to the same cities as in the first step to gain a comprehensive understanding of both challenges and benefits. 3. 10-Year Road Map Development: - Utilize our model to assist transportation officials in formulating a 10-year road map for the phased renewal of the electric bus fleet. - Implement this road map model not only in the cities selected in the initial steps but also in two additional metropolitan areas, ensuring a thorough and inclusive approach. 4. Recommendation Letter to Transportation Official: - Based on the results of the first three questions, we wrote the letter in terms of the broker's reliability and effectiveness in addressing environmental issues. 1.2 Analysis of the Question For question 1, we are asked to build a model to show the impact of change to e-bus system will have on environment. We mainly focus on the emission of buses that have impact upon the environment. We divide emissions in to two parts: carbon emission and pollutant emission and build model 1 to evaluate the emission level of each substance, and give a comprehensive index to evaluate the influence of bus emission. And use real data in Sendai to see the effectiveness of e-bus transitional plan. For question 2, we need to focus on the financial impact of the plan. We build model 2 to calculate the cost and the revenue of the transitional plan. Then we plug in Sendai’s data to the model 2 to see whether it can afford the 50% transitional cost. Furthermore, we use the result of the model 2 to give practical advises to Sendai government to eliminate costs in transitional period. The electric transition planning is considered in this section. We seek to find the optimal planning solution that can satisfy the emission reduction goal that we set while being the most economical, the most cost-efficient solution. The finance of the transition is related to the last problem. Containing the price of electric buses, the salvage revenue of diesel buses, the price of chargers and their installation, the price difference between the maintenance of electric buses and diesel buses, and the operational cost. Since we are considering a time span as long as a decade, the inflation of currency must as well be considered. A mathematical function can be established to describe the total finance of the transition; additional equations and in-equation must be set to serve as constraints, some describing the emission goal. At last, we can find the computational result of the planning in each year. 2. Assumptions and Justifications 2.1 General Assumptions Assumption 1: We assume that electric buses do not produce polluting gases when they are traveling, www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 192 Published by SCHOLINK INC. but only when they are generating electricity. Assumption 2: In order to simplify our calculation, we assume that all electric buses that are switched are all of the same type, and there is no difference between large and small. The speed and price of such a replacement electric bus are certain. Assumption 3: I assume that the relationship between the number of conventional buses to electric buses and the carbon emissions found in the first question is true for electric buses in any city. Assumption 4: In solving the second question, we assume that the conversion rate from conventional buses to electric buses is constant and the time period is ten years 2.2 Variables and Definitions variable description t Time vs The velocity of the small bus vm The velocity of the medium bus vb The velocity of the big bus EQjw the annual emissions of bus type j for emission substance w Pj the inventory of bus type j in the statistical year Mj the average annual mileage of bus type j Efjw the emission factor of bus type j for emission substance w E the energy in once electricity  the efficiency of thermal power generation H the enthalpy change that 1 mol carbon interacts with 1 mol oxygen to produce 1 mol carbon dioxide Ms the average annual mileage of the small buses Mm the average annual mileage of the medium buses Mb the average annual mileage of the big buses Ps the inventor of the small buses Pm the inventor of the medium buses Pb the inventor of the big buses ki the electricity cost of bus type i per kilometer Bj the emission factor of atmospheric pollutants from thermal power generation K the ratio that the area use thermal power generation to generation electricity Di, j the annual mileage of Class j vehicles using fuel i Si, j the energy consumption per unit mile of Class j vehicles using fuel i Pi the fuel density of fuel i Gi the net calorific value of fuel i EFi, j the carbon emission factor of fuel i www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 193 Published by SCHOLINK INC. c the concentration of the emission Em the total annual emission S the area of the city Zt the total expenditure Zc the cost of transitioning to electric buses Zr the revenue that will be generated after the replacement Peb the cost of purchasing electric buses and the batteries Pcs the cost of building charging stations Pc the fee of maintaining electric buses and diesel buses Pe the carbon tax Pw the total wage given to the drivers xt the amount of e-buses that are used in year t Pe-bus the expense of purchasing one e-bus pc the price of per unit charging pile np the number of new parking lot build to charge electricity bus pp the price to build a new parking low ce the cost of generating electricity sufficient for an electric bus to travel 1 kilometer cd the cost of purchasing diesel fuel sufficient for a diesel bus to travel 1 kilometer xe the total distance covered by all electric buses during the transitional period xd the total distance covered by all diesel buses during the transitional period T the regular inspection cycle of the diesel/electricity bus cin the cost of each inspection of one diesel/electricity bus pb the cost to change one battery, with the unit dollar tax the carbon tax imposed on per unit of carbon emission w annual wage of drivers Rf the revenue from car fares Rad the revenue from advertisement Rs the subsidy from Japanese government Rb the budget from the government Np the number of passenger Pt the prices of the tickets Ne the number of e-buses with ads Pad 1 the ad-rates on e-buses Nd the number of traditional diesel buses with ads Pad 2 the ad-rates on diesel buses pe the average price per advertisement on electric www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 194 Published by SCHOLINK INC. pd the average price per advertisement on diesel buses F(k) Total cost of transition of the K year k The k’th year xi Number of buses switched from diesel bus to electric bus ß Coefficient of inflation N Total number of buses pi Cost per charging pile fe Price per electric bus We Expenditure on maintenance per EB per year (without battery replacement) Wb Expenditure on maintenance per diesel bus per year 3. Ecological Consequence In problem 1, we will analyze Sendai, a city in Japan situated on the main island of Honshu. It spans approximately 800 square kilometers, with a population of 1.09 million. Thanks to governmental efforts, Sendai boasts a relatively favorable ecological environment. To the northwest lie Okoyama and Nishiyama, where forests are diligently protected and managed to preserve biodiversity, absorb carbon dioxide, and purify water. The southeastern edge of Sendai features pastoral and coastal areas, benefiting from Pacific cold summer sea breezes that extend inland, alleviating rising temperatures in the downtown area. The urban zone, nestled between western mountains and the eastern coast, sees the government strategically arranging green spaces and promoting green building development to enhance carbon dioxide absorption, improve the landscape, and provide leisure opportunities. Despite the government's commendable planning, Sendai faces atmospheric challenges. According to the summary of Sendai's greenhouse gas emissions, carbon dioxide emissions have shown a downward trend in the past decade, amounting to 7.45 million tons in 2021. While Sendai's urban carbon dioxide emissions are comparatively low compared to major cities like Tokyo, Osaka, and Nagoya, the global context reveals that 7.45 million tons of carbon emissions remain relatively high. Many cities worldwide are taking steps to reduce carbon emissions and promote sustainable development. For instance, Helsinki, Finland, estimates annual emissions of 3.2 million tons, and Stockholm, Sweden, estimates 4.5 million tons. One significant factor contributing to Sendai's situation is its reliance on traditional forms of buses, with approximately 50 routes, all serviced by diesel buses and diesel-electric hybrid buses. Therefore, it is imperative for Sendai to implement additional measures to reduce carbon emissions, making the establishment of an all-electric bus fleet an urgent necessity. Through our research, we aim to assist Sendai in addressing ecological and environmental challenges to some extent. The overall plan of our study is shown in the figure below. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 195 Published by SCHOLINK INC. Figure 1. Modeling Process 3.1 Reduction of Polluting Gases To thoroughly assess the impact of electric buses on Sendai's ecological environment, our first step is to gather information on the current environmental conditions in Sendai and the existing bus data. By consulting the Sendai Transportation Bureau's website, we can glean insights into the current bus fleet in Sendai, which includes: Table 1. Different Bus Classes in Sendai Type Number of bus Large size General type 7 Low floor 419 Medium size Low floor 28 Small size 12 All 466 To streamline our calculations, we assume that the "general type" and "low floor" large-sized buses are equivalent, resulting in three distinct bus categories: "Large size buses," "Medium size buses," and "Small size buses." Next, we delve into the analysis of emitted pollutants from different bus types. For this study, we employ the COPERT IV model to calculate bus emission factors in Sendai City. The COPERT model, originating from research conducted by the European Commission (EC) on vehicle emission factors, draws upon a wealth of reliable experimental data. It is designed to be compatible with the statistical criteria and parameter variables of various countries. Given that Sendai's bus types, vehicle emission regulations, and classification standards closely align with European standards, utilizing the COPERT IV model stands as our optimal choice. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 196 Published by SCHOLINK INC. Regarding the parameters of the COPERT model, key factors include cumulative mileage, the number of buses, travel time, and speed. According to data from the Sendai City Transportation Bureau, the average speed for large, medium, and small buses is 35 km/h, 30 km/h, and 25 km/h, respectively. By inputting these essential parameters into the model through the "emisa" website, we can derive the fundamental emission factors for the three types of buses. Table 2. Emission of Different Bus Classes Types of bus The Emission Factor of Different Substances ( 11   vehkmg ) CO VOC NOx PM2.5 Small bus 2.653 0.075 7.377 0.105 Medium bus 3.105 0.623 11.587 0.261 Big bus 3.306 0.989 12.773 0.492 We discovered that the operational hours of buses in Sendai extend from 8:30 a.m. to 6:30 p.m., totaling 10 hours each day. Throughout the entire year, the bus system operates daily, with the exception of the period from December 29th to January 3rd. Therefore, it operates for 360 days annually, and the annual operation time is as follows: Additionally, we have assumed that the average speed of a small bus (vs) is 35 km/h, the average speed of a medium bus (vm) is 30 km/h, and the average speed of a large bus (vb) is 25 km/h. With the data presented above, we can calculate the average annual mileage (M) for different types of buses using the formula. The resulting average annual mileage (M) is presented in the table below: Table 3. Average Annual Mileage of Different Bus Classes Type of bus The average annual mileage Small bus 1.26×105 Medium bus 1.08×105 Big bus 9.00×104 We use following equation to calculate the emissions of bus.    j jwjj j jww EfMPEQEQ 610 (2) Let EQjw be the annual emissions of bus type j for emission substance w, measured in t· a-1; Pj represents the inventory of bus type j in the statistical year, measured in veh; Mj represents the average annual mileage of bus type j, measured in km· a-1; Efjw represents the emission factor of bus type j for hourst 360010360  (1) www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 197 Published by SCHOLINK INC. emission substance w, measured in g· km-1· veh-1. This approach allows us to calculate the total emissions for each substance: Table 4. Total Emission Level of Different Substances Type of emission Total Emission level(t.a-1) CO 140.152 VOC 39.9155 NOx 535.9098 PM2.5 19.8111 3.2 Reduction of Carbon Dioxide After computing the emissions of these pollutants, the next step is to calculate the carbon dioxide emitted by conventional diesel vehicles. Utilizing the bottom-up method endorsed by the Intergovernmental Panel on Climate Change (IPCC), this paper computes carbon emissions by considering vehicle ownership, unit mileage, fuel consumption, and the fuel carbon emission coefficient. The calculation formula is as follows:   ji ,,, ][Emission ， jiiijiji EFGPSD (3) "Emission" represents the total carbon emission of urban traffic over a specific period, measured in kilograms. The variable "i" signifies the type of fuel consumed by urban transportation, predominantly diesel in the case of all buses in Sendai City. "j" represents the vehicle type in urban traffic. "Di, j" denotes the annual mileage of Class j vehicles using fuel i, measured in kilometers. "Si, j" represents the energy consumption per unit mile of Class j vehicles using fuel i, expressed in L/km or kwh/km. "Pi" indicates the fuel density of fuel i, measured in L/kg. "Gi" is the net calorific value of fuel i, measured in TJ/kg. "EFi, j" is the carbon emission factor of fuel i, kg/TJ or kg/Kwh. To calculate the number of carbon dioxide molecules produced to generate one unit of electricity, we use the following formula: H E nCO   2 (4) E is the energy in once electricity, with the unit KJ; is the the efficiency of thermal power generation; H is the enthalpy change that 1 mol carbon interacts with 1 mol oxygen to produce 1 mol carbon dioxide, with the unit KJ/mol. The energy in once electricity is 33600KJ, and the efficiency of thermal power generation is about 30% to 40%, so we assume it to be 35%. So we can calculate the thermal energy to generate once electricity: 10287KJ35%3600  We know the principle of thermal power generation is the complete combustion of carbon to generate www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 198 Published by SCHOLINK INC. carbon dioxide: )()()( 22 gCOgOsC  (5) 151.393  molKJH (6) Therefore, we can calculate that to generate once electricity, it will produce following amount of CO2. 26.14mol=393.5110287 (7) We observed that electric buses consume an average of 0.736 kWh per kilometer. Consequently, we make the assumption that small buses will consume 0.55 kWh per kilometer, medium buses will require 0.70 kWh per kilometer, and large buses will use 0.80 kWh per kilometer. With this information, we can proceed to calculate the total carbon emissions (mCO2): tPMPMPMm bbmmssCO 5104.426.14)80.070.055.0( 2  (8) Ms represents the average annual mileage of the small buses; Mm represents the average annual mileage of the medium buses, and Mb represents the average annual mileage of the big buses. Ps represents the inventor of the small buses, Pm represents the inventor of the medium buses, and Pb represents the inventor of the big buses. So we get that the carbon emission of the electricity bus system is: t103.8668 4 2 COm (9) Now, let’s consider the pollutant emission if we use electricity bus. We use following formula to calculate the emission of each type of pollutant:   i jiii i jij KBkMPEQEQ -6 , 10. (10) EQi,j represents the annual emission of pollutant j from bus type i, with the unit t·a-1; Pi represents inventory of bus type i, with the unit veh. Mi represents average annual milage of bus type i, with the unit km·a-1. ki represents the electricity cost of bus type i per kilometer, with the unit kWh·km, we have mentioned before this is 0.55, 0.70, 0.80 for small bus, medium bus and big bus respectively. And Bj represents the emission factor of atmospheric pollutants from thermal power generation, with the unit g·kWh. Lastly, K represents the ratio that the area use thermal power generation to generation electricity. By inviting the government websites in Sendai, we get the power structure of Sendai: Table 5. Energy Structure Power Generation Method Percentage of Power Generation Thermal power generation 71.5% Atomic power generation 26.8% Hydroelectric power generation 1.4% www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 199 Published by SCHOLINK INC. Wind power generation 0.3% Other 0% So we get the equation that is showed below. 715.0K We found that the main emission pollutants of thermal power generation is NOx, SO2 and dust. Using formula above, we calculate the emission level of each pollutant: Table 6. Total Emission Level of Thermal Power Plants Type of emission Total Emission level(t.a-1) NOx 165.86 SO2 193.028 Dust 80.528 Compared with the emission of diesel bus system, they have one common pollutant: NOx. We can calculate the percentage reduction of the emission level of NOx: %0.69%100 909.535 865.165-535.909  (11) Switching from a diesel bus system to an electric bus system could result in a nearly 70% reduction in NOx emissions, a significant advantage for atmospheric environmental protection. Although the thermal power generation process for electricity production introduces pollutants such as dust and SO2, these emissions occur at the factory and can be more effectively processed, resulting in substantially lower actual emission levels. In contrast, diesel buses immediately release pollutants like CO, VOC, and PM2.5 into the air at high levels, causing irreversible damage to the environment. The carbon emission factor for diesel is 74,100 kg/TJ, the net calorific value of diesel is 4.3x10 -5 TJ/kg, and the density of diesel is 0.85 g/ml. The energy consumption per unit mile for small, medium, and large buses is 0.33 L/km, 0.35 L/km, and 0.40 L/km, respectively. Moreover, since the bus system exclusively uses diesel as fuel, we can simplify the formula to:   j ][Emission deiseldieseldieseljj EFGPSD (12) Substitute the data, we can calculate the total emission of CO2 of the diesel bus system: t4104.5753Emission  If we change the diesel bus system to electricity bus system, we can calculate the percentage reduction in CO2: www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 200 Published by SCHOLINK INC. 15.5%100% 104.5753 103.8668-104.5753 4 44    (13) A reduction of approximately 15% in greenhouse gases can significantly contribute to slowing down global warming and advancing efforts towards carbon peaking and carbon neutrality. By comparing the annual carbon dioxide emission levels between the diesel bus system and the electric bus system, we can create a histogram to visually depict the disparity in carbon dioxide emissions. Figure 2. Carbon Dioxide Emission Level to Ratio of Traditional Buses and e-buses Graph Furthermore, we can holistically assess the environmental pollution levels of both bus systems by considering all their emissions. Initially, we must convert emissions into concentrations. Assuming an even distribution of emissions from diesel and electric vehicles in the air of Sendai City, we can utilize the following formula to convert emissions into concentrations: S E c m (14) c is the concentration of the emission, with unit t/km2; Em is the total annual emission, with unit t; and S is the area of the city, with unit km2. 3.3 The Results of Reducing Pollution We know that the area of Sendai is 2305 km2, then we can get the concentration of each emissions in the two bus systems: www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 201 Published by SCHOLINK INC. Table 7. Emission for Diesel Bus The Diesel Bus System Emission Concentration of The Emission (t/km2) CO 0.0608 VOC 0.0173 PM2.5 0.0086 NOx 0.2323 CO2 19.87 Table 8. Emission for EBs The electricity bus system Emission Concentration of the Emission (t/km2) SO2 0.0838 Dust 0.0349 NOx 0.0720 CO2 16.78 Subsequently, we can employ a formula akin to the Air Quality Index (API) to compute a comprehensive indicator. Given that the specific calculation methods of API vary by country and region, we will utilize a simplified approach to determine these indicators: 2 25.2 CO DustSOPMNOVOCCO c cccccc index x   By calculation, we can get the index of the two bus system: 0177.0dieselindex 0144.0yelectricitindex Since indexelectricity is smaller than indexdiesel, we are able to make the overall conclusion that electricity bus system is more beneficial to the environment than the diesel bus system. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 202 Published by SCHOLINK INC. 4. Economic Consequences Figure 3. Capital Management Structure When addressing the financial implications associated with the transition to electric buses, we categorize it into two components: costs and profits. The equation is displayed as follows: rct ZZZ  (16) In this equation, Zt represents the total expenditure, Zc represents the cost of transitioning to electric buses, and Zr represents the revenue that will be generated after the replacement. In the following section, we will provide the general formula for each cost component while providing a rough estimate of the transition cost for Sendai. However, as the cost is contingent on decision-making regarding the shift from the diesel bus system to the electric bus system, for the purposes of this discussion, we will assume a continuous and constant rate of the transition process. 4.1 Cost of Switching to e-buses For the Zc component, the expenditure is bifurcated into two segments: one entails the funds required to operate the traditional bus, and the other involves the funds necessary to operate the electric bus. Regarding the cost of electric buses, it encompasses the expenses associated with procuring buses and batteries, the charging infrastructure costs, the construction of charging stations, and the maintenance costs of electric buses, and the emission of carbon dioxide. In this manner, we can derive the formula for Zc. In this formula, Peb represents the cost of purchasing electric buses and the batteries, Pcs represents the cost of building charging stations, Pc represents the fee of maintaining electric buses and diesel buses, Pe shows the carbon tax, and Pw is the total wage given to the drivers. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 203 Published by SCHOLINK INC. weccseb PPPPPZ c (17) 4.1.1 Purchasing Electric Buses Based on the data from the Sendai Transportation Bureau, it is evident that Sendai employs the BYD K9 series e-buses exclusively. We assume that all the electric buses in use are BYD K9 e-buses. Upon consulting BYD's official website, we determined that the cost of an electric bus (inclusive of the battery) is 270 thousand dollars. Therefore, Peb can be expressed using the equation outlined below: In this equation, xt is the amount of e-buses that are used in year t, Pe-bus is the expense of purchasing one e-bus. From the passage above, we are capable to know that Pe-bus is 270 thousand dollar. buse t t Px ebP (18) Bring the data of Sendai in the formula, we can get the cost of purchasing electric buses and the batteries: dollar83 eb 101.258246610270P  (19) Furthermore, to determine Pcs, we need information about the mileage of electric buses. As per the data from the Sendai Transportation Bureau, we find that the average speed of an electric bus is 30 km/h, which is the same as that of a medium diesel bus. Additionally, in the course of addressing the initial question, we established that each bus operates for 3600 hours per year. Consequently, the annual mileage achievable for each electric bus is equivalent to that of a medium diesel bus: 1.08 × 105 km annually. 4.1.2 Cost of Charging Piles A big difference between diesel bus system and electricity bus system is that electricity bus system need charging piles to charge the electricity bus. Every electricity bus will be charged at night at a bus parking lot when it’s not operating. So we think the coast of charging piles consists of two part: the cost of building charging piles and the cost of build new parking lot. We use following formula to calculate the fee: I is the inventor of the electricity bus, with unit veh; pc is the price of per unit charging pile, with unit yuan; np is the number of new parking lot build to charge electricity bus; pp is the price to build a new parking low, with the unit yuan. ppccs pnpIP  (20) For Sendai, since it’s bus system scale is not so big, we think that there is no need to build extra bus parking lot, so we can simplify the Pcs of Sendai to be: ccsSentai pIP  (21) We searched that the cost of per charger is 15000 dollar, so we can calculate that the cost of charging piles: www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 204 Published by SCHOLINK INC. dollarPcsSentai 6106.9915000466  (22) 4.1.3 The Cost of Maintaining During the transition period from the diesel bus system to the electric bus system, there are costs associated with maintaining the existing mixed bus system. This type of cost comprises two parts: the cost of power generation and the cost of maintaining and renewing equipment. To begin with, let's consider the cost of power generation. For diesel buses, power is supplied by burning diesel fuel, while for electric buses, power is generated through thermal power generation. We can formulate the following equation to calculate this component of the cost: Here, ce represents the cost of generating electricity sufficient for an electric bus to travel 1 kilometer, and cd represents the cost of purchasing diesel fuel sufficient for a diesel bus to travel 1 kilometer, both measured in yuan per kilometer. The variables xe represent the total distance covered by all electric buses during the transitional period, and xd represents the total distance covered by all diesel buses during the transitional period (regardless of whether these diesel buses are replaced by electric buses after the transitional period), both measured in kilometers. ddeec xcxcP  1 (23) Upon research, we found that ce is 0.02725 dollars, and cd is 0.03950 dollars. As per our earlier assumption, the bus system undergoes a continuous and constant rate transformation from a diesel system to an electric system. It's evident that the total mileage of diesel buses and electric buses is the same and equals half of the total mileage. Additionally, assuming our transitional period is 10 years (consistent with the condition in problem 3), we can calculate xe and xd: 8 5 102.5164 2 104661008.1 2    total de x xx (24) So then we can calculate the Pc1: dollarPc 788 101.685102.51640.03950102.51640.02725 1  (25) Then let’s consider the cost to maintain and renew equipment. For the two buses, they all need to be regularly inspected and maintained; but for electricity bus, there is one another important component of this cost: the cost of battery replacement. As a result, we get the formula to calculate this part of cost: b i b e iin e i e e iin d i d d i c p T t c T t c T t P                    2 (26) d always represents the diesel bus and e always represents the electricity bus. t represents the time the diesel/electricity bus have been operating during the transitional period of each bus, with the unit day; and T represent the regular inspection cycle of the diesel/electricity bus, with the unit day; cin represents the cost of each inspection of one diesel/electricity bus, with the unit dollar; pb represents the the cost to www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 205 Published by SCHOLINK INC. change one battery, with the unit dollar. Based on data we have researched, we assumed that Td to be 30 days, Te to be 50 days, the cin of diesel bus and the cin of electricity is 1000 dollars. Tb is 2500 days, pb is 150000 dollars per battery. So now we can get the Pc2, by calculating with the help of program, we can get that: dollarPc 7106.6943 2  (27) Now we get the final formula to calculate the cost of maintaining: b i b e iin e i e e iin d i d d i ddeeccc p T t c T t c T t xcxcPPP                    21 (28) So we can get the total pc: dollarPPP ccc 777 108.3793106.6943101.685 21  (29) 4.1.4 The Cost of Carbon Emission To achieve the goals of carbon peaking and carbon neutrality, governments worldwide are implementing carbon taxes on emissions per unit. These taxes are directed towards higher levels of government or environmental protection organizations, further contributing to environmental conservation in various sectors. Hence, we can derive the formula to calculate the cost of carbon emissions: ue taxEP  (30) E is the annual total carbon emission of the area, with the unit t. tax unit is the carbon tax imposed on per unit of carbon emission, with the unit dollar/t. The carbon tax in Japan is 10 dollars per ton, and we have calculate the annual carbon emission level of diesel bus system and electricity system before. We can generally think the average carbon emission level in transitional period is the average of the level of the two system. So we can calculate the cost of carbon emission of Sendai: dollarsPe 6 44 104.22111010 2 104.5753103.8668    (31) 4.1.5 The Cost of Wage We can easily get the formula to calculate the wage expenditure: IwPw 10 (32) w is the annual wage of drivers, and I is the inventor of all buses. We assumed the annual wage of bus driver in Sendai 60000 per year, so we can get the wage cost: dollarPw 8102.7964666000010  (33) www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 206 Published by SCHOLINK INC. 4.1.6 The Total Cost Now, we can finally calculate the total money send out during the transitional period of Sendai: dollar PPPPPZ weccseb 886768 c 10004.510796.2104.2211108.3793106.99101.2582   (34) We can draw a pie cart to see the proportion of each branch's expenditure to total expenditure: Figure 4. Cost Components Pi-chart We found that the bus driver's wages contribute to more than half of the total cost. Therefore, if Sendai wants to eliminate transitional costs, it should consider options such as cheaper labor or technologies like driverless operation. Additionally, purchasing and maintenance also have a relatively large proportion. Plans that aim to eliminate these costs should be considered. Meanwhile, the expenses related to carbon emissions and charging piles are negligible. 4.2 Revenue of Switching to e-buses For the Zr part, it includes first, the fares that passengers pay for the rides. Second, advertising, to be more specific, using electric bus vehicles as an advertising platform will bring additional advertising revenue to the Sendai government. Third, external funding, such as subsidies from the Japanese government. And, Sendai’s government’s budget. In this way, we can get the formula of Zr. bRsadfr +RR+R=Z (35) In this formula, Rf represents the revenue from car fares, Rad represents the revenue from advertisement, Rs indicates the subsidy from Japanese government. Rb represents the budget from the government. 4.2.1 Revenue of Car Fares Rf is the total car fares that can earn, it depends on the number of passengers taking the buses and the www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 207 Published by SCHOLINK INC. ticket prices, thus we can get the formula of Rf. tpf PN =R  (36) In this formula, Np is the number of passenger, and Pt represents the prices of the tickets. According to Sendai's bus station, the average price ticket for each station is 200 yen, which is about 1.3 dollar. We also research that the average daily discharge of Sendai bus system is 50000 people. So we can calculate it’s revenue of car fares during the transitional period: dollar84 f 102.37251.310365105 =R  (37) 4.2.2 Revenue of Advertisement Rad is the total money that buses can earn by being the platform of advertising. It depends on the ad-rates, the number of buses, and different types of buses. As a result, we can get the formula of Rad. 28 )+( =R ad 2e ad 1e ad TpPNppN dd  (38) In this formula, Ne represents the number of e-buses with ads, and Pad1 represents the ad-rates on e-buses. Moreover, Nd represents the number of traditional diesel buses with ads, and Pad2 represents the ad-rates on diesel buses. T represents the total time for advertising, measured in days. pe and pd represent the average price per advertisement on electric and diesel buses, respectively. The division of T by 28 is based on our findings that the advertisement change cycle on buses is typically 28 days. The discrepancy in advertising fees between diesel buses and electric buses in our formula is due to several reasons. Electric buses feature more advanced equipment and electronic screens compared to traditional diesel buses, which tend to be older. As a result, electric buses are more effective in helping other companies achieve advertising objectives, such as attracting more customers, leading to higher advertising costs for electric buses. In our research, the cost of advertising on buses ranges from $150 to $600, influenced by factors such as brand awareness, vehicle type, advertising format, and geographical location. We assumed costs within this range, with the advertising cost for any diesel bus set at $250 and the cost for an e-bus at $500. These amounts are costs for advertising companies but represent revenue for bus companies, specifically the government of Sendai. Based on the data we gathered, we assumed an ad-rate of 2 for e-buses and an ad-rate of 1.5 for diesel buses. Thus, we can calculate the revenue from advertising in Sendai: dollar7 ad 104.1648 28 10365500)2233+2505.1(233 =R   (39) 4.2.3 Government Budget We search that Sendai government has 14 billion yan for the transitional plan, that’s equal to 0.092 billion dollar. So Rb is 9.2×107dollar. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 208 Published by SCHOLINK INC. 4.2.4 Revenue of Subsidy Rs is the subsidies from the Japan government. According to the question we know that 50% of the conversion cost can be covered by external funds. In this case, we believe that this 50% external funding comes from the highest government subsidies in Japan. As we get the total money send out and all other types of revenue, we can now calculate the subsidy and determine whether it’s feasible. The subsidy from government is: dollar RRR badf 87788 ts 102947.1102.9101678.4103725.210004.5 Z=R   (40) And we can calculate the ratio of subsidy in total expenditure to see whether the subsidy is feasible: 50%25.8%100% 105.004 102947.1 8 8     t s Z R (41) Because the subsidy we need is smaller than the maximum level, so we think the subsidy is feasible. 4.2.5 The Total Revenue Similarly, we can draw a pie cart to see the proportion of each branch's revenue to total revenue: Figure 5. Revenue Component Pi-chart We observe that the car fare (48%) and government support (subsidies and budget, 44%) collectively constitute almost half of the total revenue. For the Sendai government, there is room to reasonably increase bus ticket fees as a means to boost revenue. In conclusion, we assert that the transitional plan will absorb a portion of the losses, but the government subsidy can compensate for these losses, rendering the transitional plan acceptable in Sendai. However, our assumption here is that the transitional process continues at a constant rate. In www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 209 Published by SCHOLINK INC. question 3, we will delve into further discussions on how to strategize the process to enhance the financial situation and social perception. 5. 10 Years Plan In order to discuss the plan for transitioning the city's traditional bus fleet to an electric bus fleet within a decade, we aim to identify an optimal solution for the shift from fuel vehicles to electric vehicles, essentially electrifying the bus fleet. Such transitions must take into consideration the primary goal of emission reduction and the associated costs. In this section, we have devised a mathematical model to represent the financial costs incurred during the transition and the emission reduction goals that must be achieved. This model helps identify the most cost-efficient solution for the electrification of the bus fleet. According to our goal, we can make a formula. In this formula, we have adopted an analytical approach similar to that of Samuel et al., 2019, by dividing the transition time-span into multiple periods. We consider the planning horizon as a total of periods, converting the problem into an examination of operations within each period, which are elements of the set T. Additionally, F(k) represents the expense of year k, β denotes the coefficient of inflation, k represents the number of years, xk indicates the number of electric buses switched in that year, oe signifies the cost of operating one electric bus for a whole year, N is the total number of buses, od stands for the cost of operating one traditional bus for a whole year. fe denotes the expenditure of purchasing one electric bus, pk signifies the expenditure of purchasing one electric charging station. rd represents the revenue gained when selling one traditional bus; s1 represents the time needed to maintain electric buses, We is the cost to maintain one electric bus; s2 represents the time needed to replace batteries of electric buses; Wb denotes the expense of one battery. Furthermore, we should focus on the carbon emission condition. To simplify our calculation, we will standardize the models of traditional buses and calculate the emissions per kilometer of traditional buses based on the average carbon emissions of large, medium, and small buses. The formula we utilize is formula (3) tb i tbie i ceiemi MExNMExC    10 1 10 1 )( (43) In order to encourage the government to commit to continuing its support for the electric bus project, our plan must achieve a significant reduction in the city's carbon emissions in the initial years. According to data from the World Environment Information website and the information obtained in the first question, it is evident that replacing all conventional buses with electric buses can result in a 15% reduction in carbon emissions. Therefore, to showcase the effectiveness of our plan in reducing carbon emissions, our target is to decrease the total carbon emissions from buses by approximately 6% within bskeskdkpkek k i d k i iei WxWxrxfpfxoxNox       21 ])([F(k) 1 1 (42) www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 210 Published by SCHOLINK INC. the first three years. With this objective in mind, we aim to identify the solution with the lowest cost. In the initial question, we analyzed the impact of reducing CO2 emissions under different ratios of the number of electric buses to the number of conventional buses. From this analysis, we determined the point at which CO2 emissions were reduced by 6%. Consequently, we found that when carbon emissions reduce by 6%, the optimal ratio of electric buses to traditional buses is approximately 6:4. Figure 6. Emission Goal Chart As a result, after three years, the number of electric buses must greater than 40% of total number of buses. In this way, we are able to get the equation: Nxi i   4.0 3 1 (44) In addition, there are other restrictions. Adding up the number of electric buses that are switched each year must equal the total number of original buses. Therefore, we can get the formula as follows:    10 1i i Nx (45) To determine the limitation on the number of charging stations, I searched for information on the official website of the Transportation Bureau. We discovered that each electric bus requires a dedicated charging station. Therefore, ten years later, the total number of charging stations must be equal to the total number of electric buses. The equation is presented below.    10 1i i Np (46) Besides, in our plan, all electric buses are charged at the same time, so the number of charging stations must be greater than or equal to the number of electric buses at any given moment. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 211 Published by SCHOLINK INC. Zkkpx k i k i ii     ],10,1[, 1 1 (47) All in all, according to our goals and limitation, the comprehensive formula stated as the following integer linear program.    10 1 )(min k kkF  (48) Subject to    10 1i i Nx (50) In the formula above, β is the coefficient of inflation. We're going to analyze Sendai, Nashville and Kunshan. First of all, these three cities have a population of more than 500,000, so they are considered big cities. In addition, these three cities have plans to replace traditional gasoline buses with electric buses, so our group thinks these three cities are good choices to discuss this question. By querying the data, we incorporated the data of Sendai, Nashville and Kunshan into this formula. The data we have queried is shown below: Table 9. Information for Different Cities Sendai Nashville Kunshan Cost of running a e-bus a year 2943 3239 2845 Fuel money for a diesel bus per year 4266 4529 4100 Price of an e-buses 270000 320000 280000 Charging pile price 15000 18000 15000 Money for recycling diesel buses 4000 6000 4200 Time between repairs e-buses 7.3 years 5 years 6.8 years Maintenance fee 1000 2000 1200 Time between repair a battery 12.16 years 9.2 years 10.4 years Taking this data into the model we built earlier, we can conclude that the number of electric buses bskeskdkpkek k i d k i iei WxWxrxfpfxoxNox       21 ])([F(k) 1 1 (49)    10 1i i Np (51) Nxi i   4.0 3 1 (52) Zkkpx k i k i ii     ]10,1[, 1 1 (53) www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 212 Published by SCHOLINK INC. Sendai should replace each year over this decade is as follows: Figure 7. Number of e-buses to Switch in Each Year From this chart, we can find that the overall trend of the 10-year plans of the three cities is that a large number of traditional buses will be converted into electric buses in the first three years, a small number of Great Wall buses will be converted into electric buses in the middle stage of 4-8 years, and a large number of traditional buses will continue to be converted into electric buses in the later period, that is, 9-10 years. Such a plan can better accomplish our goals and reduce government spending as much as possible. 6. Strengths and Weaknesses 6.1 Strengths  Deep and detailed data analysis: Our model has conducted detailed research and analysis on multiple parameters such as operating time, speed, mileage, and searched for a large amount of data, providing sufficient data support for the establishment of the model.  Comprehensive consideration from multiple perspectives: Not only have the carbon emissions of public transportation vehicles and the financial issues of the plan been studied separately, but a comprehensive solution with comprehensive benefits has also been proposed by combining the two in Model 3. 6.2 Weaknesses  Limitations of assumptions: Our model has some assumptions, such as assuming the transformation of e-buses in batches, which may be more complex in reality due to factors such as policies and external environment.  Parameter certainty: Our model has a certain degree of subjectivity in setting parameters that are difficult to find accurate values, such as the advertising parameters of buses and the true average speed of buses in the city. This may affect the accuracy and reliability of the model. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 213 Published by SCHOLINK INC. 7. Conclusion For the first question, we developed Model 1 to precisely calculate and compare the emission levels of the electric bus (e-bus) system against the diesel system. Our findings indicate that transitioning from a diesel system to an e-bus system could result in a 15% reduction in carbon emissions, a remarkable 70% decrease in NOx levels, and a more effective approach to managing various other emissions in Sendai. These results strongly support the assertion that the proposed transition plan will unquestionably yield significant environmental benefits. Moving on to the second question, Model 2 was constructed to assess the total cost and revenue of the transition plan. Our preliminary calculations suggest that the government subsidy required in Sendai is approximately 25% of the total transitional cost, falling within an acceptable range. This implies that the transition plan is financially feasible. Addressing the third question, Model 3, based on the Electric Bus Fleet Transition Planning (EBFTP), was devised to offer a more nuanced and optimized plan for the replacement of diesel buses with electric buses. This model takes into account both environmental considerations, specifically carbon emissions, and financial aspects. We applied Model 3 to three diverse cities—Sendai, Nashville, and Kunshan—to generate tailored and specific electric bus transition plans. References Cai Hao, & Xie Shaodong. (2010). Determination of Emission Factors from Motor Vehicles under Different Emission Standards in China. Peking: Acta Scientiarum Naturalium Universitatis Pekinensis. Li Aimin. (2020). Study on cost management of new energy buses in the whole life cycle. MS thesis. Qingdao University of Science and Technology. Pelletier, Samuel, et al. (2019). The electric bus fleet transition problem. Transportation Research Part C: Emerging Technologies, 109, 174-193. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 8, No. 3, 2024 214 Published by SCHOLINK INC.