Sustainability optimization model of tourism in Juno city based on genetic algorithm

Summary

This study proposes a mathematical model aimed at addressing how Juneau, Alaska, can balance economic benefits, environmental protection, and social well-being when facing sustainable tourism challenges. With the surge in the number of tourists, Juneau is confronted with issues such as environmental degradation, infrastructure pressure, and a decline in residents' quality of life. To promote the sustainable development of the tourism industry, the model in this study has been optimized from multiple perspectives, involving factors such as the number of tourists, overall income, environmental impact, and social satisfaction.

First, the model sets the main objectives, including maximizing economic profit, minimizing environmental burden, and enhancing social satisfaction. Considering the limitations of resources and infrastructure in Juno City, the model takes environmental carrying capacity and infrastructure carrying limits as constraints. Additionally, the model suggests using additional tourism revenue to support environmental restoration, infrastructure upgrades, and community building to promote sustainable tourism development.

To solve this problem, this paper uses a genetic algorithm to solve the model and finds the optimal solution under different combinations of tourist numbers and revenue. Subsequently, we conducted sensitivity analysis, focusing on which factors have the greatest impact on the results. The study found that environmental protection and social satisfaction are crucial for the sustainability of tourism, and effective management of tourist numbers is key to achieving these goals.

On this basis, we extend the model to over-tourism regions such as Bali and Venice, exploring the impact of each region's specific circumstances on optimal strategy selection. Ultimately, the model provides strategies such as directing tourists to less crowded attractions and optimizing resource allocation by adjusting the weight of attractions' appeal and targeted marketing. By analyzing tourists' interests and behavior patterns, the model can identify underdeveloped areas and recommend corresponding promotion strategies. The relationship between the characteristics of attractions and tourists' preferences can be expressed through mathematical formulas.

In summary, the model proposed in this paper provides a scientific decision-making tool for Juneau and other similar tourist destinations, which not only helps promote economic growth but also ensures environmental protection and social harmony

Key words: Overtourism, Optimization Strategy, Community Development, Genetic Algorithm, Targeted Marketing

Contents

I. Introduction  3

1.1 Background 3

1.2 Our works 3

II. The Description of the Problem 4

2.1 Problem statement 4

2.2 Analysis of Specific Issues 4

2.2.1 Analysis of Problem 1 4

2.2.2 Analysis of Problem 2 4

2.2.3 Analysis of Problem 3 4

2.2.4 Analysis of Problem 4 5

III. Basic assumption 5

IV. Glossary & Symbols 5

4.1 Glossary 5

4.2 Symbols 6

V. Models 6

5.1 Analysis and Solving of Question One 6

5.1.1 Model Preparation 6

5.1.2 Model Establishment 7

5.1.3 Results 8

5.1.4 Analysis of the Result 8

5.2 Analysis and Solving of Question Two 8

5.2.1 Model Preparation 8

Model Establishment9

5.2.3 Results 10

5.2.4 Analysis of the Result 10

5.3 Analysis and Solving of Question Three 10

5.3.1 Model Preparation 10

5.3.2 Model Establishment 12

5.3.3 Results 12

5.3.4 Analysis of the Result 13

5.4 Analysis and Solving of Question Four 13

5.4.1 Model Preparation 13

5.4.2 Model Establishment 14

5.4.3 Results 14

5.4.4 Analysis of the Result 15

VI. Error Analysis and Sensitivity Analysis 15

6.1 Error Analysis 15

6.2 Sensitivity Analysis 16

6.2.1 Sensitivity Analysis of Model One 16

6.2.2 Sensitivity Analysis of Model Two 16

6.2.2 Sensitivity Analysis of Model Three 16

VII. Model Evaluation and Promotion17

7.1 Strength and Weakness 17

7.1.1 Strength 17

7.1.2 Weakness: 17

7.2 Promotion 17

Ⅷ. Conclusions 17

8.1 Conclusions of the problem 17

I X. References 18

I. Introduction

Background

Juneau City (Juneau), located in the state of Alaska, USA, is a city dependent on tourism, with about 30,000 residents.In 2023, Juneau set a record of 1.6 million visitors, especially during peak season, receiving about 20,000 visitors daily, mainly driven by cruise tourism. However, although the large number of tourists brought about $375 million in economic income to the city, the excessive number of tourists also raised serious environmental and social challenges. Especially the retreat of Juneau's main tourist attraction—Mendenhall Glacier—has become an obvious sign of environmental pressure. Excessive tourism activities have exacerbated the retreat of the glacier, potentially threatening the long-term appeal of the attraction.

With the increase in the number of tourists, Juneau's infrastructure, resource consumption, and quality of social life have been severely impacted, particularly placing pressure on the lives of local residents. To address these issues, the city of Juneau has taken several measures, such as raising hotel taxes, limiting the number of tourists, increasing visitor fees, and using the additional tax revenue for infrastructure development and conservation projects. However, some residents who rely on tourism income oppose the increased fees, fearing it may lead to a decrease in tourists, thereby affecting their businesses.

Therefore, how to ensure economic benefits while managing and alleviating environmental pressure and enhancing social sustainability has become a key issue for the future development of the tourism industry in Juneau

Our works

Juneau's sustainable tourism management faces a series of challenges, mainly focused on the following aspects:

Tourist number management: As the number of tourists increases year by year, the infrastructure and environmental carrying capacity of Juneau are gradually under greater pressure. How to effectively manage tourist flow to avoid overcrowding and overconsumption of resources has become the core issue of this study.

Policy and measure formulation: Formulating effective tourism management policies, reasonably adjusting the number of tourists, resource consumption, and socio-economic balance, is the key to ensuring the sustainable development of the tourism industry in Juneau.

Balance between income and pressure: While maximizing tourism income, how to ensure that the pressure on the environment and infrastructure does not exceed carrying capacity is a key objective of optimization strategies.

This study aims to optimize Juneau's tourism management strategies by establishing a mathematical model that comprehensively takes into account the number of tourists, income, environmental pressure, and infrastructure burden, thereby achieving comprehensive sustainable development in economic, environmental, and social aspects

II. The Description of the Problem

Problem statement

While tourism promotes local economic development, it can also have a profound impact on local resources, the environment, and the community. Juneau, Alaskafaces the challenge of balancing between attracting tourists and protecting the natural environment. Every year, more than1.6 million tourists flood in, putting great pressure on local infrastructure, social environment, and natural attractions likeMendenhall Glacier. Although tourism brings in$375 million annually to Juneau, the overwhelming number of tourists overburdens the infrastructure and exacerbates environmental and social issues.The retreat of Mendenhall Glacieris a microcosm of this problem, where excessive tourist activities directly accelerate the depletion of natural resources, potentially threatening Juneau's core tourist appeal in the future. To ensure the long-term sustainability of tourism, a balance must be found between economic benefits, environmental protection, and social equity. Therefore, this analysis focuses on how to optimize tourism development and establish a sustainable economic model without harming the environment and community.

Analysis of Specific Issues

2.2.1Environmental Pressure and Carbon Footprint

Environmental pressure is particularly evident in the tourism industry of Juneau, especially against the backdrop of a sharp increase in the number of tourists. The influx of too many tourists has exerted tremendous pressure on local natural attractions, especially the Mendenhall Glacier's retreat, reflecting the ecological damage caused by overtourism. In addition, the issue of tourists' carbon footprints cannot be ignored, particularly since most tourists rely on high carbon emission transportation methods such as cruise ships, which further exacerbates the emission of greenhouse gases. Reducing the carbon footprint should become a key element of Juneau's sustainable tourism strategy, including promoting low-carbon travel methods, developing green tourism, and adopting environmentally friendly technologies. Furthermore, Juneau also needs to strengthen infrastructure construction, particularly in transportation, energy, and waste management, to reduce overall carbon emissions and resource consumption.

2.2.2Social Impact

While local residents enjoy the economic benefits brought by tourism, they also face a series of social issues. With the increase in the number of tourists, the cost of living and daily stress rise, especially with housing shortages and declining quality of life. Additionally, the overcrowding and noise brought by tourists may cause dissatisfaction among residents, particularly those not reliant on the tourism industry. The Juneau community is divided on attracting more tourists: residents dependent on tourism seek to increase income by attracting more tourists, while another group wishes to limit the number to protect their quality of life. Balancing the interests of these different groups has become an important challenge for sustainable tourism development. To alleviate social pressure, the city of Juneau must enhance and upgrade infrastructure to ensure it can accommodate more tourists without affecting residents' quality of life. Meanwhile, sustainability should be considered when increasing infrastructure investment by adopting environmentally-friendly measures such as green buildings and renewable energy, and reducing environmental burdens by improving public transportation and increasing waste treatment capacity.

2.2.3Objective Optimization

(1)Economic Goal:Increase per capita tourist income, avoid solely relying on total tourist numbers

The tourism revenue of Juneau is dependent on the number of tourists, but over-reliance on the total number of tourists can lead to environmental and social issues, and may result in a decline in tourist experience. To achieve sustainable development, we should shift our focus from simply increasing the number of tourists to raising per capita tourist income, which not only increases economic benefits but also alleviates the pressure brought by excessive numbers of tourists. Specifically, the optimization of economic goals can be achieved through the following methods:

1.Increase tourist spending: Increase each tourist's spending level by raising ticket prices and adding additional fees (such as environmental protection charges, special event tickets, etc.).

2.Increase the proportion of high-value tourists: Attract those willing to pay higher fees through targeted marketing, such as high-end eco-tourism and customized trips. These tourists not only bring higher economic benefits but may also focus more on environmental and cultural protection, promoting the development of sustainable tourism.

3.Develop tourism in non-traditional seasons: Achieve stable year-round visitor flow by enhancing the appeal to off-season tourists, prevent excessive concentration in certain periods, and relieve the pressure on the environment and infrastructure during peak seasons

(2)Environmental Goals:Alleviate the carrying pressure on core attractions and protect natural resources

Mendenhall Glacier and other attractions experience a rapid decrease in carrying capacity under excessive tourist conditions. To ensure the sustainability of these attractions, environmental goals must be established to control the number of visitors and the intensity of activities. Specific environmental goal optimization can include:

•Visitor Count Control: Set a daily visitor limit based on the maximum capacity of each attraction. This not only reduces the physical burden on attractions but also lessens the environmental impact from visitors (such as trash, noise, carbon emissions, etc.).

•Environmental measures: While increasing tourist income, invest in ecological conservation and resource restoration, such as funding glacier protection, reducing greenhouse gas emissions, and promoting green travel methods. Use these funds for environmental restoration projects by charging environmental fees or taxes.

• Development of alternative attractions: Reduce over-reliance on core attractions like Mendenhall Glacier, develop

Develop new attractions or optimize the management of existing attractions to disperse visitor flow and reduce the pressure on any single attraction.

Figure1

2.2.4 Key Constraints

(1) Tourist attraction capacity:

The maximum carrying capacity of each tourist attraction is a key factor in formulating sustainable tourism strategies. If the number of visitors exceeds the carrying capacity of an attraction, it will not only exacerbate environmental damage but may also affect the visitor experience, causing the attraction to lose its appeal. Based on this consideration, the maximum number of visitors for each attraction (carrying capacity) should be set in the model, and the number of visitors received daily should be dynamically adjusted according to factors such as visitor distribution and tourist seasons. By setting this constraint, the development of the tourism industry can ensure that irreparable damage is not caused to natural attractions.

(2)Infrastructure Capacity:

Infrastructure is the foundation for the smooth operation of Juneau's tourism industry. If infrastructure (such as roads, electricity, water resources, waste treatment facilities, etc.) cannot support too many tourists, it may lead to an overload of public services, thereby affecting the quality of life of residents and the experience of tourists. To optimize infrastructure capacity, the model should include predictions of infrastructure demand, and balance tourist flow with the infrastructure's carrying capacity by adjusting the number of tourists or changing the timing of tourist activities.

III. Glossary & Symbols

IV.Modeling Process and Concept

Problem Understanding and Modeling Background Analysis

Specifically, the tourism industry in Juneau must balance economic benefits, environmental impact, and social well-being. To optimize sustainable tourism in Juneau, we need to design a model that comprehensively considers economic income, environmental burden, and social impact, with the optimization goal of finding an appropriate balance among these three aspects.

4.1.1Optimization Factors

•Economic benefits: Mainly composed of the number of tourists, tourist spending (including tickets, accommodation, dining, etc.), and tourist taxes or additional fees.

•Environmental impact: Consider the pressure on the environment due to the number of tourists, such as carbon emissions, waste generation, and site degradation.

•Social Satisfaction: This includes tourist satisfaction and resident satisfaction to ensure social sustainability and avoid social conflicts caused by excessive tourism.

We need to optimize the model so that Juneau achieves a balance between tourism revenue and other benefits (such as environmental protection and social well-being).

4.1.2Constraints

When modeling, we need to set multiple constraints to ensure the model's rationality:

•Environmental carrying capacity constraint (M): There is an upper limit to the carrying capacity of attractions for tourists, exceeding this capacity may lead to severe environmental damage or a decline in visitor experience.

•Infrastructure capacity (K): Local infrastructure, such as transportation, power, water sources, etc., must be able to accommodate visitor flow. If the capacity is exceeded, it may lead to overloading of infrastructure, affecting the visitor experience and local residents' lives.

•Community Acceptance (L): Local residents have a limited tolerance for the number of tourists, and if the number is too high, it may cause social discontent and affect local social stability.

4.1.3Expenditure Plan for Additional Income

In the use of income, additional income (such as tourist taxes or surcharges) should be used for: •Environmental protection: including site restoration, reducing carbon emissions, waste management, etc.

•Infrastructure investment: Used to enhance local transportation, energy, and waste management systems, ensuring the infrastructure can accommodate more tourists.

•Social welfare: Including increasing housing supply, improving public service levels, supporting community cultural projects, etc., to enhance residents' quality of life.

These expenditures will be fed back into the model, indirectly enhancing the tourist experience, reducing environmental burdens, and increasing community acceptance of tourism through environmental restoration, infrastructure improvements, and social welfare investments.

Goal Setting and Optimization

4.2.1Objective Function

We can divide the objective function into several parts, mainly optimizing economic benefits,environmental impact,and socialwelfare in three major aspects.

(1)Maximization of Economic Benefits

We hope to maximize the total revenue of Juneau City's tourism. Specifically, the income mainly comes from tourists'expenditures (including tickets, accommodation, dining, etc.) and additional fees (such as ecological protection fees)=

= Maximize (1)

Where: V is the number of tourists; P is the average expenditure of tourists (which may include tickets, accommodation, dining, etc.); T is the tourist tax or additional fees.

(2).Minimization of Environmental Load

To reduce the environmental burden, we need to minimize the carbon emissions and environmental restoration costs generated by tourist activities. The environmental burden can be represented by the number of tourists, each tourist's carbon footprint, and environmental restoration costs.

Environmental Impact =g(V,C,R)= Minimize (2)

Among them: V_i is the number of tourists, directly affecting the environmental burden; Cis the carbon footprint per tourist, which can be estimated by their mode of travel (e.g., cruise);Ris the cost of environmental restoration.

(3).Maximizing Social Satisfaction

Social satisfaction includes tourist satisfaction and resident satisfaction. We aim to maximize tourist experience and residents' quality of life, avoiding the negative impacts of overtourism on the community. The social satisfaction function can be expressed as:

Social Impact =Maximize (3)

Among them:Ziis tourist satisfaction, which directly affects the quality of life of residents;Wiis the satisfaction of residents, usually determined by factors such as the number of tourists, the burden on infrastructure, and social management policies. The satisfaction of residentsWimay be a nonlinear function of the number of tourists, and as the number of tourists increases, the satisfaction of residents decreases.

4.2.2Constraints

(1)Environmental carrying capacity constraint

There is a maximum carrying capacity of the environment, and the number of tourists must not exceed this limit, otherwise it will have an adverse impact on the environment and tourist experience

(2)Infrastructure Capacity Constraints

The capacity of infrastructure has a direct impact on the number of tourists. If the infrastructure is overloaded, it will affect the tourist experience and increase the environmental burden.

(3)Community Acceptance Constraint

The acceptance and tolerance of local residents have a restrictive effect on the growth of the number of tourists.

4.2.3Model Solving

To solve this multi-objective optimization problem, theWeighted Sum Method and the Pareto Optimal Method are often used. Here we briefly introduce them:

(1) . Weighted Sum Method

The Weighted Sum Method is a commonly used approach for solving multi-objective optimization problems. It simplifies the multi-objective optimization problem by linearly combining multiple objective functions into a single aggregate objective function. In practice, each objective function is assigned a weight, and then they are summed up to form a single objective function. The ultimate optimization goal of the model is to maximize (or minimize) this aggregate objective function.

(2). Pareto Optimal Method

Pareto Optimal Method is a multi-objective optimization method, which differs from the Weighted Sum Method as it does not combine multiple objectives into a single objective, but rather seeks the Pareto optimal set by comparing the strengths and weaknesses of different solutions. A Pareto optimal solution is one where no other solution can outperform it on all objectives simultaneously.

A Pareto optimal solution (also known as a non-dominated solution) refers to a solution for which no other solution is better in all objectives. If a solution is better than another solution in at least one objective and no worse in others, it is said to "dominate" the other solution. If a solution cannot be dominated by any other solution in all objectives, it is a Pareto optimal solution.

Table1Comparison between Weighted Sum Method and Pareto Optimal Method

To solve this multi-objective optimization problem, we can use the weighted sum method or the Pareto optimal method. Here we use the weighted sum method to combine the three objective functions into a single objective function:

Maximize (4)

V. Optimization and Solving Methods

Solution method

5.1.1Linear/Non-linear Programming

If the objective function and constraints are linear, the Simplex Method or Interior Point Method can be used to solve them. The Simplex Method finds the optimal solution through iterative searches along the vertices of the constraint space and is suitable for small- to medium-scale problems; the Interior Point Method starts from the interior of the constraint space and is suitable for handling large-scale problems. If the objective function or constraints are nonlinear, nonlinear programming (NLP) methods such as the Gradient Descent and Newton's Method need to be used. The former gradually approaches the optimal solution through the gradient of the objective function, while the latter quickly converges by combining second-order derivatives. Additionally, heuristic algorithms such as genetic algorithms and particle swarm optimization can escape local optima and are suitable for handling non-convex optimization problems or complex constraint scenarios. Choosing the appropriate algorithm based on the problem's characteristics can effectively enhance optimization efficiency and the quality of results.

Figure2Comparison of Two Methods

5.1.2Sensitivity Analysis

To ensure the robustness of the model, we can conduct sensitivity analysis to evaluate the impact of different factors on the results. For example:

(1).Number of tourists: Sensitivity of the number of tourists to income, environmental burden, and social impact. An increase in the number of tourists will directly boost total income, but it will also increase the pressure on infrastructure and environmental burden, potentially leading to a decrease in resident satisfaction.

(2).Additional fees:The impact of different additional fees (such as environmental protection fees, tourist taxes) on income and environmental protection

(3).Impact. Reasonable additional fees can increase revenue and be used for environmental protection, but if too high, they may have a negative impact on the number of tourists.

(4).Weight setting:Different weight settings will affect the optimization focus (e.g., placing more emphasis on economic benefits or environmental protection). By adjusting weights, one can balance the relationship between economic, environmental, and social goals.

(5).Other key factors:For example, the average spending level of tourists, the proportion of infrastructure and environmental protection expenditures, tax rates, etc. Changes in these factors can have a significant impact on the optimization objectives and constraints of the model.

We can analyze the impact of changes in factors such as tourist tax, limits on the number of tourists, and infrastructure investment on total revenue, environmental impact, and social impact. Through sensitivity analysis, it is possible to determine which factors have the greatest impact on the results, thereby providing more targeted recommendations for decision-makers.

 
Policy simulation and feedback mechanism

5.2.1Policy Simulation

For different policies (such as visitor limits, ecological taxes, etc.), we can simulate and predict their effects. For example, by setting a limit on the number of visitors, we can assess whether it can effectively reduce congestion at attractions, lower environmental impact, and ensure the visitor experience at the same time.

5.2.2Dynamic Feedback Mechanism

The model can include a dynamic feedback mechanism to adjust policies based on real-time data (such as the number of tourists, environmental conditions, etc.). For example, if the number of tourists at a particular site exceeds the expected limit, the model can automatically suggest taking further control measures, such as restricting tourist entry or increasing infrastructure investment.

Global applicability analysis

This model is not only applicable to the city of Juneau but can also be promoted to other cities affected by overtourism. When applying it to other cities, it may need to be adjusted according to each city's cultural, economic conditions, and resource characteristics. For example, some cities may face greater pressure to protect cultural resources, while others may focus more on environmental protection. Based on specific needs, we can flexibly adjust the model's parameters and constraints.

VI. Modeling Results of Sustainable Tourism in Juneau

This study is based on theWeighted Sum Methodto construct the sustainable tourism development model for the city of Juneau and uses a genetic algorithm to solve the model. By optimizing the three major objectives of economy, environment, and society, the model aims to achieve sustainable tourism development, balancing economic benefits, environmental protection, and social satisfaction. Below is a detailed analysis and visual presentation of the model's solution results.

6.1Parameter Definition and Data Overview

6.1.1.Tourist attraction data

The city of Juneau has a total of 5 major tourist attractions, the data related to each are as follows:

•Average tourist spending (P):Average spending per tourist at each attraction, in dollars.

•Additional fees (T):Additional costs for each attraction (such as environmental protection fees, special activity fees, etc.)are in US dollars.

•Carbon footprint (C)：The cost caused by the carbon footprint of each tourist at the attraction, measured in dollars.

•Environmental Restoration Cost (R):The cost required to restore the environment for each attraction, measured in dollars.

•Tourist Satisfaction (Z): Tourist satisfaction at each site, with a rating range from 1 to 10.

•Resident satisfaction (W): The impact of each attraction on local residents' satisfaction, with a rating range of 1 to 10.

We believe that the satisfaction level of residents and tourists is a non-linear relationship related to the number of tourists, satisfying the following relationship:

Z=W=1/ (1 + 0.001 * V) (5)

Table 2Parameters of Economic, Environmental, and Social Impact for Each Attraction in Juneau

6.1.2.Constraints:

•Environmental Capacity (M):The maximum number of visitors for each attraction, restricted based on environmental capacity.

•Infrastructure Capacity (K): The maximum total number of tourists that the overall infrastructure of the City of Juneau can support.

•Community acceptance (L):The maximum number of tourists a community can accommodate, avoiding overcrowding and resident dissatisfaction.

Table3Economic, Environmental, and Social Constraints for Each Attraction in Juneau

6.2Results Display

6.2.1Optimized Results Analysis

By analyzing the optimized tourist number distribution map, we can see that attraction 4 attracted the most tourists, exceeding 1200 people, followed by attraction 2 and attraction 5, each attracting around 1100 people. This suggests that these attractions may be the most popular, or they offer a more attractive tourist experience. Attraction 3 had relatively fewer tourists, slightly below 1000 people, which might be due to environmental carrying capacity limits, or because the attraction is relatively less appealing.

The upper part of the chart shows the economic contribution of each attraction. Attraction 4 has the highest economic contribution, nearly 10,000 dollars, which corresponds to the largest number of visitors it attracts. Attraction 1 has the lowest economic contribution, slightly above 6,000 dollars, which may be due to fewer visitors or lower ticket prices and additional fees. The lower part of Chart 2 shows the environmental impact of each attraction. Attraction 4 has the largest environmental impact, exceeding 10,000 units, possibly due to the large number of visitors or high environmental restoration costs. Attraction 1 has the smallest environmental impact, slightly below 5,000 units, possibly because of the attraction's

Figure3Tourist Satisfaction and Resident Satisfaction

The number of tourists is relatively small, or because the cost of environmental restoration at the site is relatively low. The comprehensive economic effect, which is the economic contribution minus the environmental impact, of site 4 is the highest, close to $10,000 , indicating that the site has achieved a good balance between economic benefits and environmental costs. The comprehensive economic effect of site 1 is the lowest, slightly above $5,000 , which may be because the environmental impact of the site is greater, or because the economic contribution is smaller.

Finally, the bar chart of tourist satisfaction and resident satisfaction indicates that tourist satisfaction and resident satisfaction are relatively high for all attractions, but for attraction 3 tourist satisfaction and resident satisfaction are slightly higher than other attractions. This suggests that the attraction is not only providing a good tourist experience but also gaining local resident approval.

Overall, these charts and analysis results provide valuable information for tourism management in Juno City. Through this data, decision-makers can better understand the performance of different attractions and formulate strategies to achieve sustainable tourism goals. For example, Juno City can increase the promotion of attraction 4 to attract more visitors, while carrying out environmental restoration and enhancement of attraction 3 to improve its capacity and appeal. Additionally, improving the infrastructure and service level of attraction 1 may help enhance the experience of visitors and residents, thus increasing overall satisfaction. Through these measures, Juno City can achieve sustainable development in tourism while protecting the environment and enhancing residents' well-being.

Figure4The Impact of the Number of Tourists on Other Factors

6.2.2Sensitivity Analysis

(1).Influence of Different Weights on the Tourism Model

To further explore the factors affecting sustainable tourism development, we investigated different weights for influencing factors. We selected the following different influencing factors: weight_combinations = [

0.4, 0.3, 0.3; % Initial weights

0.3, 0.3, 0.4; % Increase in environmental goals

0.5, 0.2, 0.3; % Economic targets increased

0.3, 0.5, 0.2; % Increase in social goals

Environmental impact

From the environmental impact diagram, it is evident that different weight combinations have significant differences in environmental impact. When the weight of social goals increases (weights 4), the environmental impact is relatively lower. This may be because the increase in social goals leads to a decrease in the number of tourists, thereby reducing environmental pressure. Conversely, when the weight of economic goals increases (weights 3), the environmental impact is greater. This might be because, in pursuit of higher economic benefits, the number of tourists increases, leading to a heavier environmental burden.

Economic contribution

The economic contribution chart shows that when the weight of economic goals is the highest (weights 3), the economic contribution is greatest. This indicates that in pursuit of maximum economic benefits, significantly increasing economic income can be achieved by boosting the number of tourists and increasing consumption. However, when the weights of environmental or social goals increase, the economic contribution is relatively lower. This is because to protect the environment and social welfare, it may be necessary to limit the number of tourists or increase environmental taxes, thereby affecting economic returns.

Comprehensive economic effect

The comprehensive economic effect chart shows that when the weight of economic goals is highest (weights 3), the comprehensive economic effect is greatest. This indicates that while maximizing economic benefits, if environmental impacts can be effectively controlled, a high comprehensive economic effect can be achieved. When the weight of environmental goals is increased (weights 2), the comprehensive economic effect decreases somewhat, possibly because measures taken to reduce environmental impact (such as limiting the number of tourists) affect economic benefits.

Figure5Changes in Environmental Factors Under Different WeightsFigure6Changes in Total Economic Effect Under Different Weights

(2).Impact of Different Ticket Prices on the Tourism Model

• Environmental Impact

Analysis: The environmental impact chart shows the environmental impact on various attractions at different ticket prices. As ticket prices increase, the environmental impact tends to decrease in most attractions. This might be because higher ticket prices limit the number of visitors, thereby reducing environmental pressure. Observation: Among all the prices, attraction 4 has the greatest environmental impact, possibly due to high visitor attraction or lower environmental carrying capacity.

• Economic contribution

Analysis: The economic contribution chart shows that as ticket prices increase, economic contribution also increases. This is because higher ticket prices directly increase revenue, although they may reduce the number of visitors. Observation: attraction 4 in all

The highest economic contribution under the price indicates that it may be the most popular attraction or offer a higher added value.

Satisfaction

Analysis: The satisfaction chart indicates that different ticket prices have relatively little impact on the satisfaction of tourists and residents, but the overall satisfaction varies between different attractions. Observation: Attraction 3 has slightly higher satisfaction, possibly because it strikes a better balance between the tourist experience and residents' lives.

Number of tourists

Analysis: The visitor number graph shows that as ticket prices increase, the number of visitors generally decreases. This is because higher prices may suppress the demand of some visitors. Observation: Attraction 4 has a high number of visitors at all price levels, indicating it has strong appeal to tourists.

Comprehensive economic effect

Analysis: The comprehensive economic effect chart combines economic contribution and environmental impact, showing the net economic effect at different ticket prices. Higher ticket prices usually lead to a higher comprehensive economic effect, but this effect varies between attractions. Observation: Attraction 4 has the highest comprehensive economic effect, indicating that it strikes a good balance between economic benefits and environmental costs.

Figure7Parameter Sensitivity Analysis

Figure8Changes in the number of visitors at different ticket pricesFigure9Changes in economic factors affecting different ticket prices

Figure10Changes in environmental factors under different ticket pricesFigure11Changes in total economic effects under different ticket prices

VII. Migrate to tourist destinations affected by overtourism

7.1Influence of choosing a travel destination

Different tourist destinations face different challenges, so when transferring Juneau's sustainable tourism model to other destinations affected by overtourism, the unique circumstances of each destination must be considered. Here is an example analysis of two typical tourist destinations:

Bali:

•Environmental Challenges: Bali attracts global tourists with its unique beaches and coral reefs, but excessive tourism development is leading to beach pollution, coral reef degradation, and overuse of water resources. Environmental protection in this area is clearly the top priority.

•Economic Dependency: Tourism is the main economic pillar of Bali, and any measures that might lead to a reduction in tourists (such as limiting tourist flow) could cause economic losses. Therefore, a balance must be found between environmental protection and economic benefits.

Venice:

•Heritage Protection:The historic center of Venice is a world-renowned cultural heritage site. The massive influx of tourists, especially cruise ship visitors, has caused physical damage to historic buildings and overloading of infrastructure.

• Resident quality of life: Apart from cultural preservation, Venice also faces the issue of declining quality of life for residents. An excessive number of tourists impacts the daily life of local residents and has sparked social protests. Therefore, optimizing tourist flow and increasing resident satisfaction are also crucial goals.

When choosing different places, the following factors will affect the most important measures:

Priority of environmental protection:

For destinations that rely on natural landscapes, such as Bali, environmental protection may be the most important goal. This might require measures such as reducing the number of tourists, controlling tourists' carbon footprint, and promoting ecotourism.

Relatively speaking, for destinations rich in cultural heritage, such as Venice, protecting historical heritage and preventing damage to buildings from tourists may be more of a priority.

Protection of Cultural and Historical Heritage:

For places with important cultural or historical heritage (such as Venice), it may be necessary to increase the weight of social goals (resident satisfaction and cultural protection) in the model. This helps to better balance the conflict between cultural preservation and tourism development.

Community acceptance:

The acceptance of the community is an issue that most tourist destinations must consider. The increase in the number of tourists may overload infrastructure and lead to dissatisfaction among residents. Therefore, it is essential to reasonably control the number of tourists and optimize the distribution of tourism.

7.2Model Adjustment

To adapt to different tourist destinations, we need to make the following adjustments:

7.2.1Environmental Carrying Capacity (M) and Infrastructure Capacity (K):

•In resource-scarce areas (like Bali's coral reefs or Venice's historical sites), the environmental carrying capacity can be appropriately reduced (M) value to reflect the pressure on natural landscapes or cultural heritage.

•We can also appropriately reduce the infrastructure capacity (K) to simulate an infrastructure overload scenario. For example, Venice's infrastructure is already at its limit, so the number of tourists must be strictly controlled.

7.2.2Tourist Expenditure and Additional Costs (P and T):

•The consumption level of tourist destinations usually varies, with relatively low tourist spending in Bali compared to higher tourist spending in Venice. Therefore, the consumption levels of tourists (P) and additional costs (T) should be adjusted according to the actual situations of different destinations. For example, by increasing the admission fees or other additional charges in Venice.

Costs to increase revenue, or by reducing costs in Bali to attract more tourists, while also considering the impact of these measures on the number of tourists.

7.2.3.Weights of the objective function (alpha, beta, gamma):

•Bali:Due to the importance of environmental protection, the weight of environmental goals (β) should be increased to ensure that eco-tourism and environmental protection are prioritized.

•Venice:Due to the importance of protecting cultural heritage and resident satisfaction, the weight of social goals (γ) can be increased to ensure a balance between cultural heritage and residents' quality of life.

7.3Promote attractions or areas with fewer tourists:

To alleviate the pressure caused by overtourism, this model can be used to promote attractions or areas with fewer visitors. Methods include:

(1).Adjust the weight of the attractions:

In the model, assign higher weights to attractions or areas with fewer tourists to increase their appeal. For example, in Venice, reducing the concentration of tourists at certain historical sites can guide them towards less-popular cultural attractions.

For Bali, reducing tourists' overreliance on beaches can be achieved by increasing the emphasis on non-beach attractions, such as cultural villages or mountainous areas.

(2).Targeted Marketing:

An additional constraint or objective function term can be introduced in the model to direct tourists toward these less-visited attractions. For example, enhancing the spending level of these attractions (such as tickets, additional fees, etc.) to attract more tourists.

Methods of targeted marketing include enhancing the promotion of less popular attractions, creating more attractive travel packages, or promoting less crowded areas through online platforms.

(3).Optimize travel times:

By changing the time distribution of tourist flows, tourists can be prevented from concentrating during certain peak periods. For example, tourism can be promoted during off-peak seasons through models, using the low season to disperse tourist flows and reduce pressure on attractions and infrastructure.

For example, for Bali, tourists are encouraged to visit inland attractions during the rainy season, while in the dry season they are encouraged to choose less crowded beaches or eco-tourism activities.

7.4Summary

By implementing the above policy recommendations, the city of Juneau can achieve sustainable development of tourism while protecting the environment and society. These policies are not only applicable to Juneau but can also serve as a reference for other tourist destinations facing similar issues.

VIII.Memorandum

To:Juneau City Tourism Committee

Subject: Predictions, Measures, and Optimization Suggestions for Sustainable Tourism Development in Juneau Dear Members of the Juneau Tourism Committee,

With the yearly increase in the number of tourists in Juneau, especially driven by cruise tourism, we are presented with opportunities for economic growth, but also face increasingly severe environmental pressures and social challenges. In order to maintain the sustainable development of the tourism industry and ensure the quality of life for residents, here are the forecasts, assessment of measures, and optimization suggestions I propose based on current data and analysis.

1.Future Development Forecast

Based on the 2023 tourism data analysis, the number of visitors to Juneau is expected to continue to grow in the coming years, with cruise visitors projected to reach 2025 1.8 million by . Although this will bring us immense economic benefits (with total revenue expected to reach $4.5 billion), if not properly managed, the excessive number of visitors will lead to the retreat of natural attractions like the Mendenhall Glacier and excessive strain on infrastructure and social resources.

2.Analysis of Management Measures' Effectiveness

To address these challenges, I suggest considering the following measures:

• Increase hotel tax: Raising the hotel tax can provide additional funds for infrastructure construction, alleviating resource constraints

Pressure. This measure is expected to provide funding support for municipal construction projects.

• Imposing a tourist entry tax: Through revenue from the tourist tax, funds can be specifically allocated for environmental protection projects, alleviating excessive

Impact of tourism on the natural environment.

•Limiting the number of visitors: Setting a daily visitor cap can effectively reduce the pressure on attractions during 'peak days'

Enhance the visitor experience and protect natural resources.

•Establish community involvement mechanisms: Improve the quality of life of local residents through subsidies and incentives,

And reduce excessive resentment towards tourists.

3.Optimization Suggestions

To better balance economic interests, environmental protection, and social welfare, here are my optimization suggestions:

• Comprehensive management strategy: Combine the above measures to create a dynamic feedback model, where part of the additional tax revenue is used for infrastructure construction and part is used to support environmental protection projects. This ensures the sustainable development of tourism without impacting the environment and community quality of life.

•Flexible visitor management:By monitoring visitor flow in real-time and dynamically adjusting the number of visitors and resource usage,

Ensure the sustainable use of infrastructure and natural resources.

•Promote secondary attractions: Disperse tourists by increasing promotion of attractions such as rainforest adventures and whale watching.

Traffic, avoid over-relying on popular attractions like the Mendenhall Glacier.

By implementing these measures, I believe Juno City can not only maintain its appeal as a tourist destination but also ensure the sustainable development of its natural landscape and quality of life for its residents.

I X. References

https://abc7.com/post/juneau-alaska-cruise-ship-limits-overtourism/15048713/

Guo Yajun. A New Dynamic Comprehensive Evaluation Method[J]. Journal of Management Science, 2012(4):49-54.

Junsong Jia, Hongbing Deng, Jing Duan, Jingzhu Zhao, Analysis of the major drivers of the ecological footprint using the STIRPAT model and the PLS method—A case study in Henan Province, China [J]. Ecological Economics, 2009(68):2818-2824.

Dantzig, G. B., & Thapa, M. N. (1997). "Linear Programming 2: Theory and Extensions"

Li, X., & Zhang, Q. (2010). "A Comprehensive Comparison of Multi-Objective Evolutionary Algorithms: A Case Study on Two Benchmark Problems"