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2017美赛E 一篇 O奖 美国数学建模比赛 获奖论文 2017
Team#71672 Page 2 of 22 List of tables 1 Table of individual metrics and final success level for the cur- rent growth plan of Boulder, CO, USA 8 2 Table of individual metrics and final success level for the cur- rent growth plan of Canberra, ACT, AUS 10 3 Table of individual metrics and final success level for our proposed growth plan for Boulder, CO, USA 13 4 Table of individual metrics and final success level for our proposed growth plan for Canberra, ACT, AUS 16 5 Table of the effects of individual initiatives on success level for boulder Co, USA and Canberra, ACt, aUS 17 1 Introduction Smart growth is a strategy used to direct sustainable development of cities particularly those that face rapid urbanization. Smart growth can be eval- uated using the three e's of sustainability economically prosperous, so cially Equitable, and Environmentally Sustainable [2]. More specifically, smart growth can be defined in terms of ten principles [2] 1. Mixed land uses 2. Taking advantage of compact building design 3. Creating a range of housing opportunities and choices 4. Creating walkable neighborhoods 5. Fostering distinctive, attractive communities with a strong sense of lac ce 6. Preserving open space, farmland, natural beauty, and critical envi- ronmental area 7. Strengthening and directing development towards existing commu- nities 8. Providing a variety of transportation choices 9. Making development decisions predictable, fair, and cost effective Team#71672 Page 3 of 22 10. Encouraging community and stakeholder collaboration in develop ment decisions Two cities that have already made considerable efforts in smart growth de velopment, and that have the potential to improve through future grow th plans, are Boulder, CO, USA, and Canberra, ACT, Australia. In this paper, we propose growth plans for both of these cities first by analyzing their current growth, and then by suggesting improvements. In Section 2,we outline a metric we created to quantify the level of success of smart growth in each city. In Section 3, we discuss the current growth plans of boulder and Canberra, and we evaluate their current success by referring to our computed metric. In Section 4, we then propose a plan for future growth of each city, based on the 3 E's of sustainability, the 10 principles of smart growth, and the current growth plans. In Section 5, we assess how our growth plans hold up to a 50 percent increase in population. Finally, we address the strengths of our model and its outstanding issues 2 A Metric for Smart Growth In developing our smart growth success metric, we first developed one metric for each of the ten principles. These metrics were based on the data available for the two cities and some are more mathematically precise than others. Since the most recent growth plans available for Boulder and Can- berra were developed or updated in 2010 and 2012 respectivcly, wc decided that current city statistics were appropriate to evaluate the success of those plans. We use a modification of van Rijsbergen's information retrieval ef- fectiveness measure [9] to merge the metrics for principles that are strongly related, then sum these combinations and compare the result to an optimal valuc. This is our metric for the level of success of smart growth plans 1. Principle 1 is about mixed use land. We identified the ratio of land zoned for mixed use by the city to the city's total land. Based on current values, we determined that an optimal, achievable value for this metric is 0.15 2. Principle 2 concerns building compactly. We found a paper that com- puted compactness of European cities, in part using population den sity in people per square mile [17]. We use population density (di vided by 2000 as neither of our cities will end up with a population density higher than this, even if the population is increased by 50%0 Team#71672 Page 4 of 22 by 2050). The number of people living in an area can easily represent how compactly the buildings in the area are built. The optimal value for this metric is, then 1 3. Principle 3 is about availability of diverse housing. We focused on affordable housing and looked at the planned percentage of newly available housing intended to be permanently affordable according to each city's growth plan. The optimal value for this metric is 25%, 0.25 4. Principle 4 identifies that neighborhoods should be walkable, mcan ing that both workplaces and stores should be in close proximity to residential areas. We use the percentage of people in each city who walk to work as this metric. The optimal value is 25%, or 0.25, which should account for people living in and near mixed use areas. As such, this logically correlates with Principle 1 5. Principle 5 is to develop and maintain the character of individual neighborhoods. This proved to be very difficult to quantify. Our met- ric is to examine how this goal is described in the cities growth plans ind rate their dedication to the goal subjectively on a scale from0 to 1. The optimal value is 1 6. Principle 6 is to preserve open space, farmland, etc. We look at the ratio from open land to total land in the city. The optimal value, which we determined based on the current level of open space in the cities studied, is 0.75 7. Principle 7 suggests redeveloping existing communities instead of building on new land (greenfield development). We did not find data on the extent that each city is doing this currently, so we settled on as signing a rating from 0 to 1 based on the stated goals in thcir growth plans. The optimal value is 1. Since Principles 7 and 5 both concern existing neighborhoods, we have correlated them 8.P1 8 is about providing alternative methods of transportation We use the percentage of people in each city who use an alternative method (i.e. not driving alone)to commute to work. The optimal value for this is 100%, or 1. This is correlated with compact building design, as building compactly allows more space for bicycle lanes, pedestrian trails, bus depots, and train stations Team#71672 Page 5 of 22 9. Principle 9 is about making smart development decisions. One factor of this is that a city is willing to work with private developers onnew development. We subjectively rated this on a scale from o to l based on the cities growth plans. The optimal value is 1 10. Principle 10 concerns engaging community members in development planning. We searched the city growth plan web pages for unique means for community members to give feedback on the plans. We counted these unique means and divided the totals by 12, as we con cluded that 12 different ways that are easily found by us(people rela- tively unfamiliar with the city government websites) should be more than sufficient for community members to provide feedback. The op timal value for this is 1. This is correlated with Principle 9, as another factor of Principle 9 is making development choices that the commu- will expect and be satisfied with As stated above, we correlate Principles 1 and 4, Principles 2 and 8, Prin- ciples 5 and 7, and principles 9 and 10. To combine these metrics we use a modification of the following effectiveness measure originally intended for use on precision P and retrieval P, two variables which interact [9] E=1 a方-(1-a)k We weighted each correlated metric equally, so we set ae=0.5. Because a higher value for each of our principle metrics corresponds to a higher level of success used only the second term made positive. For metrics a and b then this gave us the equation 0.51+0.5 + We then summed the results from each of these four pairs, as well as the metric values for Principles 3 and 6, to obtain a success rating S4+S2.+S57+S910+S3+S6 Finally, we computed the optimal success rating using the optimal values for each metric to be s 4.1875. We compare the computed success rating to the optimal success rating to obtain our final, fractional success level l L We use L to evaluate the success of both the current and proposed growth plans for each city Team#71672 Page 6 of 22 3 Current Growth plans 3.1 Boulder, CO, USA Boulder's growth plan is the Boulder Valley Comprehensive Plan, last up- dated in 2010 [10]. We will evaluate how the city is satisfying each smart rowth principlc 1. Currently Boulder has 5% of its land area zoned as commercial or mixed use [13. Thus, 5% of its land is zoned as mixed use 2. Boulder has a population density of 1107 people per square mile cal culated from city population and area (including open space in the city area)[13]. It is also worth noting that Boulder typically limits buildings, particularly residential buildings, to thrce stories(35 fcct) [18]. This limits the current capacity for housing and redevelopment 3. The median detached home sale price in Boulder is approximately $750,000 [13]. The city plans to preserve existing mobile home parks and to add permanently affordable housing until 10% of the housing stock is permanently affordable [10] 4. Boulder's older, western neighborhoods are predominantly walkable and bakeable, while other parts of the city are not. The city's growth plan specifies plans to make neighborhoods more walkable and de velop more pedestrian trails [10]. In 2011(the date of the last readily available survey)8.3% Of Boulder's working population walked to work [111 5. Boulder's building height restrictions help to preserve views of the nearby mountains [16], which helps to maintain community charac ter. The citys growth plan cites several specific neighborhoods that each have distinct styles(e.g. the historic downtown area)and spec ifies that it will ensure that both redevelopment and any greenfield development will fit into the neighborhoods 6. Boulder has 71 square miles of open space as compared to 25.8 square miles of city space [13]. It is dedicated to preserving"natural areas, environmental and cultural resources, critical ecosystems, water re sources, agricultural land, scenic vistas and land for passive recre ational use, as well as a defined boundary between rural and urban reas [10 Team#71672 Page 7 of 22 7. Boulder plans to complete new development and redevelopment pri- marily in areas where public services already exist (i.e. in existing communities). There is little open land in Boulder that has not al ready been designated as preserved open space [10]. Therefore, rede velopment is boulder's most viable option 8. Boulder has more than 300 miles of bike lanes, paths, and shoulders [15]. It is served by the Colorado Department of Transportation's Re gional Transport District (rTD) public transit system, which consists of local and regional buses as well as light rail trains. Boulder in- tends to continue working with rid to encourage alternative means of transportation and reduce traffic [10]. a commuter light rail train route from Denver, the nearest major city, to Boulder is also under construction [19]. In 2011 (the date of the last readily available sur- vey)36.8% of Boulder's working population commuted to work us ing a method other than driving alone [11] 9. Boulder encourages private development that fits with the city's other goals [10]. It also requires private developers to construct city infras tructure that would directly benefit their project [14] 10. Boulder encourages community engagement in its development de cisions. We easily found 10 unique means for community members to engage with and provide feedback on development planning [12] Table 1 summarizes the metrics described above, as well as the final success level of o7753 3.2 Canberra Act aus The latest growth plan for Canberra was proposed in 2012 by the Aus- tralian Capital Territory government, which outlines outcomes for 2030 1. The ACT's current plan to increase mixed land uses includes devel- opment of existing city centres to create more concentrated centres of commerce and living. The plan does not outline an exact target for land designed for mixed use, but it is clear from the city land map that very little land area is currently zoned for mixed use [5]. We approximate this as 5% 2. Canberra has a population density of 1161 pcople per squarc milc cal culated from the city population and area [4]. The government plans Team#71672 Page 8 of 22 Metric alue P1 0.05 P20.5535 P3 0.1 P40.083 P6 0.733 1 0.368 Q P100.8333 0.7753 Tablc 1: Tablc of individual metrics and final success lcvcl for the current h plan of Boulder, CO, USA to use the area around existing transit routes to concentrate hous ing and commerce development [4]. These initiatives will allow for igher population density and compactness. 3. The ACT introduced an update to the Affordable Housing Action Plan phase ili in 2016, outlining cost thresholds for affordable hous g [6]. This plan maintains the requirement that 20%o of new housing must meet these thresholds [6 4. About 4.5% of people in Canberra walked to work in 2011(according to the most recent, readily accessible survey)[3]. However, people in Canberra rely heavily on vehicle transportation The act's plan outlines goals to increase walking commutes by creating more mixed land spaces, and by developing walking networks around existing rail lines 5. The act government seems concerned with creating new attractive communities with the hope of creating larger centres of commerce and living. In particular, the government suggests making neighbor hoods more focused towards healthy living [4] 6. The act government plans to create new open spaces and maintain existing ones. The mention the need to"enhance Canberras system of public spaces, providing vibrant, pleasant urban parks and places Team#71672 Page 9 of 22 that everyone can enjoy by ensuring they are safe and accessible [4]. In 2008( the most recent, readily available data), the percentage of open space to total area in Canberra was 63.4%l1 7. One of the 9 key strategies in the ACT Plan includes ensuring that everyone has access to"services and opportunities for social interac- tion by reinforcing the role of group and local centres as community hubs"[4]. However, community development seems more directed towards new, attractive, communities [4]. Thus, the value for this metric is 0.5 8. As stated above transportation by car is still prevalent in Canberra despite the relatively new development of a light rail system. Ac- cording to the survey from 2011, 15.8% of people used transportation other than driving alone to commute to work [3I 9. The act government plans to bring new jobs into existing communi ties, and therefore willing to work with private developers. The plan states that the government should provide a framework for private sector innovation and investment [4] 10. Canberra didn't have as many readily accessible means for commu- nity contribution as did boulder on the community engagement and city planning sites, we found 6 distinct ways for the community to of- fer feedback on city initiatives [7[8 Table 2 summarizes the metrics described abovc, as wcll as the final success level of 0.5882 4 Proposed growth plans Boulder and Canberra can adjust their growth plans to accommodate a population that continues to increase over the next 30 years. Using our netric, we determined optimal values for each of the smart growth prin ciples for both Boulder and Canberra. To reach these optimal values, we propose the following growth plans for Boulder and Canberra 4.1 Boulder, co, USa Our proposed growth plan for Boulder involves encouraging the city to continue some initiatives that it already has in place, and adds the follow-

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