一种小型机动除冰装置的设计[含全套图纸】【答辩毕业资料】

目录摘要 1Abstract 2前言 31 概论 41.1 道路除冰技术的发展 41.2 国外道路除冰设备的研究现状 61.3 国内道路除冰设备的研究现状 71.4 道路除冰技术的发展趋势 81.5 小型除冰装置的研制现状和发展 82 路面压实冰雪物理力学性质 102.1 路面压实冰雪成因与影响因素 102.1.1 路面压实冰雪分类 102.1.2 路面压实冰雪成因 102.1.3 影响因素 112.2 路面压实冰雪力学性质 122.2.1 抗压强度 122.2.2 抗切强度 122.2.3 相关系数 132.3 压实冰雪破坏准则 142.4 除冰作业性能参数 173 小型机动除冰装置总体设计 193.1 除冰装置整体方案设计 193.1.1 除冰装置的结构特性和工作原理 193.1.2 除冰装置的功率分配 203.1.3 机架设计 203.1.4 行走装置设计 203.1.5 动力装置选定 203.1.6 传动装置选定 214 主要部件的设计及计算 224.1 传动比的确定 224.2 铲冰装置设计 224.2.1 曲柄连杆机构 224.2.2 铲冰刀刀具的设计 224.3 碎冰装置设计 274.4 主要部件结构参数的确定及计算 284.4.1 汽油机计算功率的确定 284.4.2 带传动计算 284.4.3 铲冰刀理论铲冰频率和碎冰刀盘理论转速 294.4.4 减速长轴的尺寸和强度校核 304.5 设计考虑因素 314.5.1 生产效率 314.5.2 除净率 315 结论 32参考文献 33致谢 35 摘要在我国东北、西北的大部分地区，冬季持续低温，积雪数月不化和路面湿滑成为堵塞交通甚至引发恶性事故的重要因素。因此，在寒冷地区如何快速清除公路和城市道路冰雪已成为保证公路安全和畅通的重要任务。目前，世界各国采用的除冰（雪）方法，应用最普遍的有两种，即融解除冰（雪）法和机械除冰（雪）法。融解法是依靠热作用或撒布化学药剂使冰雪融化，其优点是除净率高，但这种方法成本高，且容易造成环境污染。虽然环保型融雪剂已经问世，对环境和植被的影响减少了，但并未彻底根除，因此使用范围受到一定的限制。机械法是通过机械直接作用解除冰雪的危害，虽然除净率较低，但是对环境及植被无污染，能实现冰雪的异地转移，应用范围比较广。针对目前国内外的除雪或除冰车结构复杂、售价高、使用维修成本大、推广和普及困难的发展现状，成功研制具有：机动灵活，操作简单，价格低廉，适合于小型公路和街道的使用的小型机动除冰装置具有广阔的发展前景。关键词：道路；机械除冰（雪）法；机动的；除冰装置；除净率 AbstractIn most parts of China's Northeast and Northwest, winter continues to be cold, that months ofsnow and the road surface is wet become important factors for blocking traffic or even cause afat-al accident. Therefore, how to quickly clear roads in cold regions and urban road snow and ice h-as become to ensure road safety and the smooth flow of important tasks.At present, there are two of the most popular methods of removing ice and snow are adoptedin the world, that is melting ice(snow) method and mechanical deicing(snow) method. Melting ice(snow) method depends on the rmalor spreading chemical agents to make the ice and snow melted,the benefit is that the removing ice net rate is high, but this approach brings the high costs, and it is likely to cause environmental pollution. Eco-friendly snow-melting agents have greater reducedimpact on the environment and vegetation, but not completely eradicated, sousing range is subject to certain restrictions. Mechanical method is a direct role by means of machinery to get rid of hazards of ice and snow, while the removing ice net rate is lower, and there is no pollution to the environment and vegetation, snow off-site transfer and abroad errange of applications could be achieved. In terms of the deicer for ice and snow removal has complex structure at home and abroad,high prices, high maintenance costs and difficult popularization and universal development, successfully create a flexible, simple operation, lowprice, suitable for use on small roads and streets of thesmall motor deicer has broad prospects for development.Keywords:Road; Mechanical deicing(snow) method; Flexible; Deicer; Removing ice net rate 前言在我国北方冬季普遍降雪，特别是一些高寒地区降雪期长达（5-6）个月，积雪给道路、机场及人们出行带来极大的不便，甚至造成交通中断，屡屡发生事故。目前，除雪的常用方式有：机械除雪、融雪除雪、综合式除雪等。机械除雪是通过机械设备清除积雪的方法；融雪除雪是利用热能或撒布化学药剂而使积雪融化的一种方法；综合式除雪是机械除雪与融雪除雪相结合的一种除雪方法。机械除雪应用最为广泛。其除雪效率高、成本低、无污染、但对结冰路面及低等级路面除雪效果差。除雪车在国外已有很多厂家生产如:瑞士的某公司和美国的某公司；德国的某公司。国内在除冰机械的开发和生产比除雪机械的时间还要短，除冰机械按其工作原理可分为以下几种类型。振动式：液压系统驱动振动马达，带动偏心块的旋转，在离心力的作用下，使得振动轮沿圆周径向运动。静碾压裂式：通过悬挂于装载机前端滚压轮上的组合刀片将冰层压碎。柔性链条击打式：采用特制链条，前端安装吊环，在主机的驱动下，链条作高速旋转，对路面进行柔性抽打，从而获得破冰效果。纵观除雪破冰机械的发展现状，现有设备绝大部分功能单一、外形大、价格高。所以研制具有：小巧轻便，操作简单，价格低廉，适合于小型公路和街道的使用且同时具有扫雪除冰功能的设备具有广阔的发展前景。

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关键词：: 一种小型机动除冰装置设计 pdf 全套 cad 图纸答辩毕业资料

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摘要
在我国东北、西北的大部分地区，冬季持续低温，积雪数月不化和路面湿滑成为堵塞交通甚至引发恶性事故的重要因素。因此，在寒冷地区如何快速清除公路和城市道路冰雪已成为保证公路安全和畅通的重要任务。
目前，世界各国采用的除冰（雪）方法，应用最普遍的有两种，即融解除冰（雪）法和机械除冰（雪）法。融解法是依靠热作用或撒布化学药剂使冰雪融化，其优点是除净率高，但这种方法成本高，且容易造成环境污染。虽然环保型融雪剂已经问世，对环境和植被的影响减少了，但并未彻底根除，因此使用范围受到一定的限制。机械法是通过机械直接作用解除冰雪的危害，虽然除净率较低，但是对环境及植被无污染，能实现冰雪的异地转移，应用范围比较广。针对目前国内外的除雪或除冰车结构复杂、售价高、使用维修成本大、推广和普及困难的发展现状，成功研制具有：机动灵活，操作简单，价格低廉，适合于小型公路和街道的使用的小型机动除冰装置具有广阔的发展前景。
关键词：道路；机械除冰（雪）法；机动的；除冰装置；除净率

Abstract
In most parts of China's Northeast and Northwest, winter continues to be cold, that months ofsnow and the road surface is wet become important factors for blocking traffic or even cause afat-al accident. Therefore, how to quickly clear roads in cold regions and urban road snow and ice h-as become to ensure road safety and the smooth flow of important tasks.
At present, there are two of the most popular methods of removing ice and snow are adoptedin the world, that is melting ice(snow) method and mechanical deicing(snow) method. Melting ice(snow) method depends on the rmalor spreading chemical agents to make the ice and snow melted,the benefit is that the removing ice net rate is high, but this approach brings the high costs, and
it is likely to cause environmental pollution. Eco-friendly snow-melting agents have greater reducedimpact on the environment and vegetation, but not completely eradicated, sousing range is subject to certain restrictions. Mechanical method is a direct role by means of machinery to get rid of hazards of ice and snow, while the removing ice net rate is lower, and there is no pollution to the environment and vegetation, snow off-site transfer and abroad errange of applications could be achieved. In terms of the deicer for ice and snow removal has complex structure at home and abroad,high prices, high maintenance costs and difficult popularization and universal development, successfully create a flexible, simple operation, lowprice, suitable for use on small roads and streets of thesmall motor deicer has broad prospects for development.
Keywords:Road; Mechanical deicing(snow) method; Flexible; Deicer; Removing ice net rate

前言
在我国北方冬季普遍降雪，特别是一些高寒地区降雪期长达（5-6）个月，积雪给道路、机场及人们出行带来极大的不便，甚至造成交通中断，屡屡发生事故。
目前，除雪的常用方式有：机械除雪、融雪除雪、综合式除雪等。机械除雪是通过机械设备清除积雪的方法；融雪除雪是利用热能或撒布化学药剂而使积雪融化的一种方法；综合式除雪是机械除雪与融雪除雪相结合的一种除雪方法。机械除雪应用最为广泛。其除雪效率高、成本低、无污染、但对结冰路面及低等级路面除雪效果差。除雪车在国外已有很多厂家生产如:瑞士的某公司和美国的某公司；德国的某公司。
国内在除冰机械的开发和生产比除雪机械的时间还要短，除冰机械按其工作原理可分为以下几种类型。振动式：液压系统驱动振动马达，带动偏心块的旋转，在离心力的作用下，使得振动轮沿圆周径向运动。静碾压裂式：通过悬挂于装载机前端滚压轮上的组合刀片将冰层压碎。柔性链条击打式：采用特制链条，前端安装吊环，在主机的驱动下，链条作高速旋转，对路面进行柔性抽打，从而获得破冰效果。
纵观除雪破冰机械的发展现状，现有设备绝大部分功能单一、外形大、价格高。所以研制具有：小巧轻便，操作简单，价格低廉，适合于小型公路和街道的使用且同时具有扫雪除冰功能的设备具有广阔的发展前景。

内容简介：: Socio-Economic Planning Sciences 36 (2002) 183202Sector design for snow removal and disposal in urban areasA. Labellea, A. Langevina,*, J.F. Campbellba!Ecole Polytechnique de Montr! eal and Gerad, C.P. 6079, succ. Centre-ville, Montr! eal, Qu! e., Canada H3C 3A7bSchool of Business Administration, University of Missouri - St. Louis, 8001 Natural Bridge Road,St. Louis, MO 63121-4499, USAReceived 1 November 1999; received in revised form 1 July 2001AbstractSnow removal and disposal are important and expensive winter operations in many cities. When a largeamount of snow accumulates in an urban area and impedes traffic, the snow must be removed to snowdisposal sites. This paper first briefly describes snow disposal operations in Montreal, Quebec, Canada. Itthen presents models and efficient algorithms for partitioning a city into sectors for snow disposaloperations, and for assigning the sectors to disposal sites. These algorithms are incorporated in adecision support system (DSS) built on a geographic information system. The DSS provides initialsolutions, and allows the planner to interactively design sectors to incorporate difficult constraints. Resultsand some sensitivity analyses are presented for the City of Montreal.r 2002 Elsevier Science Ltd. All rights reserved.1. IntroductionSnow has important economic, environmental, social and political impacts on the inhabitantsof large northern cities 1,2. For each significant snowfall, public works agencies must readilyproceed to spread abrasives and/or de-icers on streets and sidewalks, and to plow the snow aside.However, when the temperature remains below freezing for long periods, snow plowed to the sidesof streets accumulates and impedes circulation of pedestrians and vehicles. In this case, the snowmust be removed from the roadways and sidewalks to maintain mobility. This is usuallyaccomplished by loading snow into trucks, and hauling it away to disposal sites. Snow disposalcan also be required in cities with less wintry climates that experience infrequent, but largesnowfalls, such as was the case in Washington DC for the Blizzard of 96. This major storm*Corresponding author. Fax: +1-514-340-4463.E-mail address: andrelcrt.umontreal.ca (A. Langevin).0038-0121/02/$-see front matter r 2002 Elsevier Science Ltd. All rights reserved.PII: S 00 3 8- 01 2 1 ( 0 1) 00 0 24 - 6closed the United States federal government offices for several days until the snow could beremoved and mobility regained. Snow removal and disposal can be an extensive and expensiveoperation for large municipalities. For example, in an average winter in Montreal, Quebec,Canada, more than 7 million cubic meters of snow in 300,000 truckloads are hauled to disposalsites.For efficient administration and operations, a large city is usually partitioned into sectors forsnow removal, and the removal activities are carried out simultaneously in every sector. A sectormay consist of 2040km of streets that are cleared by a specific crew. Each sector is assigned to asingle disposal site to which all snow from the sector is hauled. The sector design problemaddressed in this paper involves partitioning an urban area into sectors, and assigning the sectorsto disposal sites in order to optimize snow removal and disposal. The problems and costs involvedin spreading de-icers and abrasives, or in snow plowing, are not considered here. Our focus is onthe snow removal and disposal activities that occur after spreading and plowing. We have twogoals: first, to develop an efficient solution method; second, to imbed the method into a decisionsupport system (DSS) utilizing a geographical information system (GIS) to allow the planner tointeractively design the sectors. The remainder of this section describes snow removal and disposalactivities in Montreal.1.1. Snow removal and disposal operationsWith an area of 187km2and more than one million inhabitants, Montreal is the largest city inthe Province of Quebec. The average annual snowfall exceeds 200cm and there are 2000km ofstreets and 3200km of sidewalks to clear of snow. The annual budget for snow removal anddisposal is in excess of 60 million Canadian dollars (note that all money values in this article are inCanadian dollars).Snow plowing begins as soon as the accumulation of snow and ice reaches 2.5cm. Plows pushthe snow to the sides of the roadways and sidewalks to facilitate traffic flow. Once the snow hasstopped falling, a decision is made whether or not to haul it to disposal sites, depending on theaccumulation and weather forecast. Snow disposal operations begin by plowing the snow backtoward the center of the street to form a long windrow, which is then loaded into trucks by asnowblower. All the snow removed from each sector is sent to the same disposal site, formanagerial and contractual reasons. Snow disposal operations are subject to a time limit thatdepends on the total accumulation and the size of the sector. For example, a sector of o25km ofstreets must be cleared within 72h for a snow accumulation of o20cm, within 84h for anaccumulation of 2025cm, and within 96h for more than 30cm of snow.Based on the deadlines for removing snow, and the size of the street network in Montreal, thecity is divided into approximately 60 sectors. A separate crew of personnel and equipment forloading snow (plows and snowblowers) and hauling snow (trucks) is assigned to each sector.There are 20 disposal sites of four types: surface sites, sewer sites, river sites, and a large quarry.The disposal costs vary from site to site according to the equipment used and labor forceoperating a site. The amount of snow sent to each disposal site is subject to a maximum hourlyrate due to constraints on unloading trucks, while the surface sites and quarry are subject toannual limits due to physical capacity.A. Labelle et al. / Socio-Economic Planning Sciences 36 (2002) 183202184A brief review of literature is presented in the next section. In Section 3, the problem isformulated and decomposed into two components for which separate solution methods aredeveloped. Section 4 presents a DSS that integrates the methods in a user-friendly environmentbased on a GIS. Section 4 also describes the data required for the DSS. A complete design ofsectors for Montreal is presented in Section 5, along with several sensitivity analyses. Theconclusion follows.2. Literature reviewManagement science has long played an important role in improving operations in a variety ofurban public service systems 36. Some research has addressed a variety of problems involved insnow removal and disposal for North American cities, and 7,8 review much of the relevantliterature. Routing snow plows and trucks spreading de-icers and abrasives has received the mostattention because these operations are common to snow fighting in all urban and rural regions.Routing problems for spreading and plowing are practical examples of the Chinese PostmanProblem and related arc routing problems 920. These problems are similar to other arc routingproblems such as garbage collection and street sweeping (e.g., see 2124).Interestingly, snow disposal operations have received very little attention. Two fundamentalproblems in this scenario involve assigning sectors to disposal sites, and partitioning an urbanregion into sectors. Leclerc 25,26 was the first to study the problem of assigning sectors for snowremoval and disposal to snow disposal sites. It was modeled as a Transportation Problem wherethe assignment of snow from a given sector was not restricted to a single site. Campbell andLangevin 27 modeled the assignment problem as a multi-resource generalized assignmentproblem. Due to the computational burden of solving large-scale instances, they proposed aheuristic method that combines a penalty-based construction algorithm followed by a 2-optexchange improvement procedure. Reinert et al. 28 considered a related problem and presentedan integer programming model to simultaneously determine locations for salt and sand storagefacilities, and to assign specified vehicle routes to these facilities.The design of sectors for snow removal and disposal has not previously been addressed in theliterature. There is considerable research, however, on other public sector districting problems,such as those involving school districts (e.g. 2932), and political districts (see 33,34 foroverviews). Criteria for districting often include demographic, political and, of course, geographicfactors. Heuristics have generally been employed for districting to capture political and legalconditions, as well as to address the demographic issues especially important in school andpolitical districting. The development of geographic information systems (GIS) has facilitatedredistricting work by simplifying the visual display of what is inherently a spatial problem (see, forexample, 35,36).3. Problem formulationThe result of the sector design process for snow removal and disposal is a set of sectors, each ofwhich is assigned to a disposal site. This requires solving a districting problem to define theA. Labelle et al. / Socio-Economic Planning Sciences 36 (2002) 183202185boundariesofeachsector(bypartitioningageographicregionintonon-overlappingsubregions), and solving an assignment problem to determine which disposal site receives thesnow from each sector. Because the shape and size of a sector may influence its assignment, andvice versa, the districting and assignment problems are interdependent. These decisions are alsosubject to several geographical, economic, and political constraints that are generally difficult tomodel.The costs that affect the sector design procedure include operational (or variable) costs thatdepend on the quantity of snow and/or the distance snow must be hauled, and fixed costs forequipment. Relevant operational costs account for hauling snow from sectors to disposal sites,and for operating snow disposal sites. These costs depend on the assignment of sectors to disposalsites, but not directly on the shape of a sector. Operational costs for loading trucks do not dependon the size and shape of the sectors, since all snow must be loaded, so these costs are notconsidered.Relevant fixed costs account for the number of trucks used to haul snow. Fixed costs to loadsnow (i.e., for snowblowers in Montreal) are not included, because the number of snowblowers isdetermined by the number of sectors, which is set by the level of service specified as deadlines forclearing snow. In Montreal, the City provides trucks for hauling snow in some sectors, whileprivate contractors provide trucks in other sectors. There is no common fixed cost per truck, andthe determination of the number of trucks required for each sector has previously been an ad hocprocedure. Therefore, in this paper, we will seek to minimize the number of trucks required as aproxy for minimizing the fixed costs for trucks. The appropriate number of trucks to employdepends on both the assignment of the sectors to disposal sites, and on the shape of the sector, aswill be described in Section 3.2.A micro approach to sector design would use a single street segment as the unit of analysis.However, this level of detail may lead to very slow response time in a DSS for a large city due tothe huge number of street segments in a large city (around 40,000 in Montreal). One tractableapproach is to define the basic entities as geographic zones that contain a collection of neighboringstreet segments. As zone size increases, both the number of zones and the computational effortrequired for solution decreases, but so does the accuracy. Thus, the zone size captures the tradeoffbetween accuracy and response time of the DSS.The snow disposal sector design problem can be solved by aggregating small geographic zonesinto sectors, and assigning each sector to a snow disposal site (i.e., all the snow removed from agiven sector must be sent to the same disposal site). The zones are specified and, for each zone, thelength of streets is known, as is the annual volume of snow in cubic meters and the distance fromthe farthest part of the zone to each disposal site. A set of disposal sites is specified, and eachdisposal site has both an hourly and annual receiving capacity. The level of service provided isspecified in terms of the maximum sector size to ensure that every sector can be cleared within aspecified time. The number of snowblowers available is specified wherein each sector must containexactly one snow blower. The truck size in cubic meters and the average truck speed are alsoknown.We define the following decision variables:xij 1 if zone i is assigned to sector j and 0 otherwise, andyjk 1 if sector j is assigned to site k and 0 otherwise.A. Labelle et al. / Socio-Economic Planning Sciences 36 (2002) 183202186We define the following operational parameters:dik=distance from zone i to site k (km),li=length of streets in zone i (m),vi=annual volume of snow in zone i (m3/yr),rj=snow removal rate in sector j (m3/h),Vk=annual capacity of site k (m3/yr),Rk=maximum snow receiving rate of site k (m3/h),M=maximum number of zones per sector,tv=truck size (m3), andts=truck speed (km/h).We define the following cost parameters:Cik=cost per cubic meter for hauling snow from zone i to site k ($/m3),CVk=variable cost for disposal site k (e.g., cost for disposal) ($/m3), andCT=fixed cost for trucks ($/yr).The annual volume of snow sent to site k in m3isXiXjvixijyjk:The total cost per year for transporting snow to disposal sites can be approximated byXiXjXkCikvixijyjk:(The cost Cikfor Montreal is described in Section 3.1.) The number of trucks used isNT2dj maxts?rjtv? t;where dj maxis the maximum distance from a zone in sector j to its assigned disposal site:dj max maxi;kfdikxijyjkgand t is the number of additional trucks assigned to a sector. The first ratio in NTis the time ittakes a truck to travel from the farthest zone in a sector to the disposal site and back. The secondratio is the snow removal rate in trucks per hour. The product of these two ratios provides the(possibly fractional) number of trucks that would be filled by a continuously operatingsnowblower during the longest truck trip to and from the disposal site. The additional number oftrucks t helps to account for variability in the truck travel time. The formulation of NTis based onnot allowing the blower to become idle. If t 0; then the blower would be idle whenever theactual travel time is greater than the average travel time to the farthest zone. Values of t greaterthan zero allow the blower to stay busy when travel times exceed the average value.A. Labelle et al. / Socio-Economic Planning Sciences 36 (2002) 183202187The total annual cost ($/yr) can be formulated as follows:TC XiXjXkCikvixijyjkXkCVkXiXjvixijyjk CTXj2rjts?tv?maxi;kfdikxikyjkg? t?:This objective includes three costs: the transportation cost for hauling snow from the sectors tothe disposal sites, the variable cost to operate the disposal sites, and the fixed cost for the trucks.The (non-linear) objective contains the product of the decision variables and a maximumcomponent in the last term.The following constraints apply:Xjxij 1for all zones i;1xijpXkyjkfor all zones i and sectors j;2XixijpMfor all sectors j;3XiXjvixijyjkpVkfor all sites k;4XiXjrixijyjkpRkfor all sites k;5each sector is a contiguous collection of zones; and6xij;yjkAf0;1gfor all i;j;k:7Constraints (1) assure that each zone is assigned to a sector. Constraints (2) link the zone andsector assignments. They assure that if any zones are assigned to sector j; then sector j must beassigned to some site. Note that sectors are not pre-defined and there may be sectors to which nozones are assigned. (For example, if there are 300 user-defined zones and 80 sectors, the solutionmay result in 20 sectors having no zones assigned to them i.e., 20 non-existent sectors.)Constraints (3) limit the size of the sectors to a maximum of M zones. This is to ensure that thespecified level of service can be achieved in terms of the maximum time to clear the snow from asector. This could also be specified in terms of the length of streets in a sector as follows:Xilixijpmaximum length of streets per sectorfor all sectors j:Constraints (4) and (5) limit the assignment of sectors to disposal sites according to the annualand hourly receiving capacity of the disposal sites. Constraints (6) are required to ensure that eachsector is composed of a contiguous set of zones, as discussed below. Integrality constraints (7)prevent fractional assignments.Contiguity constraints (6) are very difficult to write in an efficient or linear form 35. However,without these constraints a sector might consist of several disjoint collections of zones, which isA. Labelle et al. / Socio-Economic Planning Sciences 36 (2002) 183202188undesirable from an administrative standpoint. This can also be operationally undesirablebecause the snowblower would have unproductive travel (i.e., while not blowing snow to loadtrucks) between the disjoint collection(s) of zones. Real-world districting problems are oftenaddressed with heuristic procedures, in which the contiguity condition is more easily handled bysequentially aggregating adjacent zones to build districts, and also by improvement heuristics thatonly consider changes in districts that maintain contiguity.Given that an optimal integer programming solution is not feasible because of the non-linearities in the objective function, and that there are difficulties imposed by contiguityconditions, a heuristic procedure is developed. The global problem of sector design is split intotwo components to be solved sequentially: first, we determine for each disposal site its area ofinfluence as the streets or zones that are assigned to it; and second, partition the area of influencefor each site into sectors. This heuristic of assign first, partition second is analogous to a routefirst, cluster second approach for vehicle routing.The objective for the assign phase is to minimize relevant operational costs; the objective forthe partition phase is to minimize the number of trucks for the given zone assignments.Assigning zones to disposal sites in the first step allows sectors to be defined in the second stepbased on the known assignments. Alternative heuristic approaches that define sectorsindependently of their assignment to disposal sites are possible (such as a partition first, assignsecond, which first aggregates zones into sectors, and then assigns sectors to disposal sites).However, if sectors are created before the assignments to disposal sites are known, then the shapeof the sector may not reflect the assignment. Because the shape of a sector depends on itsassignment (as shown below in Section 3.2), the aggregation of zones into sectors should occursubsequent to (or simultaneous with) the assignment of streets to disposal sites. Section 3.1presents the proposed heuristic for the assignment component. Section 3.2 addresses thedistricting component.3.1. Assignment of zones to disposal sitesThe aim here is to assign each zone to a disposal site in order to minimize the cost of haulingsnow to disposal sites and for operating these sites, while satisfying capacity constraints at thesites. The cost of hauling snow in a truck has been approximated by the city of Montreal asCik adik b;8where Cikis the transport cost per cubic meter of snow from zone i to site k ($/m3), and dikthedistance from zone i to site k (km), and a and b are parameters. In Montreal, a 0:1395 andb 0:513: The values for these parameters can be determined for other cities by regression with asuitable set of data. The costs of operating disposal sites are evaluated in dollars per cubic meterof snow at a disposal site. These costs vary from site to site depending on the method, equipmentand manpower used.Every disposal site has an hourly capacity constraint for unloading trucks. This depends on theconfiguration of the disposal site, and the available equipment and manpower. For example, inMontreal, the hourly unloading capacity of the sewer sites is limited by the small size of theopening into the sewer system. In contrast, the quarry site has a very large hourly unloadingcapacity because it is composed of multiple unloading stations around the perimeter of the quarry.A. Labelle et al. / Socio-Economic Planning Sciences 36 (2002) 183202189Disposal sites may also have an annual capacity constraint due to the limited space available tostore snow. In Montreal, the surface and quarry sites have specified annual capacities.The problem of assigning zones (or streets) to disposal sites can be formulated as a multi-resource generalized assignment problem, which is NP-hard 7,37. In such an integer linearprogramming (ILP) formulation, there is a variable for each zone-disposal site combination. Alarge city like Montreal might require approximately 400 zones and 20 disposal sites, whichproduce 8000 variables. Because of the large size of this ILP formulation, optimal solution viamathematical programming is impractical within an interactive DSS. We have therefore devised afast heuristic approach to provide timely solutions.3.1.1. Heuristic approachThe heuristic method proposed here allows high quality solutions to be obtained in a shorttime. It utilizes a heuristic called two-resource assignment problem (TRAP) which was developedby Campbell and Langevin 7 to solve the problem of assigning snow removal sectors to disposalsites. This algorithm was chosen for the quality of its solutions and its speed. It may be adapted ina straightforward manner to the present problem of assigning zones (rather than sectors) todisposal sites.The heuristic has two components. Initially, zones are assigned to disposal sites based on apenalty calculation. The penalty is the difference between the cost of assigning a zone to the best(lowest cost) disposal site and second best disposal site. Let fi be the lowest cost feasible disposalsite for zone i; likewise, let si be the second lowest cost feasible disposal site for zone i: Thepenalty for zone i is then the difference between the cost to assign i to si and the cost to assign itto fi:Penaltyi Ci;si ? Ci;fi;where Ci;k is the transportation and elimination cost for assigning zone i to site k:The second part of the heuristic is a 2-opt exchange procedure that considers reassigning everypair of zones to every pair of sites. Zones are reassigned whenever the total cost decreases and thecapacity constraints remain satisfied. The TRAP heuristic is presented in Table 1.The proposed heuristic is effective for providing reasonable response times in an interactivedecision support environment. The heuristic was coded in C and the total time on a 266MHz PCto assign 390 zones to 20 disposal sites was approximately 13s, including 1s for the initialassignment and 12s for the 2-opt procedure. These solution times are very much lower than couldbe obtained with an exact approach.3.2. Districting to define sectorsThe assignment of zones to disposal sites (as explained in Section 3.1) defines each sites area ofinfluence. Sectors can then be designed for each area of influence by agglomerating neighboringzones into sectors. The sectors should be of similar size or workload (for the snowblower) forreasons of equity (i.e., operations should finish in all sectors at about the same time). Sector size islimited by the specified service level, i.e., the requirement to complete removal of the snow withina specific time interval (e.g., 72h). The sector size limit can be expressed in terms of a limit on thenumber of zones, the length of streets, or the annual amount of snow in each sector. Sector sizeA. Labelle et al. / Socio-Economic Planning Sciences 36 (2002) 183202190and service level could be determined by the amount of equipment available (e.g., snowblowers),since each sector requires a snowblower and trucks. For logistical reasons, a sector should be acontiguous set of zones, and not split by obstacles such as railroads, major highways, rivers, etc.The objective then is to aggregate zones to form non-disjoint sectors of similar specified size tominimize costs for snow disposal operations.The major costs relevant to the sector design problem arise from the trucks used to transportsnow from sectors to disposal sites. The elimination costs for operating disposal sites and thetransportation costs for hauling snow to disposal sites are fixed by the assignment of zones todisposal sites. Snowblower operating costs (i.e., $ per cubic meter of snow removed multiplied bythe total quantity of snow) are determined by the total amount of snow needing disposal and donot depend on the shape of a sector. In Montreal, private contractors provide snow-haulingtrucks in some sectors, and the City provides trucks for other sectors. Designing sectors to reducethe number of trucks required reduces costs to the City, both directly for City serviced sectors andindirectly through contract specifications for privately serviced sectors.The number of trucks required to serve a sector depends on the snow removal policy within thesector, and the distance from the sector to its assigned disposal site. To minimize the time tocomplete snow removal operations in a sector, snowblowers generally operate in a continuousmanner loading trucks. To have the snowblower idle while waiting for the arrival of an emptytruck to fill is to be avoided, both to minimize the time required to clear the streets and toeliminate citizen complaints about non-working crews. Therefore, minimizing the number oftrucks while having the snowblowers run continuously guides the design of the sectors.To allow continuous operation of snowblowers, there will typically be a queue of trucks movingslowly down the street alongside the snowblower, and as soon as the first truck is filled with snow,the second truck takes its place to begin being filled. The first truck departs for the disposal site,dumps its load of snow and returns to the end of the queue alongside the snowblower in itsassigned sector. The number of trucks needed in a sector to allow continuous operation of thesnowblower depends then on the time to load and unload a truck, and on the travel time betweenthe snowblower and the disposal site.Table 1TRAP heuristicA. Penalty-based assignment phase1. Calculate the penalty for each zone i: penaltyi Ci;si2Ci;fi2. Find the unassigned zone with the largest penalty, say i?, and assign it to its best site fi?3. Update the set of feasible zones for site fi?; and update fi; si and penaltyi for all zones i for whichfi fi? or si fi?4. Repeat steps 23 until no more zones can be assigned5. Assign any unassigned zones to a dummy site at infinite costB. Two-opt exchange6. For each pair of zones i and j; with assigned sites sitei and sitej; try to reassign zones i and j to every other pairof sites k and lkasitei;lasitej: Reassign the zones if the cost decreases and the assignment is feasible, i.e., thehourly and annual capacities are satisfied7. Repeat step 6 until no more zones can be reassignedA. Labelle et al. / Socio-Economic Planning Sciences 36 (2002) 183202191Because the loading and unloading times are independent of sector shape, we focus on thetravel time component. Travel time depends on the location of the truck when it departs from,and returns to, the snowblower, relative to the assigned site. When the snowblower is far from thedisposal site, a truck must travel a long distance to and from the site. The number of trucksassigned to the sector must therefore be large to ensure that an empty truck will always beavailable to be filled. Conversely, when the snowblower is near its disposal site, only a smallnumber of trucks is needed. Thus, the number of trucks needed to ensure the snowblower is neveridle increases with distance from the disposal site. Because trucks are not allocated dynamically tosectors, in practice, the number of trucks required in a sector depends on the maximum travel timebetween a sector and its assigned disposal site. A more sophisticated operational strategy thatcould dynamically re-deploy trucks between different sectors according to changing needs is leftfor future research.The cost for snow hauling trucks can thus be minimized by designing sectors to minimize thesum of the maximum distances from sectors to disposal sites (under the assumption thatminimizing distance minimizes travel time). Consider a region to be partitioned into two sectors ofequal area. For one of the sectors, the maximum distance to the disposal site must equal themaximum distance from the region to the disposal site. The objective then is to partition theregion to minimize the maximum distance to the other (closer) sector. For the Euclidean metric,the region should be divided by a circular arc centered on the disposal site to create two sectors ofequal area. Similarly, to partition a region into more than two sectors, the dividing lines (i.e.,sector boundaries) should be circular arcs centered on the disposal site. For a rectilinear metric,the results are similar, but the partitions that define sectors are lines of equal rectilinear distancefrom the disposal site. These lines will be at a 451 angle relative to the directions of rectilineartravel as shown in Fig. 1.The design principle is the same for either metric: sectors should be elongated in a directionperpendicular to the direction to the disposal site to reduce the number of trucks required. This isthe opposite of the general guideline for forming sectors for a vehicle routing problem, where thesectors should be elongated towards the depot to reduce travel distance in each route.A strict application of the sector design principle described above can lead to a variety ofproblems. For example, when the region to be partitioned is not compact, then the resultingDisposal site Fig. 1. Sectors with the rectilinear metric.A. Labelle et al. / Socio-Economic Planning Sciences 36 (2002) 183202192sectors may be disjoint. Another problem arises when there are many sectors to be created, orwhen the region to be partitioned is elongated in the direction perpendicular to the direction to thedisposal site. Then, the resulting sectors may be very narrow, which would be impractical in viewof the street network. (In a very narrow sector, the snowblower route will be inefficient because itmay include many very short street segments across the narrow width of the sector and thusrequire numerous turns.) Also, for the rectilinear metric, if the region is too elongated in thedirection perpendicular to the direction to the disposal site, then partition lines may createnoncontiguous sectors, as shown in Fig. 2. However, in practice, snow disposal sectors can beformed by aggregating adjacent zones, allowing the minimum zone size to help achieve practicalsectors. Thus, zones should not be too small or too narrow, or the resulting sectors could beimpractical.Based on this analysis, the sector design procedure should ideally aggregate zones to producesectors of the appropriate elongated shape and orientation in order to minimize the total numberof trucks required. Unlike many other districting problems, extremely compact sectors are notparticularly desirable due to the increased number of trucks required. The appropriate shape of aset of sectors is determined by the tradeoffbetween the cost savings from reducing the number oftrucks needed in elongated sectors and the added cost for inefficient operations if sectors are tooelongated. The size of zones (and, hence, the number of zones) plays an important role in theshape of sectors.The algorithm for aggregating zones into sectors considers each area of influence separately.For each such area, the distance between each zone and the disposal site is required. (Distance iscalculated using a shortest path algorithm on a subset of streets used by the trucks 38,39.) Alsorequired is the zone adjacency matrix whose element in row i and column j is equal to 1 if zones iand j are adjacent, and to 0 otherwise. Sector size is constrained by the specified level of service,which limits the maximum number of zones (or km of street) that can be combined into a sector.The basic idea behind the sector aggregation algorithm is to combine two zones whose unionresults in the greatest decrease in the sum of the maximum distances from the zones to the disposalsite. Thus, combining two zones produces a savings corresponding to the trip to the closer ofthe two zones, which is somewhat analogous to the approach in the ClarkeWright savingsalgorithm 40 for vehicle routing.The first step of our proposed algorithm consists of calculating the savings obtained bycombining two adjacent zones. Then, sectors are assembled by aggregating zones two at a time toform larger zones, as long as the sector size constraint is satisfied. (The term zone is used hereto refer to the original set of geographic zones assigned to disposal sites, and to the agglomerationA B C C D D Disposal site Fig. 2. Multiple sectors in an elongated region.A. Labelle et al. / Socio-Economic Planning Sciences 36 (2002) 183202193of several of these original zones.) The aggregation process begins with any zones that have only asingle adjacent zone. This reduces the number of small sectors that result from the aggregationprocess. After all zones with a single adjacent zone are treated, aggregation continues by joiningthe zone pair with the largest savings (that satisfy the sector size constraint). Each time two zonesare joined, the adjacency matrix is adjusted. Table 2 presents the districting algorithm to createsectors.The algorithm was programmed in C. The running times to create the sectors for areas ofinfluence with up to 80 zones (in Montreal) were always under 1s on a Pentium-266MHz PC.Most of the sectors obtained have the desired shape. Some sectors consisting of isolated zonesremained near the disposal site because zones with the smallest savings were treated last. The nextsection describes how the two algorithms presented here were imbedded in a GIS to form a DSS.4. Decision support systemThe key objective of our project was to build a user-friendly interactive DSS for use by snowdisposal planners and managers. This DSS needed to combine the tools of operations researchwith the graphical and analytical capabilities of a GIS. It was aimed at allowing the manager toparticipate in the decision process of sector design. A GIS is software for maintenance, displayand analysis of geographic or spatial data. Geographical data such as disposal sites, streets, andzones are represented by points, arcs (or line segments), and polygons. The GIS used in thisproject is MapInfo 41. MapInfo runs in Windows and provides powerful tools to work withdatabases. It has a programming language, MapBasic, that enables development of tailoredapplications. Subroutines can be written in any programming language.The first step in the solution procedure is the preparation of data. Solutions can then beproduced using the DSS that incorporates the heuristics described earlier. The remainder of thissection concentrates on data preparation.The basic geographic data required for Montreal are the streets, disposal sites, and zones. Toeach street segment is associated information such as geographical location, length, width, andtype (highway, boulevard, etc). For the disposal sites, the information required includes: location,annual and hourly capacities, and elimination costs (see Table 3). These data were provided by theCity of Montreal. Fig. 3 shows the locations of the disposal sites.The elimination cost represents the cost per cubic meter for operation of the disposal site. Thesecosts are relatively low for sewer sites, river sites and the quarry, where trucks dump snow directly,Table 2Districting algorithm1. For each pair of adjacent zones i and j; calculate the savings: savings: min fdik;djkg where dikrepresents the distancebetween the zone i centroid and site k2. If a zone has only one adjacent zone and their union will not exceed the size limit, then join the two zonesRepeat while there are zones with only one neighbor3. Join the two adjacent zones with largest value of savings whose union will not exceed the size limit4. Repeat steps 13 until all zones belong to a sectorA. Labelle et al. / Socio-Economic Planning Sciences 36 (2002) 183202194Table 3Disposal site informationSiteTypeElimination cost($/m3)Hourly capacity(m3/h)Annual capacity(m3/yr)AnbarSewer chute0.16700NBeauharnoisSewer chute0.38400NBrousseauSewer chute0.251000NDe l!Ep! eeSewer chute0.48400NDickson NordSewer chute0.25600NIbervilleSewer chute0.29700NMillenSewer chute0.172000NPoincar! eSewer chute0.38700NSauv! eSewer chute0.32600NSt-PierreSewer chute0.222800NArmand-ChaputSurface0.6860001,050,000ContrecoeurSurface0.574000700,000M.A. FortinSurface0.622000400,000Mont! ee St-L! eonardSurface0.342000600,000Parc NewmanSurface0.431000154,000RoyalmountSurface0.852000250,000Pont de la ConcordeRiver0.1710,000NQuai #30River0.1410,000NQuai #52River0.175000NFranconQuarry0.3410,0003,000,000Quarry River site Sewer chute Surface site Fig. 3. Current disposal site locations.A. Labelle et al. / Socio-Economic Planning Sciences 36 (2002) 183202195but somewhat higher for surface sites where the snow must be moved and formed into a large pileafter dumping. The hourly capacity of a site depends on its configuration, and the availableequipment and personnel for unloading. Most sewer sites have relatively low annual capacitiesdue to the limited size of the openings into the sewer system, and the requirement that thetemperature of the water not fall too low. The surface sites have moderate hourly capacities, whilethe river and quarry sites have high hourly capacities due to multiple unloading stations. Theannual capacities of the surface and quarry sites are restricted by the physical space available forstorage of snow. The river and sewer chute sites have effectively unlimited space due to the actionof the water to remove the snow.The City of Montreal estimates the hourly removal rate from sectors (m3/h) based on thecapabilities of snowblowers for filling trucks. The annual volume of snow in a sector (m3/yr) isestimated based on the historical amount of snow per linear meter of street (m3per linear meter ofstreet). Thus, the total length of streets in a sector determines the annual volume of snowgenerated by the sector to be sent to a disposal site.Zones must be defined based on the street data and city boundaries. They should be numerousenough (i.e., small enough) that the change of assignment of a single zone would have only aminor effect on the total cost. This also allows more flexibility in assembling the zones into sectors.The zones should also be large enough so that the sector aggregation procedure does not result inimpractical sectors. The City of Montreal was divided into 390 zones. Thus, to obtainapproximately 60 sectors (the number of sectors currently used by the City), each sector shouldinclude approximately 6 zones. The number of zones (390) was based on consideration of localroad geometry, neighborhoods, infrastructure, etc. to provide a reasonable tradeoffbetweenaccuracy and computation time.The zones were constructed with the help of the GIS. For each zone, a set of street segments wasselected by an individual familiar with the city and with the snow disposal operations. The GISautomatically calculates the total length of streets selected. The GIS also facilitates constructionof balanced zones and zones not traversed by a natural barrier such as a river or a railroad. Thetotal annual amount of snow in each zone was calculated by the GIS based on the street data andhistorical snowfall averages.Once zones are created, the next step consists of determining zone centroids and calculating thedistances from the zone centroids to the sites. The centroid is defined as follows. Each segment ofstreet i of a zone is replaced by its center point Pi; where the length of the segment constitutes theweight of the point. The centroid X is that point minimizing the weighted sum of the distancesfrom X to the Pi:XiwidX;Pi;where Piis the position of point i; withe weight of point Pi; X the position of centroid to bedetermined, and dX;Pithe distance between the centroid and point Pi:The transportation costs are then determined by Eq. (8). The distances between the zonecentroids and the disposal sites are calculated with a shortest path algorithm as describedin Labelle 39. This algorithm was developed specifically for the current type application, anduses a reduced network of major roadways likely to be traveled by the heavy trucks haulingsnow. The total distance is the sum of an analytical approximation for travel to a nodeA. Labelle et al. / Socio-Economic Planning Sciences 36 (2002) 183202196on the reduced network, and the shortest path on the reduced network. For details, see38,39.The sector design algorithm requires a zone adjacency matrix, which can be easily automatedusing the geographical tools of MapInfo. The zone adjacency matrix has a row and a columncorresponding to each zone. The entry for row j and column k is 1 if zone j is adjacent to zonek; and 0 otherwise. The adjacency matrix can be manually modified to take into accountgeographical and political constraints as desired. Other parameters can also be modified as desiredwith a few clicks of the mouse.Once the data are prepared, the TRAP heuristic in the DSS assigns the zones to the disposalsites. The DSS automatically calculates the total cost and the residual capacity for each disposalsite. It is then possible to manually modify the assignments. A program allows the user to reassignone or two zones at a time. All the costs and residual capacities are adjusted accordingly by theDSS.When satisfied with the assignment, the planner moves to the districting step. For each site, theheuristic automatically partitions its region of influence into sectors using the districting algorithmpresented earlier. Then, the sectors can be manually adjusted. This allows the planner to assignany isolated zones to sectors and to explore any desired adjustments. Costs and capacities areautomatically updated. Manual adjustments continue until the planner is satisfied with theresulting sectors, disposal site utilization, and costs. In the next section, we present a case studybased on data from the City of Montreal.5. Case studyThis section presents a complete solution obtained by the DSS system developed in this projectalong with several sensitivity analyses using data for the City of Montreal. Fig. 4 presents theassignment of zones to disposal sites obtained using the zone assignment heuristic TRAP 7. Thetransportation and elimination cost of this solution was $9,752,300, while the computing time ona PC (Pentium-266MHz) was 13s.The solution was then modified to make it more realistic. Fig. 5 presents the assignment ofzones to disposal sites following such manual modifications. The circles in Figs. 4 and 5 indicatethe regions where zone assignments were modified. In Fig. 5, disposal sites denoted with an xare not being used. Circle A in Fig. 4 shows a single isolated zone assigned to a small sewer chutedisposal site. Circle A in Fig. 5 shows how the single zone was incorporated into the neighboringsector. The heuristic TRAP does not take into account the fixed costs of the disposal sites. Hence,it is possible that only one or two zones are assigned to a disposal site; such a situation shouldgenerally be avoided in practice.Circle B in Fig. 4 shows several zones in the lower portion of the circle that are assigned to asurface disposal site near the top of the circle. Because travel between these zones and disposal sitewould involve driving through other municipalities (in the empty gap across the center of thecircle), these zones were reassigned (see Fig. 5) to disposal sites that did not involve travel throughother municipalities. (Another way to handle such a problem would be to add a large travel timeon to the appropriate arcs or to remove such arcs within the GIS.) These manual adjustmentsincreased the cost by only 0.37% to $9,788,257, but also eliminated the use of a disposal site.A. Labelle et al. / Socio-Economic Planning Sciences 36 (2002) 183202197The next step was to define the sectors. For the case study we set the maximum number ofzones per sector to seven. The heuristic was applied to each area of influence that contained10 or more zones. Areas of influence with nine or fewer zones were treated manually. The sectordesign algorithm required approximately 1s for each area of influence. The designed sectors arepresented in Fig. 6. In general, the sectors have the desired shape relative to the assigned disposalsite. However, one sector is made up of a single isolated zone (depicted in black within rectangle CFig. 4. Assignment obtained with TRAP heuristic.Fig. 5. Assignment after manual modifications (sites not used indicated by an x).A. Labelle et al. / Socio-Economic Planning Sciences 36 (2002) 183202198of Fig. 6). Fig. 7 presents the sectors designed following manual modifications. The sectors (inrectangle C) surrounding the isolated zone have been reshaped to integrate it. Manualmodifications may also be required to address selected geographic, political, and/or economicconcerns.6. Sensitivity analysesOne of the main advantages of the DSS is its ability to quickly evaluate several alternativescenarios. For example, transportation and elimination costs, or disposal site capacities could bemodified. Another interesting scenario is to vary the site capacities. For instance, one may explorethe impact of substantially reducing the quantity of snow dumped in the river for environmentalpurposes. Table 4 presents the results of sequentially closing the three river disposal sites. Thesesites have large capacities and are relatively inexpensive, so they are heavily used if available. Theresults show that although the capacities of the other sites are sufficient to take the snow formerlysent to the river, the increase in cost can be substantial.7. ConclusionSnow removal and disposal are expensive and essential activities in cities subject to largesnowstorms. A key strategic planning problem is to divide a city into sectors for concurrent snowFig. 6. Sector design.A. Labelle et al. / Socio-Economic Planning Sciences 36 (2002) 183202199removal and disposal operations. The objectives guiding sector design include the fixed andoperational costs for trucks hauling snow, and the costs for operating disposal sites. This paperpresents a flexible GIS-based decision support system for designing sectors for snow removal anddisposal. It allows the planner to incorporate a variety of difficult-to-quantify constraints. Such anapproach also provides the planner with a valuable tool for exploring and evaluating alternativedesigns. The DSS was demonstrated with data from the City of Montreal.In the current paper, the level of service in terms of the number of sectors was assumed as given.One interesting use for our DSS is to explore alternative levels of service. For example, with fewerbut larger sectors, the time to complete snow removal would increase, but the costs for equipmentand manpower would decrease. These cost savings could be compared against the addedinconvenience and cost of the degraded mobility. Other issues for future research include theTable 4Increase in costs when closing river sitesCost ($)Cost increase (%)Original assignment9,752,300FClosing Pont de la Concorde9,766,987+0.15Closing Pont de la Concorde & Quai 3010,277,742+5.39Closing Pont de la Concorde & Quai 30 & Quai 5210,973,310+12.52Fig. 7. Sectors after manual modifications.A. Labelle et al. / Socio-Economic Planning Sciences 36 (2002) 183202200influence of sector shape on snowblower routing, alternate aggregation schemes to create sectors,the impacts of changing parameters (e.g., increasing hourly capacities at disposal sites by addingmore equipment or workers), opening new disposal sites, or closing existing ones. One importantconcern is the environmental impact of dumping snow contaminated with urban pollutants intowater bodies 42. Bodies of water adjoin most large cities, and often provide a relativelyinexpensive place for snow dumping. Closure of snow disposal sites along rivers and the lakes,and the opening of new disposal sites can be evaluated efficiently with the proposed DSS.AcknowledgementsThis research was supported by the Natural Sciences and Engineering Research Council ofCanada and by the Fonds FCAR of the Quebec Ministry of Research, Science and Technology.The authors would like to thank the Editor-in-Chief, Barnett R. Parher, and two anonymousreferees for their valuable comments that led to this improved version of the article.References1 Guterbock T. The effect of snow on urban density patterns in the United States. Environment and Behavior1990;22:35886.2 Savas ES. The political properties of crystalline H2O: planning for snow emergencies in New York. ManagementScience 1973;20:13745.3 Eisenstein DD, Iyer AV. Garbage collection in Chicago. Management Science 1997;43:92233.4

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