mcm2003C Aviation Baggage Screening Strategies 航空行李的扫描对策 - matlab数学建模

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标题：mcm2003C Aviation Baggage Screening Strategies 航空行李的扫描对策
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所属分类: 数学建模资源类型：文档文件大小: 16.73 KB 上传时间: 2019-08-19 20:38:32 下载次数: 87 资源积分：1分提供者: jiqiren 20190819083919176

内容：
(MCM 2003C)

You are an analysis team in the Office of Security Operations for the Transportation Security Administration(TSA), responsible for the Midwest Region of the United States. New laws will soon mandate 100% screening of all checked bags at the 429 passenger airports throughout the nation by explosive detection systems (EDSs; see Figure 1). EDSs use computed tomography (CT) technology to scan checked bags, similar to how CAT scans are used in hospitals. Using multiple x-rays of each bag, EDSs create three-dimensional images of a bag’s content, showing the density of each item. This information is utilized to determine whether an explosive device is present. Experimentation with EDSs indicate that each device is operational about 92% of the time and each device can examine between 160 and 210 bags per hour.

The TSA has been actively purchasing EDSs and deploying them at airports throughout the nation. Given that these devices cost nearly $1 million each, weigh as much as eight tons, and cost several thousand dollars to install in an airport, determining the correct number of devices to deploy at each airport and how to best use them(once operational) are important problems.

Currently, manufacturers are not able to produce the expected number of EDSs required to meet the federal mandate of 100% screening of checked luggage. Because of the limited number of EDS machines available, the Director of Airport Security for the Midwest Region (Mr. Sheldon) is not surprised that the TSA is requesting a detailed analysis on the estimated number of EDSs required at all airports. In addition, given the limited space and funds available for each airport, Mr. Sheldon believes that at some point a detailed analysis of emerging technologies will be needed. Promising technologies with more modest space and labor costs will emerge in the coming decade (e.g. x-ray diffraction; neutron-based detection; quadropole resonance; millimeter wave imaging; and microwave imaging).

Task 1: You have been tasked by your Director, Mr. Sheldon, to develop a model to determine the number of EDSs required at two of the largest facilities in the region, Airports A & B, which are described in the Technical Information Sheet (TIS)–Appendix A. Carefully describe the assumptions that you make in designing the model, then use your model to recommend the number of EDSs required using the data provided in Table 1 of the TIS.

Task 2: Prepare a short (one page) position paper to accompany your model that describes the security-related objectives of the airlines and the constraints that the airlines must work within for the sets of flights described in Table 1 of the TIS.

Task 3: Since security screening takes time and might delay passengers, the airport managers at Airports A & B request that you develop a model that can help the airlines determine how to schedule the departure of different types of flights within the peak hour. Carefully describe all the assumptions that you make in designing the model and use your model to produce a schedule for the two airports with the data provided in Table 1.

Task 4: Based on your analysis, what can you recommend to Mr. Sheldon and the airlines about checked baggage screening for the flights during the peak hours at your two airports?

Task 5: Mr. Sheldon realizes that your work may have national impact and requests that you write a memo explaining how your models can be adapted to determine the number of EDSs and airline scheduling for all 193 airports in the Midwest Region. He will send the memo along with the models and the analysis to the Director of the Office of Security Operations (his boss) at the TSA and to all security directors of other airports in the region for their comment and possible implementation.

Additional security measures associated with higher risks may require that up to 20% of the passengers will need to have all their checked bags screened through both an EDS and an explosive trace detection (ETD) machine, even though an EDS is 98.5% accurate in identifying explosive devices in checked bags. ETD machines use mass spectrometry technology to detect minute particles of explosive compounds. Each ETD machine costs $45,000 to purchase, however, the labor cost to operate the ETD machine is approximately 10 times that of the EDS. ETD can process 40 to 50 bags per hour; they are operational 98% of the time, and they are 99.7% accurate in identifying explosive materials on checked bags. At this time, ETD machines have not been federally certified, but Mr. Sheldon believes that they will soon be an integral part of national airport security systems.

Task 6: Modify your EDS models to incorporate the use of ETD machines and determine how many ETD machines are needed for Airports A & B and if the schedules need to be changed. Since this information may affect national level decisions, write a memo to the Director of Homeland Security and the Director of TSA with a technical analysis of this enhanced screening policy. Is the cost of such a policy justified in light of the value that it provides? Should the ETDs replace any of the EDS devices?

Task 7: The Director of Homeland Security must also decide how to best fund future scientific research programs. Use your EDS/ETD model to examine the possible effect of changes in the device technology, cost, accuracy, speed, and operational reliability. Include recommendations for the science, technology, engineering, and mathematics (STEM) research areas that will have the biggest impact on security system performance. Add your recommendation to the memo prepared in Task 7.

Appendix A Technical Information Sheet (TIS)

Table 1: Peak Hour Flight Departures for Airports A and B

Note: On average, 2% of flights are cancelled each day

Flight

Type Number of

Seats on Each

Flight Airport A

Number of Flights

of Each Type Airport B

Number of Flights

of Each Type

1 34 10 8

2 46 4 6

3 85 3 7

4 128 3 5

5 142 19 9

6 194 5 10

7 215 1 2

8 350 1 1

Although all the flights in Table 1 depart during a peak hour, their actual departure times are set by the airline when designing their flight schedule. A flight cannot depart until all its checked bags are screened using an EDS. The airline has the flexibility to schedule their flights during the peak hour to avoid undesirable flight delays due to unscreened bags.

Historical data indicates that flights with 85 or fewer seats typically fly with between 70% and 100% of their seats occupied. Flights with between 128 and 215 seats typically fly with between 60% and 100% of their seats occupied. Flights with 350 seats typically fly with between 50% and 100% of their seats occupied. Passengers typically arrive for their flight between forty-five minutes and two hours prior to their scheduled departure time. For flights other than shuttle service, airlines claim that 20% of the passengers do not check any luggage, 20% check one bag, and the remaining passengers check two bags.

Preliminary estimates indicate that it will cost $100,000 to modify existing infrastructure (reinforced flooring, etc.) to install each EDS at Airport A and $80,000 to install each EDS at Airport B.

航空行李的扫描对策(美国竞赛2003年C题)

你们是交通安全管理局(TSA)安全运行办公室的分析作业组, 负责美国中西部地区。新的法律不久将规定, 全国429个民用机场要借助爆炸品侦测系统(EDSs，见图1)对所有验关的包裹进行100%的扫描鉴别。EDSs用计算合成的X线断层技术来扫描验关包裹，与医院里使用CAT扫描的办法差不多。利用每个包裹的多层X线影像，EDSs生成包裹内容的三维图象，显示每件物品的密度。这些信息则用来确定包裹里是否有爆炸装置。对EDSs的试验表明, 每台设备92%的时间在工作而且每小时可检查160到210个包裹。

图1：爆炸品侦测系统(EDS)

TSA一直在积极地买进EDSs并安装在全国的各个机场。据悉，购买这些设备每台要花近一百万美元，其重量达8吨，而且在一个机场安装需耗费数千美元，因而，确定配置在每个机场的准确的设备台数以及如何在应用方面(一旦可用)达到最优，是一个重要的问题。

当前，制造商不能为机场制造出联邦托管所需要的EDSs的预期台数来适应对验关行李进行100%的扫描。TSA正在要求对所有机场需求EDSs的估计台数有一个详细的分析，由于只有有限数量的EDS机可供使用，中西部地区的机场安全主任(Mr. Sheldon)对此并不感到惊讶。此外，既然每个机场可用的空间和基金有限，Mr. Sheldon认为, 对于涌现出来的各种技术实地进行详尽的分析势在必行。在未来的十年中,若干前景看好的具有更适度的空间和劳力花费的技术将会问世(例如，X光衍射造影；基于中子的侦测；四极场谐振；毫米波成像；以及微波成像)。

任务1：你们的主任Mr. Sheldon已经给你们分派了任务：建立一个模型来确定本区域的两个最大设施，机场A和B，所需要的EDS的台数，相关数据在技术信息图表(TIS)?附录A里有说明。仔细地描述你们在模型设计中所作的假设条件，然后借助TIS表1提供的数据，用你们的模型来提出所需的EDSs台数。

任务2：准备一份短的(1页)意见书附在你们的模型上，对TIS表1中所列各组航班隶属的航空公司说明安全相关的任务和航行守则。

任务3：由于安全扫描需要时间并可能拖延乘客，机场A和B的机场管理人员请求你们建立一个模型，帮助航空公司确定怎样安排不同型号的班机在高峰时间起飞。仔细地描述在模型设计中所作的假设条件，并且用你们的模型为两个机场制定一个排序表，所需数据见表1。

任务4：依据你们的分析，关于在两个机场为高峰期班机验关包裹的扫描，你们能给Mr. Sheldon和航空公司什么样的建议？

任务5：Mr. Sheldon认识到你们的工作可能引起全国的反响，请求你们写一个备忘录解释如何调整你们的模型来为中西部地区共193个机场确定所需的EDS台数和定期航线日程安排。他将把备忘录连同模型及分析一起送给在TSA的安全运行办公室主任(他的老板)和这个地区的其他机场的安全管理员，以期听取他们的意见和可能的参照执行。

与较高危险相关联的附加安全措施要求，高达20%的乘客既要把他们全部验关行李经过EDS扫描，还要经过爆炸品痕迹探测器(ETD)扫描，尽管一台EDS在分辨验关行李中的爆炸设备方面是98.5%准确的。ETD用质谱测定技术探测炸药混合物的微小颗粒。买一台ETD机要花45,000美元，不过，运行ETD机的劳力支出却相当于EDS的十倍。ETD每小时可处理40到50个包裹，98%的时间在运行，在辨别炸药物质上有99.7%的准确性。目前，ETD机还不是联邦认证的，但是Mr. Sheldon相信，它们不久将成为国家机场安全系统的一个必备的部分。

任务6：修改你们的EDS模型进而加入ETD机的应用，并且确定机场A和B所需的ETD的数目以及是否需要改变班机的排序表。因为这些信息将影响整个国家级的决定，给国土安全局主任和TSA的主任写一份备忘录，告诉他们对强化扫描政策的技术分析。根据它提供的数值判定，这个政策下的花费合理吗？应当用ETD代替所有的EDS装置吗？

任务7：国土安全局主任也必须决定怎样更好地资助未来的科学研究项目。应用你们的EDS/ETD模型来检查一下在设备技术、花费、准确性、速度和运行可靠性方面的改变所可能产生的效果。请给出对于安全系统性能影响甚大的科学、技术、工程和数学等研究领域(STEM)相关建议。并把你们的建议附在任务7的备忘录中。

附录A 技术信息图表(TIS)

虽然表1中的所有班机都在一个高峰期间起飞，但他们的实际起飞时间是由航空系统在设计他们的飞行排序表时安排的。直到所有验关包裹通过EDS扫描鉴别后班机才能起飞。为了避免因未扫描的包裹导致令人不快的航班延迟，航空系统可以灵活地安排高峰期间航班的起飞时间。

历史数据表明, 不多于85个座位的班机起飞时基本上70%到100%的座位坐满。有128到215个座位的班机起飞时一般是60%到100%的座位已满。而有350个座位的班机起飞时大体上50%到100%的座位已坐满。乘客大都提前45分钟到2个小时到达机场。对并非往返的班机而言，航空系统要求:20%的乘客不得交验任何行李，20%的乘客可以交验一个行李，其余的乘客交验两个行李。

初步估算指出,机场A安装每台EDS需耗资$100,000改善现有的基础设施(加固地面，等)，而机场B安装每台EDS只需耗资$80,000。

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mcm2003C Aviation Baggage Screening Strategies 航空行李的扫描对策 .pdf