Newsgroups: rec.puzzles
Subject: Re: National Mathematics Contest in Modeling
From: rivero@mdcbbs.com
Date: 8 Apr 92 13:21:24 GMT
Organization: M&E (Division of EDS), Cypress CA
Nntp-Posting-User: holada

In article <1992Apr7.200624.9557@leland.Stanford.EDU>, ypay@leland.Stanford.EDU (daniel cory) writes:
> 
> Problem A: Power Problem for an Air Traffic Control Radar
> 
> You are to determine the power to be radiated by an air traffic control 
> radar at a major metropolitan airport. The airport authority wants to 
> minimize the power of the radar consistent with safety and cost.
> 
> The authority is constrained to operate with its existing antennae and 
> receiver circuitry. The only option that they are considering is upgrading 
> the transmitter circuits to make the radar more powerful.
> 
> The question that you are to answer is what power (in watts) must be 
> released by the radar to ensure detection of standard passenger aircraft at 
> a distance of 100 kilometers.
> 
> Technical specifications:
> a. The radar antenna is a section of a paraboloid of revolution with focal 
> length of 1 meter. Its projection onto a plane tangent to its vertex is an 
> ellipse with a major axis of 6 meters and a minor axis of 2 meters. The main 
> lobe energy beam pattern, located at the focus, is an elliptical cone that 
> has a major axis of one radian and a minor axis of 50 milliradians. The 
> antenna and beam are sketched in the figures provided [Sorry, I don't know a
> good way to send these pictures].
> 
> b. The nominal class of aircraft is one that has an effective radar 
> reflection cross-section of 75 square meters. For the purposes of this 
> problem, this means that in your initial model, the aircraft is equivalent 
> to a 100% reflective circular disc of 75 square meters, which is centered on 
> the axis of the antennae and is perpendicular to it. You many want to 
> consider alternatives or refinements to this initial model.
> 
> c. The receiver circuits are sufficiently sensitive to process a return 
> signal of 10 microwatts at the feed horn of the radar (which is located at 
> the focus of the radar antenna).
> 
> Problem B: an Emergency Power Restoration System
> 
> Power companies serving coastal regions must have emergency response systems 
> for power outages due to storms. Such systems require the input of data that 
> allow the time and cost required for restoration to be estimated and the 
> 'value' of the outage judged by objective criteria. In the past, 
> Hypothetical Electric Company (HECO) has been criticized in the media for 
> its lack of a prioritization scheme.
> 
> You are a consultant to HECO power company. HECO possesses a computerized 
> database with real time access to service calls that currently require the 
> following information:
> 
> Time of report;
> Type of requestor;
> Estimated number of people affected;
> Location (x,y).
> 
> Crew sites are located at coordinates (0,0) and (40,40), where x and y are 
> in miles. The regions serviced by HECO is within -65<x<65 and -50<y<50. The 
> region is largely metropolitan with an excellent road network. Crews must 
> return to dispatch site only at beginning and end of shift. Company policy 
> requires that no work be initiated until the storm leaves the area, unless 
> the facility is a commuter railroad or hospital, which may be processes 
> immediately if crews are available.
> 
> HECO has hired you to develop the objective criteria and schedule the work 
> for the storm restoration requirements listed in Table 1 using the work 
> force described in Table 2. Note that the first call was received at 4:20 
> a.m. and that the storm left the area at 6:00a.m. Also note that many 
> outages were not reported until much later in the day.
> 
> HECO has asked for a technical report for their purposes and an 'executive 
> summary' in laymen's terms that can be presented to the media. Further, they 
> would like recommendations for the future. To determine your prioritized 
> scheduling system, you have to make additional assumptions. Detail those 
> assumptions. In the future, you may desire additional data. If so, detail 
> the information desired.
> 
> Table 1. Storm Restoration Requirements
>                                                              Estimated
>                                                              Repair Time
> Time                                                         (Hours for
> (a.m) Location  Type                             # Affected  Crew)
> ------------------------------------------------------------------------
> 4:20  (-10,30)  Business (cable TV)              ?             6
> 5:30  (3,3)     Residential                      20            7
> 5:35  (20,5)    Business (hospital)              240           8
> 5:55  (-10,5)   Business (railroad)              **            5
> ------------------------------------------------------------------------
> 6:00  All clear given; storm leaves area; crews can be dispatched
> ------------------------------------------------------------------------
> 6:05  (3,30)    Residential                      45            2
> 6:06  (5,20)    Area *                           2000          7
> 6:08  (60,45)   Residential                      ?             9
> 6:09  (1,10)    Government (city hall)           ?             7
> 6:15  (5,20)    Business (shopping mall)         200 workers   5
> 6:20  (5,-25)   Gov't (fire department)          15 workers    3
> 6:20  (12,18)   Residential                      350           6
> 6:22  (7,10)    Area *                           400           12
> 6:25  (-1,19)   Industry (newspaper)             190           10
> 6:40  (-20,-19) Industry (factory)               395           7
> 6:55  (-1,30)   Area *                           ?             6
> 7:00  (-20,30)  Gov't (high school)              1200 students 3
> 7:00  (40,20)   Gov't (elementary school)        1700          ?
> 7:00  (7,-20)   Business (restaurant)            25            12
> 7:00  (8,-23)   Gov't (police station & jail)    125           7
> 7:05  (25,15)   Gov't (elementary school)        1900          5
> 7:10  (-10,-10) Residential                      ?             9
> 7:10  (-1,2)    Gov't (college)                  3000          8
> 7:10  (8,-25)   Industry (computer manufacturer) 450 workers   5
> 7:10  (18,55)   Residential                      350           10
> 7:20  (7,35)    Area *                           400           9
> 7:45  (20,0)    Residential                      800           5
> 7:50  (-6,30)   Business (hospital)              300           5
> 8:15  (10,40)   Business (several stores)        50            6
> 8:20  (15,-25)  Gov't (traffic lights)           ?             3
> 8:35  (-20,-35) Business (bank)                  20            5
> 8:50  (47,30)   Residential                      40            ?
> 9:50  (55,50)   Residential                      ?             12
> 10:30 (-18,-35) Residential                      10            10
> 10:30 (-1,50)   Business (civic center)          150           5
> 10:35 (-7,-8)   Business (airport)               350 workers   4
> 10:50 (5,-25)   Gov't (fire department)          15            5
> 11:30 (8,20)    Area *                           300           12
> * Area signifies a combination of two or more of the other
>   classfication types.
> ** 25 workers; 75000 commuters
> 
> Table 2. Crew Descriptions
> 
> * Dispatch locations at (0,0) and (40,40).
> * Crews consist of three trained workpersons.
> * Crews report to the dispatch location only at the beginning and end of 
> their shifts.
> * One crew is scheduled for duty at al times on jobs assigned to each 
> dispatch location. These crews would normally be performing routine 
> assignments. Until the 'storm leaves the area,' they can be dispatched for 
> 'emergencies' only.
> * Crews work eight (8) hour shifts.
> * There are six crew teams available at each location.
> * Crews can work only one overtime shift in a work day and receive time-and-
> a-half for overtime.
> 
> Rules:
> Each school may enter up to two teams of three undergraduates.
> Any inanimate reference sources may be used.
> You may start at 12:01AM Friday morning and must mail the solution in on Monday
> 
> For more information about the National Mathematics Contest in Modeling, write:
> COMAP, Inc.
> The Consortium for Mathematics and its Applications
> 60 Lowell Street
> Arlington, MA 02174
> 
> Newsgroups: rec.puzzles
> Subject: National Mathematics Contest in Modeling
> Summary: applied math contest (long)
> Followup-To: 
> Distribution: world
> Organization: DSG, Stanford University, CA 94305, USA
> Keywords: 
> 
> Every year, the Consortium for Mathematics and its Applications runs the
> National Mathematics Contest in Modeling. Teams from colleges around the world
> work on an applied math problem for a four day weekend.
> 
> I've mentioned the contest on this group before and thought I would post this
> year's questions. The judging has already taken place so I think it's okay to
> post the questions. If you want to see the official winners and more details of
> the contest, see the UMAP journal (I think the winter issues)
> 
> I've entered this contest 5 times and now help organize the Stanford team.
> 
> Here are the questions from this year. If you want last year's questions,
> please email me or see the journal mentioned above. If you are interested in
> entering the contest, write to the address at the bottom of the post.
> 
> -Dan Cory
> 
> Problem A: Power Problem for an Air Traffic Control Radar
> 
> You are to determine the power to be radiated by an air traffic control 
> radar at a major metropolitan airport. The airport authority wants to 
> minimize the power of the radar consistent with safety and cost.
> 
> The authority is constrained to operate with its existing antennae and 
> receiver circuitry. The only option that they are considering is upgrading 
> the transmitter circuits to make the radar more powerful.
> 
> The question that you are to answer is what power (in watts) must be 
> released by the radar to ensure detection of standard passenger aircraft at 
> a distance of 100 kilometers.
> 

  Is there any reason I can't vary the power? The aircraft at 100km don't need
to be looked at as often as the ones closer in. Could I do, say one max-nominal 
power sweep for all traffic, followed by 2 or 3 low power sweeps to focus
attention on the close-in traffic? That would reduce power drain, reduce
wear on the transmitter elements, lower computer overhead, and decrease
the radiation hazard.

  Or is that against the rules?




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