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====== 1992 年美国大学生数学建模竞赛 MCM 试题 ======
===== 1992 MCM A: Air-Traffic-Control Radar Power =====
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. 

===== 1992 MCM B: Emergency Power Restoration =====
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, and 
  * location (x,y). 

Cre sites are located at coordinates (0,0) and (40,40), where x and y are in miles. The region serviced by HECO is within -65 < x < 60 and -50 < y < 50. The region is largely metropolitan with an excellent road network. Crews must return to their dispatch site only at the 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 processed 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 their 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 6:00 A.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 will 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. (table incomplete) 
^Time ^ Location ^ Type ^ # Affected ^ Est Repair Time hrs  ^
|4:20 | (-10,3) | 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 sys.) | 25 wrkrs, 75,000 commuters | 5  |
|6:00 | | Storm leaves area | | |  
|6:05 | (13,30) | Residential | 45 | 2 | 
|6:06 | (5,20) | Area* | 2000 | 7 | 


Table 2. Crew descriptions. 
| Dispatch locations at (0,0) and (40,40).  | 
| Crews consist of three trained workers.  |
| Crews report to the dispatch location only at the beginning and end of their shifts. |  
| One crew is scheduled for duty at all 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 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.  |
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