2021 Meisai B problem algorithm-AHP
Question B of the 2021 American College Students Mathematical Contest in Modeling is a discrete question.
Background of Subject B:
During the 2019-2020 fire season in Australia, devastating wildfires occurred in every state, with New South Wales and eastern Victoria having the worst impact. Wildfires occur during severe droughts and persistent heat waves, and climate change has exacerbated this phenomenon. Figure 1 shows the wildfire hotspots in the area from October 1, 2019 to January 7, 2020. The yellow color shows the fire from October 1st to January 6th and the red color shows the fire on January 7, 2020. Firefighters use UAVs have been performing surveillance and situational awareness (SSA) for several years; SSA UAVs carry high-definition and thermal imaging cameras and telemetry sensors to monitor and report data from front-line personnel wearable devices. Wearable devices can be used as personal locator beacons or more complex environmental monitors. SSA drones help monitor changing conditions, allowing the Emergency Operations Center (EOC) to provide the best command staff for the best results and maximum safety. figure 1. Wildfire hot springs in southeastern Australia, October 1, 2019 to January 7, 2020. Source: Australian Government Meteorological Service, NASA Resource Management System fire protection information. Two-way radio communication allows the "boots on the ground" forward team to provide status reports to the equal opportunity, and allows the equal opportunity to issue commands directly to the forward team. Deployers carry handheld two-way radios operating in the VHF/UHF bands. The range of a handheld radio is limited by its low transmit power, usually up to 5 watts, which mainly depends on the distance of rural areas or "buildings" and the physical terrain of urban areas; weather does not affect VHF/UHF signals. Large. A 5-watt radio has a nominal range of 5 kilometers on a flat, unobstructed ground, but it drops to 2 kilometers in urban areas. Repeaters, transceivers, and automatic replay of signals at higher power can be expanded Radio range. The repeater located between the front line and the EOC can relay radio signals from the front line to the EOC and from the EOC to the front line. The range of the repeater also depends on the distance and terrain, but is significantly larger than the low-power handheld radio Recently, hovering drones equipped with repeaters have been used to greatly expand the range of frontline low-power radios. A 10-watt repeater, weighing 1.3 kg, hovering over the ground by the drone, can reach 20 kilometers The range. Acme’s prototype Wile E-15. The 2X hybrid drone is expected to cost about $10,000 (AUD) when equipped with radio repeaters or video and telemetry capabilities. Tests show that this drone has the capabilities listed in Table 1.
Summary of topic B:
1. Create a model to determine the optimal number and combination of SSA drones and radio repeater drones for purchase for a proposed new department of the Victorian National Fire Service (CFA) "Rapid Bush Fire Response") . Your model should balance capabilities and safety with economy, and consider the needs and terrain for observation and communication tasks. Your model should also take the size and frequency of fire events as parameters.
2. Explain how your model adapts to the changing possibilities of extreme fire events in the next ten years. Assuming that the cost of the UAV system remains the same, predict what equipment cost will increase.
3. Determine a model to optimize the position of hovering VHF/UHF radio repeater drones for fires of different sizes on different terrains, as shown in Figure 2: Topographic Map of Eastern Victoria. Please note that the elevation ranges from sea level on the coast to 1,986 meters of mountains. Bogon, Victoria.
4. Prepare a two-page annotated budget request supported by your model for submission to the Victorian government.
Topic analysis (for reference only):
It can be seen that the overallAHP (Analytic Hierarchy Process)withPredictive modelCome as the basic algorithm model.
So first, make a brief analysis of the background data and the first question.
1. What is the goal we want to evaluate?
It is easy to see from the title that the main problem is the comprehensive choice of buying "SSA" and "WileE-15.2X".
2. What are the influencing factors?
Next, we need to think, what are our evaluation criteria or indicators for this comprehensive problem?
Looking at the background of the topic again, we can see that there are several necessary considerations:
Main factors (80%):
1. Capacity (capacity)
2. Safety (safety)
3. Economics
Secondary factors (20%):
4. Survey and survey topography (topography)
5. Fire event size
6. The frequency of fire event (fire event frequency)
(The proportion of primary and secondary factors can be modified, such as 70% and 30%)
3. What are the options?
I am here only based on the plan selected by some documents, you need to further consult more relevant documents to determine "more and more accurate" solutions.
1. All covered (full coverage)
Full coverage of "dangerous areas" has the highest safety, but the economy is not high.
2. Almost covered (large area coverage)
Covering a large area of "dangerous areas" has the second highest safety and higher economy.
Here, select areas with "small fire impact" for "gap coverage".
Therefore, all factors and influences need to be weighted.
3.Half covered (half covered)
The method of semi-covering "dangerous areas" has the lowest safety but the highest economic efficiency.
hereHalf coveredThis means that it is mainly to deploy and control "high-risk areas".
When a fire occurs in the surrounding "uncontrolled area", the "fire fighting force" can be mobilized from the "arranged area" in time.
There is a trade-offComprehensive factors such as traffic in controlled areas and uncontrolled areas.