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Major forest fires have been very much in the news all summer. Your team has been approached by the Forest Service to help allocate resources to fight wildfires. In particular, the Forest Service is concerned about wildfires in a wilderness area consisting of small trees and brush in a square-shaped park with dimensions 80 km on a side. Several years ago, the Forest Service constructed a network of north-south and east-west firebreaks in this park that form a rectangular grid across the interior of the entire wilderness area. The firebreaks were built at 5-km intervals. Wildfires are most likely to occur during the dry season, which extends from July through September in this particular region. During this season, there is a prevailing westerly wind throughout the day. There are frequent lightning bursts that cause wildfires. The Forest Service wants to deploy four fire-fighting units to control fires during the next dry season. Each unit consists of 10 firefighters, one pickup truck, one dump truck, one water truck (50,000 liters), and one bulldozer (with truck and trailer). The unit has chainsaws, hand tools, and other fire-fighting equipment. The people can be quickly moved by helicopter within the wilderness area, but all the equipment must be driven via the existing firebreaks. One helicopter is on standby at all times throughout the dry season. Your task is to determine the best distribution of fire-fighting units within the wilderness area. The Forest Service is able to set up base camps for those units at sites anywhere within the park area. Explain why your proposed distribution of resources is best. |
Work in a group with one or two of your colleagues from this class on this project. Each group is to turn in one (joint) report on this problem. (This does not have to be your permanent group for this semester.)
Develop the scenario, and identify an appropriate problem from this general scenario. Begin to identify some underlying assumptions. Identify some of the important variables, and possible relationships which might occur among these variables. You will find it helpful to look at some of the examples which are developed in Section 2.2 of your text.
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The design of airline terminals varies widely. Sketches of airline terminals for several cities will be available in class on Thursday, August 29. The designs are quite dissimilar. Some involve circular arcs; others are rectangular; some are quite irregular. What is the best design for an airline teminal? Explain why your design is best. |
You may discuss this problem with each other, but write up and turn in your reports individually.
Your report for each of these projects must follow the outline given in the Project Report Format and Grading Criteria.
In general your project reports will be three to five word-processed pages. However, these first two project reports will probably be only about two pages in length (plus a page for your Cover Letter). Include each of the required subheadings in your report, even if you are only able to write one or two sentences in that section of the report.
It is very important in the Problem Identification section of your report that you clearly and suscinctly state the problem as you identify it.
Since we are just beginning this course, you may not be able to fully develop the later sections of the report. Identify your underlying assumptions. Discuss any variables that you think should be taken into consideration. Of course, these assumptions and variables should be shaped by the particular problem you identfy. While you may not have the tools you need to solve the problem, formulate (as much as possible) the particular mathematical problem whose solution would lead to a solution to the problem in the given scenario. If you could solve the mathematical problem you identify, how would the solution of the math problem apply to the original problem situation?