Designing Efficient Snow Plow Routes - University of Minnesota

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particular projects were chosen to be of value to various community agencies within the city or county. In the first section below, we describe a particular project which was of interest and beneficial value to the City of Morris, a small community of about 5600 people located in rural west central Minnesota. We also give the detailed mathematical model we used to solve a specific problem posed by the city. One of the objectives of the detailed description of the model is to illustrate the fact that in a process which is rich in both useful and useless data, it behooves all parties concerned to maximize their efforts at communications. In the next section, we summarize how we conducted the course, including how students worked on the projects, how they were graded, and how they communicated with the community agencies. In the last section, we discuss the rewards we reaped as well as challenges that we encountered throughout the process. A Mathematical Model There were several questions of interest that came from various community agencies, such as: What are the traffic-flow patterns around the city and its vicinity? How efficiently can we plow the streets in the city right after a snow storm? How do we group the city and its vicinity into several zones so that traffic crossing between zones is minimized? There is no room in this paper to describe all the models used to answer all the questions, but in this section, we will discuss one specific problem in detail so that you will have a rough idea of how elaborate the analysis could be based on just one specific question. At the end of this section, we list a few other common community-related projects that can also be modeled in a similar way. Description of Project We were asked to determine and design a cost-effective way to plow the streets and alleys so that each of the different types of snow plows and sanding trucks could traverse its group of streets and return to its depot. Pertinent information and constraints had to be considered. These include the following constraints: During a snow emergency period, there are a few roads that must be cleared first before others; costs are assumed to be proportional to the distance traveled by the snow plows; also, the city has five different classifications of plows (motor grater, reversible plow on a truck, one-way plow on a truck, a V-plow with a sander, a loader), and it has two motor graters and only one of each of the other types. Table 2.6.1 and the map in Figure 2.6.1 give a summary of the aforementioned information and constraints. Table 2.6.1: Classifications of plows and the regions of the city Plow type Region Plowed Motor grater (1) Roads on the south-west of the city Motor grater (2) Roads on the north-east of the city Reversible Roads in south-east part of the city One-way Alleys in south-west of the city V-plow Alleys in north-east of the city Loader Parking lots and airport
Figure 2.6.1 Annotated map of the city of Morris
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Designing Efficient Snow Plow Routes - University of Minnesota

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