The downhill plow problem with multiple plows

In winter, a common problem is to determine a set of routes for snow plows that minimize the maximum route length. Typically, this is modelled as an arc routing problem. We begin with a variant that is motivated by the fact that deadhead travel over streets is significantly faster than the time it takes to plow the street. We incorporate the use of multiple plows and the observation that, on steep streets, it is much more difficult, or impossible, to plow uphill. Therefore, we want to design routes that try to avoid plowing uphill on steep streets and take advantage of the faster traversal time for deadheading. We generalize this problem to include multiple plows and seek to minimize the maximum route length. We present a heuristic that generates solutions with costs that are very close to a lower bound.