No abstract

The plowing with precedence problem is a variant of the windy postman problem, where a plow is required to clean streets after a heavy snowfall with traversing costs depending on the direction of traversal as well as whether a street has been previously plowed or not. We prove that this problem can be solved in polynomial time under natural cost structures. We also propose heuristics for this problem, which compare favorably with the state of the art.

The travelling repairman problem (TRP) is a scheduling problem in which a repairman must visit locations to perform some task. Each location has a time window in which the repairman is allowed to arrive. The objective of this problem is to maximize the number of tasks performed. In this paper, we consider a special case in which all the locations are on a straight line, the tasks have no processing time, and all time-windows are of unit length. We present an improvement on the analysis of the 4-approximation algorithm presented by S. L. Pérez Pérez et al. in 2014.