Abstract
We study a scheduling problem in which jobs have locations. For example, consider a repairman that is supposed to visit customers at their homes. Each customer is given a time window during which the repairman is allowed to arrive. The goal is to find a schedule that visits as many homes as possible. We refer to this problem as the Prize-Collecting Traveling Salesman Problem with time windows (TW-TSP).
We consider two versions of TW-TSP. In the first version, jobs are located on a line, have release times and deadlines but no processing times. A geometric interpretation of the problem is used that generalizes the Erdős-Szekeres Theorem. We present an O(log n) approximation algorithm for this case, where n denotes the number of jobs. This algorithm can be extended to deal with non-unit job profits.
The second version deals with a general case of asymmetric distances between locations. We define a density parameter that, loosely speaking, bounds the number of zig-zags between locations within a time window. We present a dynamic programming algorithm that finds a tour that visits at least OPT/density locations during their time windows. This algorithm can be extended to deal with non-unit job profits and processing times.
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© 2003 Springer-Verlag Berlin Heidelberg
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Bar-Yehuda, R., Even, G., Shahar, S.(. (2003). On Approximating a Geometric Prize-Collecting Traveling Salesman Problem with Time Windows. In: Di Battista, G., Zwick, U. (eds) Algorithms - ESA 2003. ESA 2003. Lecture Notes in Computer Science, vol 2832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39658-1_8
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DOI: https://doi.org/10.1007/978-3-540-39658-1_8
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