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In the traveling repairman problem with profits, a repairman (also known as the server) visits a subset of nodes in order to collect time-dependent profits. The objective consists of maximizing the total collected revenue. We restrict our study to the case of a single server with nodes located in the Euclidean plane. We investigate properties of this problem, and we derive a mathematical model assuming that the number of visited nodes is known in advance. We describe a tabu search algorithm with multiple neighborhoods, and we test its performance by running it on instances based on TSPLIB. We conclude that the tabu search algorithm finds good-quality solutions fast, even for large instances. ACM Subject Classification I.2.8 Heuristic Methods Keywords and phrases IntroductionImagine a single server, traveling at unit speed. There are n locations given, each with a profit p i , 1 ≤ i ≤ n. At t = 0, the server starts traveling and collects revenue p i − t i at each visited location, where t i denotes the server's arrival time at location i. Not all locations need to be visited. The problem is to find a travel plan for the server that maximizes total revenue. This problem is known as the traveling repairman problem with profits (TRPP) and forms the subject of this paper. In particular, we perform a computational study of the TRPP in the Euclidean plane. MotivationThe TRPP occurs as a routing problem in relief efforts. For example, consider the following situation. In the aftermath of a disaster like an earthquake, there are a number of villages that experience an urgent need for medicine. The sooner the medicine gets to a village, the more people can be rescued. Since the cost of transport is negligible compared to the value of a human life, rescue teams are only concerned with the total number of people that can be saved. Assume that at location i there are p i people in need of the medicine, and that every instance of time, there is one of them dying. Suppose also that we have one truck available. With t i denoting the arrival time of the truck at location i, the number of people that will survive equals p i − t i . Thus, the goal of the rescue team is to maximize i (p i − t i ),

We consider a rooted tree graph with costs associated with the edges and profits associated with the vertices. Every subtree containing the root incurs the sum of the costs of its edges, and collects the sum of the profits of its nodes; the goal is the simultaneous minimization of the total cost and maximization of the total profit. This problem is related to the TSP with profits on graphs with a tree metric. We analyze the problem from a biobjective point of view. We show that finding all extreme supported efficient points can be done in polynomial time. The problem of finding all efficient points, however, is harder; we propose a practical FPTAS for solving this problem. Some special cases are considered where the particular profit/cost structure or graph topology allows the efficient points to be found in polynomial time. Our results can be extended to more general graphs with distance matrices satisfying the Kalmanson conditions