A Review on Traveling Repairman Problem

Suppose G=(V,A) be an undirected graph with n nodes and a source vertex s Є V. Each node has a problem that must be solved by the repairman that has send. We are given the time required by the repairman to travel among nodes. The objective is to find a tour that minimizes the total waiting time of all the problems that are waiting to be solved. Traveling Repairman problem (TRP) is also known as delivery man problem, minimum latency problem and traveling salesman problem with cumulative costs. In literature, Traveling Repairman problem (TRP) has considered in various types. Previous literature has considered the version of the problem in which the repair time of a customer is assumed to be zero for latency calculations. A complementary version of the Traveling Repairman problem (TRP), in which a latency bound L is given the problem is to find the minimum number of repairmen required to service all the customers such that the latency of no customer is more than L. Another application of Traveling Repairman problem (TRP) is differentiates waiting times. Here the aim is to find a tour that minimizes the total traveling time plus the perceived waiting time sum across every customer. In this study we summarize the variations of TRP and explain the merits and disadvantages of each one.