A New Mathematical Formulation for the Traveling Repairman Problem based on the Mixed Integer Programming Formulation

The Traveling Repairman Problem is a customer-oriented routing problem in which a repairman is visiting a set of geographically distributed customers. The objective function is to minimize the total waiting times of all customers. The importance of this problem can be found in its applications in the following areas: blood distributing, manufacturing systems, and transportation and logistics. Apart from its importance, research on this problem is very limited. In this paper a new mixed-integer programming formulation is developed, and several properties of model are studied. Additionally, by developing lower and upper bounds, a branch and bound algorithm is developed to solve the problems with up to 30 nodes. According to the computational experiments, the developed model is very competitive.