Balancing tour durations in routing a vehicle fleet

This paper is concerned with the multiple Traveling Salesman Problem (mTSP) with lower and upper bound constraints on tour durations. The paper presents a flow-based integer linear programming formulation of the problem and some valid inequalities. The paper also describes a Benders decomposition algorithm based on this model as an exact solution approach. Computational experimentation shows that the decomposition algorithm is able to improve the performance of a standard off-the-shelf solver in solving medium-scale instances of the problem up to 71 nodes and two salesmen. The paper also presents some results in solving a practical mobile library routing problem and discusses the implications of balancing tour durations.