Mixed integer formulations for the multiple minimum latency problem

In this paper we propose five mathematical formulations for the multiple minimum latency problem. The first three mathematical models are straight derived from classical formulations and from a flow-based formulation to the multiple travelling salesman problem. The last two are obtained as generalizations of time-dependent formulations to the minimum latency problem. We carry out an extensive computational experimentation to evaluate the performance of the proposed models using routing and scheduling instances. These experiments evidence that the time-dependent formulations show a much better performance than the other formulations, regarding to the size of instances that can be solved and the elapsed computational time to reach the optimal solutions. The obtained results suggest to consider the development of time-dependent formulations for other problems that consider the latency as objective function.