Asignación óptima del personal para atención ciudadana usando programación entera mixta.

Abstract

In the present work, a multi-period problem of scheduling on parallel machines is studied. The problem is motivated by personnel assignment to customer service counters in the different agencies of the Internal Revenue System of Ecuador (SRI). The officials in charge of each of the agencies must decide how many service counters (machines) must be active at any time to serve the incoming flow of customers (jobs) and minimize the total number of man-hours that are necessary to serve such counters. Each job is characterized by an arrival time, a latest processing start time, and a processing time. Two integer linear programming models together with lower bounds and several families of valid inequalities for both formulations are provided. Moreover, the SRI has imposed a quality parameter defining that user cannot wait more than 20 minutes to be served. Thus, the first formulation consists of a continuous version in which each job is processed within a time window defined by its arrival time and its last allowed start time, and the second formulation consists of a discretized version of the time window in which the sets of work intervals are given explicitly. Finally, extensive computational results using real-world instances are reported.