On scheduling models for the frequency interval assignment problem with cumulative interferences

In this article, models and methods for solving a real-life frequency assignment problem based on scheduling theory are investigated. A realistic frequency assignment problem involving cumulative interference constraints in which the aim is to maximize the number of assigned users is considered. If interferences are assumed to be binary, a multiple carrier frequency assignment problem can be treated as a disjunctive scheduling problem since a user requesting a number of contiguous frequencies can be considered as a non-preemptive task with a processing time, and two interfering users can be modelled through a disjunctive constraint on the corresponding tasks. A binary interference version of the problem is constructed and a disjunctive scheduling model is derived. Based on the binary representation, two models are proposed. The first one relies on an interference matrix and the second one considers maximal cliques. A third, cumulative, model that yields a new class of scheduling problems is also proposed. Computational experiments show that the case-study frequency assignment problem can be solved efficiently with disjunctive scheduling techniques.