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We consider the conflict-resolution problem arising in the allocation of commercial advertisements to television program breaks. Due to the competition-avoidance requirements issued by advertisers, broadcasters aim to allocate any pairs of commercials promoting highly conflicting products to different breaks. Hence, the problem consists of assigning commercials to breaks, subject to time capacity constraints, with the aim of maximizing a total measure of the conflicts among commercials assigned to different breaks. Since the existing reformulation can hardly be solved via exact methods, we introduce three new and efficient (mixed-)integer programming reformulations of the problem. Our computational study is based on two sets of test problems, one from the literature and another that we generate. Numerical results show the excellent performance of the proposed reformulations in terms of solution quality and computation times, when compared against an existing reformulation and an effective heuristic approach. We also provide theoretical evidences to demonstrate why some of our new reformulations should outperform the existing reformulation.

New Formulations for the Conflict Resolution Problem in the Scheduling of Television Commercials