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

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  • Giovanni Giallombardo
  • Giovanna Miglionico

    (Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica, Universita della Calabria)

  • Houyuan Jiang

    () (Cambridge Judge Business School, University of Cambridge)

Abstract

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.

Suggested Citation

  • Giovanni Giallombardo & Giovanna Miglionico & Houyuan Jiang, 2015. "New Reformulations for the Conflict Resolution Problem in the Scheduling of Television Commercials," Working Papers 2015/03, Cambridge Judge Business School, University of Cambridge.
  • Handle: RePEc:jbs:wpaper:201503
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    References listed on IDEAS

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    1. Victor F. Araman & Ioana Popescu, 2010. "Media Revenue Management with Audience Uncertainty: Balancing Upfront and Spot Market Sales," Manufacturing & Service Operations Management, INFORMS, vol. 12(2), pages 190-212, December.
    2. Andreas Ernst & Houyuan Jiang & Mohan Krishnamoorthy, 2006. "Exact Solutions to Task Allocation Problems," Management Science, INFORMS, vol. 52(10), pages 1634-1646, October.
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    Keywords

    television advertising; conflict resolution problem; integer programming;

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