The TV advertisements scheduling problem

Fabián Díaz-Núñez; Nir Halman; Óscar C. Vásquez

doi:10.1007/s11590-018-1251-0

The TV advertisements scheduling problem

Fabián Díaz-Núñez, Nir Halman, Óscar C. Vásquez

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

A TV channel has a single advertisement break of duration h and a convex continuous function f:[0,h]→R+ representing the TV rating points within the advertisement break. Given n TV advertisements of different durations p_j that sum up to h, and willingness to pay coefficients w_j, the objective is to schedule them on the TV break in order to maximize the total revenue of the TV channel ∑jwj∫cj-pjcjf(t)dt, where [ c_j- p_j, c_j) is the broadcast time interval of TV advertisement j. We show that this problem is NP-hard and propose a fully polynomial time approximation scheme, using a special dominance property of an optimal schedule and the technique of K-approximation sets and functions introduced by Halman et al. (Math Oper Res 34:674–685, 2009).

Original language	English
Pages (from-to)	81-94
Number of pages	14
Journal	Optimization Letters
Volume	13
Issue number	1
DOIs	https://doi.org/10.1007/s11590-018-1251-0
State	Published - 8 Feb 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

Funding

The authors are grateful for partial support from the following sources: FONDECYT Grant 11140566 (F. Díaz-Núñez and Ó. C. Vásquez), Universidad de Santiago, Proyecto DICYT 061817VP (Ó. C. Vásquez) and Israel Science Foundation Grant 399/17 (N. Halman). Acknowledgements The authors are grateful for partial support from the following sources: FONDECYT Grant 11140566 (F. Díaz-Núñez and Ó. C. Vásquez), Universidad de Santiago, Proyecto DICYT 061817VP (Ó. C. Vásquez) and Israel Science Foundation Grant 399/17 (N. Halman).

Funders	Funder number
Universidad de Santiago
Fondo Nacional de Desarrollo Científico y Tecnológico	11140566
Israel Science Foundation	399/17

Keywords

Dynamic programming
Fully polynomial time approximation scheme
K-approximation sets and functions
Scheduling
TV rating points

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10.1007/s11590-018-1251-0

Cite this

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The TV advertisements scheduling problem

Abstract

Bibliographical note

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Keywords

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