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

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

Keywords

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

All Science Journal Classification (ASJC) codes

Control and Optimization

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10.1007/s11590-018-1251-0

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title = "The TV advertisements scheduling problem",

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 pj that sum up to h, and willingness to pay coefficients wj, 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 [ cj- pj, cj) 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).",

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doi = "10.1007/s11590-018-1251-0",

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AU - Díaz-Núñez, Fabián

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AU - Vásquez, Óscar C.

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AB - 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 pj that sum up to h, and willingness to pay coefficients wj, 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 [ cj- pj, cj) 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).

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The TV advertisements scheduling problem

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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