The TV advertisements scheduling problem

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 obj...

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Vydané v:	Optimization letters Ročník 13; číslo 1; s. 81 - 94
Hlavní autori:	Díaz-Núñez, Fabián, Halman, Nir, Vásquez, Óscar C.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 08.02.2019
Predmet:	Computational Intelligence Mathematics Mathematics and Statistics Numerical and Computational Physics Operations Research/Decision Theory Optimization Original Paper Simulation Fully polynomial time approximation scheme approximation sets and functions TV rating points Scheduling Dynamic programming
ISSN:	1862-4472, 1862-4480
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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 ∑ j w j ∫ c j - p j c j f ( t ) d t , 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 ).
AbstractList	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 ∑ j w j ∫ c j - p j c j f ( t ) d t , 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 ).
Author	Díaz-Núñez, Fabián Vásquez, Óscar C. Halman, Nir
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Title	The TV advertisements scheduling problem
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