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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Bibliographic Details
Published in:Optimization letters Vol. 13; no. 1; pp. 81 - 94
Main Authors: Díaz-Núñez, Fabián, Halman, Nir, Vásquez, Óscar C.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 08.02.2019
Subjects:
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
Online Access:Get full text
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Summary: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 ).
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-018-1251-0