The TV advertisements scheduling problem - Díaz-Núñez, Fabián; Halman, Nir; Vásquez, Óscar C. (Optimization letters, 2019)
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 ).