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1 This article was downloaded by: [ ] On: 27 June 2014, At: 04:58 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK International Journal of Production Research Publication details, including instructions for authors and subscription information: Scheduling TV commercials using genetic algorithms Farhad Ghassemi Tari a & Reza Alaei a a Industrial Engineering, Sharif University of Technology, Tehran, Iran Published online: 05 Jul To cite this article: Farhad Ghassemi Tari & Reza Alaei (2013) Scheduling TV commercials using genetic algorithms, International Journal of Production Research, 51:16, , DOI: / To link to this article: PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the Content ) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at

2 International Journal of Production Research, 2013 Vol. 51, No. 16, , Scheduling TV commercials using genetic algorithms Farhad Ghassemi Tari* and Reza Alaei Industrial Engineering, Sharif University of Technology, Tehran, Iran (Received 22 February 2012; final version received 17 February 2013) In this paper, the problem of scheduling commercial messages during the peak of viewing time of a TV channel is formulated as a combinatorial auction-based mathematical programming model. Through this model, a profitable and efficient mechanism for allocating the advertising time to advertisers is developed by which the revenue of TV channels is maximised while the effectiveness of advertising is increased. We developed a steady-state genetic algorithm to find an optimal or a near optimal solution for the proposed problem. A computational experiment was conducted for evaluating the efficiency of the proposed algorithm. A set of test problems with different sizes were generated, using the pseudorandom generation mechanism, and solved by the proposed genetic algorithm. The optimal solutions of the linear programming relaxation of these test problems were also obtained and were used for evaluating the quality of solutions obtained by the developed algorithm. The results of this computational experiment revealed the robustness of the solutions and acceptably low computational time for obtaining these solutions. The computational results also demonstrated that the proposed genetic algorithm had an appropriate ability to preserve population diversity during the search and was capable of obtaining high-quality solutions for the proposed problem. Keywords: scheduling TV commercials; combinatorial auctions; winner determination; combinatorial optimisation; genetic algorithm 1. Introduction Television plays an important role in transmitting advertising messages. Although the television industry is mainly an entertainment provider, it takes advantage of the large number of viewers to convey advertising messages. Therefore advertising is the primary source of revenue for TV industries and they are extremely dependent on advertising income. In early days, television programmes were owned by advertisers, today however, it is rare for an entire programme to be sponsored by one advertiser. Rather, TV networks sell the time slots for ads during an entertainment programme. One of the major problems faced by TV channels is how to schedule the commercials in advertising breaks in order to maximise their revenues. The problem is difficult because of limited advertising time and the existence of some constraints that should be considered to maintain the effectiveness of advertising. Hence, we gain the advantages of a profitable and efficient resource allocation mechanism called combinatorial auction (CA) to formulate this problem. Combinatorial auctions involve a single bid taker allocating multiple distinguishable items amongst a set of bidders. Unlike traditional auctions, in CAs bidders can place bids on combinations of items, called packages (bundles), rather than just individual items in order to express more complex preferences. There might be economic relations between items in an auction. Therefore, valuations on packages of items can be super- or sub-additive. We call this, complimentarily and substitutability, respectively. The items may be (1) complements: the value of a bundle is greater than the sum of the values of its parts (e.g. a construction company may perceive that securing two projects in adjacent locations is less costly than the sum of securing each contract on its own because transportation synergies arise), or the opposite case (2) substitutes (e.g. the value selling two PC devices together which are not compatible is much lower than the value selling them individually). These relations could be ignored by selling each item in a separate auction. CAs take the relations between items into consideration while allocating them by letting bidders more fully express their preferences. Due to this feature, CAs can attain much more revenue if we capture that information well. So, using CA as a resource allocation mechanism often leads to improved economic efficiency (i.e. allocating the items to those who value them most) and greater auction revenues. A comprehensive context about CAs can be found in (Cramton, Shoham, and Steinberg 2006). *Corresponding author. ghasemi@sharif.edu Ó 2013 Taylor & Francis

3 4922 F. Ghassemi Tari and R. Alaei The problem of scheduling TV commercials has attracted the attention of many researchers. Brown (1969) described various hardships in scheduling commercials manually, and he developed an algorithm for the exchange of commercials of different lengths between advertising breaks to gain space for other commercials. Hägele, Dunlaing, and Riis (2001) proved that the problem which was defined by Brown is NP-complete. Bollapragada et al. (2002), Bollapragada, Bussieck and Mallik (2004a), studied the commercial scheduling problem to generate sales plans to meet the requirements of a single advertiser. The problem was modelled as an integer programme and solutions were found sequentially for each advertiser using mathematical programming-based heuristics. Mihiotis and Tsakiris (2004) studied the problem of finding the best possible combination of placements of a commercial (which channel, when, and how often) to gain the highest rating under the limitation of an advertising budget. The problem was modelled as an integer programming mathematical model and a heuristic algorithm was developed for finding a good solution. Bollapragada and Garbiras (2004) considered the problem of scheduling TV commercials over a specific period so that the airing of the same commercials are spread out as evenly as possible. Several integer programmes were proposed and heuristics were developed to find solutions for the problem. Jones (2000) presented the advertising allocation problem as an example of designing incompletely specified combinatorial auctions in which hundreds of advertisers can submit combinatorial bids for allocating their commercials in the advertising slots. He formulated the problem as an integer programming model, and employed heuristics based on constraint programming to find a set of feasible solutions for the mathematical model. Based on his work, Zhang (2006) studied the problem of selling the advertising time to advertisers. He proposed a two-step hierarchical method to find solutions for the problem. His approach starts with selecting advertisers and assigning them to TV programmes and ends with scheduling the commercials of the selected advertisers in a programme. The problem corresponding to the first step was solved using the column generation method. Kimms and Muller-Bungart (2007) described a planning problem at a broadcasting company where advertisers place orders for commercials and the airdates of the spots are not fixed by the advertisers. The channel has to decide simultaneously which orders to accept or to reject and when spots from accepted orders should be broadcasted. They formulated the problem as a mathematical model and presented several heuristics to find solutions for the problem. Fernando, Pereira, and Dalila (2007) developed a decision support system to plan the best assignment for the weekly promotion space of a major Portuguese TV station. The aim of this heuristic-based scheduling software system was to maximise the total viewing for each product within its target audience while fulfilling a set of constraints defined by advertisers. Benoist, Bourreau, and Rottembourg (2007) studied the TV break packing problem in which the TV channel sells packages of advertisement spots instead of selling them one by one. The problem is NP-hard and a so-called constraint programming/local search hybridisation scheme was applied to find solutions for the problem. Brusco (2008) studied the problem that is investigated by Bollapragada and Garbiras (2004). He developed an enhanced branch-and-bound algorithm to produce optimal solutions for the problem and a simulated annealing heuristic for larger instances of the problem. Gaur, Krishnamurti, and Kohli (2009) extended the model proposed by Bollapragada, Bussieck and Mallik (2004). The proposed extension allows differential weighting of conflicts between pairs of commercials. They formulated the problem as a capacitated generalisation of the max k-cut problem and extended the local search procedure due to Bollapragada, Bussieck and Mallik (2004) to find solutions for the resulting NP-hard problem. They also developed a localsearch procedure for solving their model. In another research effort, Wuang et al. (2010) presented an ant colony optimisation (ACO) heuristic for establishing a mechanism for solving the problem of scheduling television advertisements. Their proposed approach was based on network structuring and recursive calculation methods. In their approach, the scheduling mechanism and ACO heuristics are developed separately, improving the performance of the method in scheduling advertisements by varying parameters within the ACO heuristic and enabling the application to be flexibly modified by adjusting the scheduling criterion. Another attempt at using ACO for solving TV ad scheduling was the work of Mao et al. (2011). They proposed an ACO algorithm to optimise the sum of products of revenue and advertisers credit information in TV advertising and evaluated it using real data in the Japanese TV advertising market. Alaei and Ghassemi-Tari (2011) considered the problem of allocating the advertising time available during the prime time of a TV channel to advertisers in order to maximise its revenue. They formulated the problem as a multi-unit combinatorial auction-based mathematical model. They proposed a genetic algorithm for finding a near optimal solution. They also conducted a computational experiment for evaluating the efficiency of their proposed algorithm. The computational results of this experiment revealed that the proposed algorithm was capable of obtaining high-quality solutions for the randomly generated real-sized test problems.

4 International Journal of Production Research 4923 In this paper, we propose a mathematical model for scheduling commercials during the peak of viewing time of a TV channel. Through this model a profitable and efficient mechanism for allocating advertising time to advertisers is developed by which the revenue of a TV channel is maximised. In the model proposed by Alaei and Ghassemi-Tari (2011) there are no constraints to increase the effectiveness of advertising, however in the proposed model of this paper some constraints are considered to maintain and increase the effectiveness of advertising. The proposed model is formulated based on a combinatorial auction mechanism in which the TV channel, as an auctioneer, sells the time units available in advertising breaks to advertisers, as bidders. The presented model is a generalisation of the winner determination problem in multi-unit combinatorial auctions which is categorised in the class of NP-complete combinatorial optimisation problems. We developed a more advanced problem-specific genetic algorithm to efficiently find good solutions for the problem. 2. CA-based mechanism for scheduling TV commercials Before explaining the CA-based mechanism for scheduling TV commercials, we assume that the timetable of TV programmes during the peak of viewing time has already been specified. This timetable includes information about the number, location, and length of advertising breaks between different programmes and hence impacts the decision of advertisers to place bids on different advertising breaks. A combinatorial auction is described by a set of rules. These rules determine the winner determination procedure and the amount of money that winners have to pay. Also, they can restrict the feasible bids. The TV channel as auctioneer sells its available time for advertising to advertisers by considering several rules that are listed below: The length of commercials and advertising breaks is measured by a time unit that is composed of a particular number of seconds (e.g. 15 s). A combinatorial bid includes the advertiser s required time units of different advertising breaks (depending on his commercials length) together with the amount of money that he is interested in paying. With the aim of giving more opportunities for advertisers to express their preferences, each advertiser can place more than one but a limited number of bids on time units of advertising breaks such that at most one bid of each advertiser will be accepted. Advertisers can compete for the first and/or last time units of an advertising break that may have higher values for them by placing more promising bids. In order to give a chance to all bidders to advertise their products or services, the TV channel broadcasts at most one commercial for each advertiser in an advertising break. It is a rule of TV advertising that competing products or services should not be advertised within the same advertising breaks (Hägele, Dunlaing, and Riis 2001). Therefore, to increase the effectiveness of advertising, competing commercials are not allocated to the same advertising breaks. 3. Mathematical model Suppose that a TV channel has designated m advertising breaks in a timetable of programmes during the peak of viewing time, and t j is the maximum number of time units available in break j. Let A represent the set of advertisers and n to be its size. We partition A into p subsets, A 1, A 2,..., A p, such that the advertisers belonging to each subset advertise similar products or services. Each advertiser can place exactly r mutually exclusive combinatorial bids on time units of advertising breaks. A combinatorial bid includes the required time units of advertising breaks together with the amount of money which can be paid. We represent the number of required time units of advertiser i (i 2 A) from break j ( j =1, 2,, m) in the kth (k= 1, 2,, r) bid by the symbol t ijk and the amount of money which is paid for the kth bid by the symbol p ik. Let us also define: and the decision variables as: d ijk ¼ 1; t ijk [0 0; t ijk ¼ 0 (1)

5 4924 F. Ghassemi Tari and R. Alaei 1; if bid k of advertiser i is accepted x ik ¼ 0; otherwise (2) The problem of scheduling TV commercials with the objective of maximising the total revenue of the TV channel is formulated as follows: subject to: Maximise TR ¼ X i2a X r k ¼ 1 p ik x ik (3) X r k ¼ 1 x ik 1; i 2 A (4) X X r i2a k ¼ 1 t ijk x ik t j ; j ¼ 1; 2; :::; m (5) X X r i2a l k ¼ 1 d ijk x ik 1; j ¼ 1; 2; :::m; l ¼ 1; 2; :::; p (6) x ik 2f0; 1g; i 2 A; k ¼ 1; 2; :::; r (7) Where constraint (4) guarantees that at most one bid from each advertiser is accepted. Constraint (5) ensures that the sum of requested time units from an advertising break in accepted bids does not exceed the number of time units available in that break, and constraint (6) guarantees that the commercials which advertise similar products or services are not allocated to the same breaks. The model is a generalised form of the winner determination problem in multi-unit combinatorial auctions in which there are exclusive or constraints (4 and 6) between some of bids. The problem of winner determination in multi-unit combinatorial auctions is categorised in the class of NP-complete combinatorial optimisation problems, even with the existence of exclusive or constraints as proved in Sandholm (2002). Consequently, the problem of scheduling TV commercials belongs to this class of problems. We now develop a genetic algorithm to efficiently find good solutions for the problem. 4. Development of a genetic algorithm We use the general framework of the genetic algorithm for developing our solution approach. Before presenting a detailed description of the proposed algorithm, let us outline the general framework of the Genetic Algorithms (GAs) as follows: Generate an initial population; Generate an initial population; Evaluate the fitness of individuals in the population; Repeat: Select parents from the population; Recombine parents to produce children; Evaluate the fitness of the children; Replace some or all of the population by the children; Until a satisfactory solution has been found We now describe how to develop each of the major steps of the proposed GA.

6 International Journal of Production Research Representation and fitness function The first step in designing of our proposed algorithm is to develop an appropriate method to represent individuals in the GA population. A solution point for the problem can be represented by a chromosome of length n, such that each gene can take a value in f0; 1; 2; :::; rg. Since each gene refers to an advertiser, its value refers to the advertiser s accepted bid if the gene has a nonzero value. If the gene has a zero value, then none of the advertiser s bids has been accepted. We could use binary coding to represent individuals in a population but we took advantage of integer coding to automatically satisfy constraint (4). We have noticed that an individual might represent an infeasible solution. Therefore, we have designed a repair operator based on a greedy heuristic which ensures the conversion of any infeasible solution into a feasible one. By restricting the GA to search only in the feasible region of the solution space, the fitness value of each individual is given by the objective function value of the corresponding solution. 4.2 Initialisation In order to have an appropriate level of diversity, the initial population with size N was randomly generated. We required that at least every possible point in the search space should be reachable from the initial population by crossover only. It is clear that this requirement can only be satisfied if there is at least one instance of every member of f0; 1; 2; :::; rg at each locus in the initial population. Given the value of n, chromosome length, we can calculate the corresponding probability P as follows: n (r þ 1)! S(N; r þ 1) P ¼ (8) (r þ 1) N where, S(N,r + 1) is the Stirling number of the second kind. It is now possible to determine values of N such that P exceeds a desired value (e.g. 0.99). For constructing each non-duplicate initial random feasible solution, a constructive algorithm is applied that repeatedly randomly selects an advertiser and accepts one of his bids at random if the constructed solution remains feasible. The heuristic terminates when the remained advertisers cannot be added to the set of winners. We require at most O(mnr) arithmetic operations to construct each initial random feasible solution. 4.3 Parent selection Parent selection is the task of assigning reproductive opportunities to each individual in the population. We use the binary tournament method to efficiently generate two parents who will have a child. In this method, two groups consists of two individuals are randomly drawn from the population. Two individuals with the best fitness, each taken from one of the two tournament groups, are chosen to be parents. 4.4 Reproduction The reproduction phase in GA includes crossover and mutation procedures. We adopted a uniform crossover with rate 1 and a particular mutation operator with rate 1 n for this phase. In uniform crossover two selected parents have a single child. Each gene value in the child solution is created by copying the corresponding gene value from one or the other parent, chosen according to a binary random number generator. If the random number is zero, the gene value is copied from the first parent; if it is one, the gene value is copied from the second parent. Once a child solution has been generated through the crossover operator, the mutation procedure is performed that mutates some randomly selected genes in the child solution. We designed the mutation operator in such a way that prevents the premature convergence of GA by preserving the genetic diversity of the population during the search. The genetic diversity is determined by gene values of individuals in the population and is maximised when the genetic diversity in every gene column is maximised. Assuming N is divisible by (r + 1), the genetic diversity in a special gene is maximised when the frequency of each N member of f0; 1; 2; :::; rg in its corresponding gene column is equal to (r þ 1). Having the frequency of each member of f0; 1; 2; :::; rg in each gene column, the mutation operator replaces the value of the selected gene with the value that has the minimum frequency in the gene column.

7 4926 F. Ghassemi Tari and R. Alaei 4.5 Repair operator Clearly, the child solution produced by crossover and mutation operators may not be feasible because the constraints (5) and (6) may not both be satisfied. In order to guarantee feasibility, a repair operator based on a greedy algorithm was applied. We considered a criterion in the following form to choose the most promising bids in a greedy algorithm. R ik ¼ p ik (1:(T (i 1)r þ k ) a ) b; a; b[0 (9) where, T is the problem s constraints matrix, T (i 1)r + k is the corresponding column of x ik in T, and 1 is the row sum vector with dimension of (n + m + mp). Gonen and Lehmann (2000) proved that this criterion with a ¼ 1 and b ¼ 1 2 guarantees, in the worst case, the best possible approximation ratio for the winner determination problem in multi-unit combinatorial auctions. Based on their result, we used the following criterion in the greedy algorithm. R ik ¼ p ik q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ P (10) m j ¼ 1 (t ijk þ d ijk ) The greater the criterion, the higher the chance that the corresponding binary variable will be equal to 1 in the solution. Our repair operator consists of two phases. The first phase examines each variable in increasing order of R ik and if the value of gene i is k, changes it to zero until feasibility is achieved. The second phase reverses the process by examining each variable in decreasing order of R ik and if the value of gene i is zero, changes it to k as long as feasibility is not violated. These two phases are done in such a way that the effect of the mutation operator is not eliminated. The repair operator requires at most O(mNp) arithmetic operations to transform an infeasible solution to a feasible one. 4.6 Replacement and termination After the reproduction and repair phases, the produced feasible child solution is replaced by an individual with the lowest fitness value in the population (steady-state replacement). Through this replacement, any duplicate child solution is discarded from the population. The GA is terminated when a particular number of non-duplicate child solutions have been generated. 5. Computational experiment We conducted a computational experiment for evaluating the efficiency of the proposed GA. By the efficiency we mean the quality of the solutions obtained by the proposed algorithm and the computational time required to obtain the final solution. To have an unbiased evaluation, we employed the concept of pseudo-random generation for building the test problems. We generated 16 test problems which are classified according to the values of m, n, and r. We selected the values of these parameters in such amounts as to have the test problem sizes similar to the real-world problem sizes, based on the information we gathered from a local TV station. It should be noted that the advertisement s demands have seasonal behaviour and they actually vary during the peak of viewing time of each season as well as during the different months of each season. To accomplish this, we first classified the test problems into two categories according to the values of m, the total number of breaks. For the first category we assigned the value 25 and for the second category we assigned the value 50 to m. In each category we generated eight test problems with two different values, 100 and 200, for n, the number of advertisers, and two different values, 5 and 10, for r, the number of bids for each advertiser. We let the value of p, the number of product or service categories, be dependent to the values of n and r, and therefore the value of p is determined by the associated values of n and r by P ¼ n 2r and n r. Given the values of n and r, we determined the population size, N, by assigning the value of 0.99 to P (Equation (8)). In order to evaluate the quality of the solutions obtained by the proposed algorithm, we need to determine the deviation of the final solutions of test problems with their associated optimal solutions. However, due to the size of the test problems, their optimal solutions cannot be determined. We therefore determined the Linear Program (LP)-relaxed solutions of the test problems and used them as an upper bound of their associated optimal solutions. We generated 10 instances for each test problem category for evaluating the efficiency of the proposed algorithm in obtaining their solutions. The steps of the GA were coded using MATLAB 7 and we used a computer with 2.40 GHz Intel Celeron CPU and 512 MB of RAM, for solving the test problems. We assigned the value of ½ m 10 Š104 for the generated non-duplicate child solutions as a terminating rule of the GA. We then solved 10 instances of each test problem using the proposed GA. We also used LINGO 8 to

8 International Journal of Production Research 4927 solve the LP relaxation of the test problems to obtain the associated upper bound of their optimal solutions. We defined the deviation of the GA solution from the associated upper bound of the optimal solution of the test problem (optimal solution of the LP-relaxed problem) as % gap as follows: %Gap ¼ 100(TR LP max TRGA max )=TRLP max (11) where, TR GA max is the objective function value of the GA s solution and TRLP max is the optimal value of the LP-relaxed problem. Tables 1 and 2 illustrate the results of the computational experiment. As is seen from these tables, the final solutions of the test problems solved by the proposed GA can be considered to be very close to their associated optimal solutions. Table 1. Computational results for problem instances in which m = 25. Problem type n r p N Ave. time for best solution Ave.% gap Table 2. Computational results for problem instances in which m = 50. Problem type n r p N Ave. time for best solution Ave.% gap Figure 1. GA s ability to preserve the population diversity for a problem instance in which m = 25.

9 4928 F. Ghassemi Tari and R. Alaei Figure 2. GA s ability to preserve the population diversity for a problem instance in which m = 50. It is due to the fact that in most cases their solutions are greater than 90% of the upper bound of their associated optimal solutions. Another notable result regarding the quality of the solution is the fact that the deviation of the GA solutions from the optimal solutions of the LP relaxation of test problems is decreased as the number of binary variables is increased. Considering the size of these test problems, which are in the form of the combinatorial optimisation models, it can be concluded that the computational time to obtain these robust solutions are acceptably low. Also, a notable result regarding the computational time is the fact that the computational time grows almost linearly as the number of binary variables is increased. Furthermore, computational results show that the proposed algorithm has an appropriate ability to preserve population diversity during the search due to using our specific mutation procedure. Figures 1 and 2 illustrate the GA s ability to preserve the population diversity for a problem instance in which m = 25 and m = 50, respectively. As illustrated in Figures 1 and 2, the search experienced a similar level of macroscopic population diversity (i.e. the distance between minimum and maximum fitness values in the population) at the starting and final iterations of the GA. 5. Conclusions In this paper we proposed a mathematical model, based on a combinatorial auction mechanism for scheduling TV commercials during the peak of viewing time of a TV channel. The successful application of the genetic algorithm for solving similar problems (Alaei and Ghassemi-Tari 2011) motivated us to develop a genetic algorithm for solving the developed mathematical model. We therefore developed a steady-state genetic algorithm for solving the corresponding NP-complete combinatorial optimisation mathematical model. We have used a greedy heuristic in our GA that guarantees the feasibility of the produced child solutions. Furthermore, we have applied a particular mutation procedure that helps GA to overcome the premature convergence by preserving the proper population diversity during the searching process. The proposed mutation procedure can be applied in GAs for other problems when integer coding is used for the representation of solutions. We conducted a computational experiment for evaluating the efficiency of the proposed algorithm with respect to the solution quality and computational time. We employed the concept of pseudo-random generation and we generated a set of test problems. We then solved the test problems using the proposed GA and used a linear programming method for solving the LP relaxation of the test problems. The computational results revealed that the final solutions of the test problems solved by the proposed GA can be considered to be very close to their associated optimal solutions. They also revealed that the computational time to obtain the robust solutions of the test problems is acceptably low. Furthermore, the computational results demonstrated that our proposed algorithm has an appropriate ability to preserve the population diversity during the search and is capable of obtaining high-quality solutions for the problem. Although the experimental results confirm that the developed genetic algorithm performed very well in solving the proposed problem, in future research it would be worthwhile to consider other metaheuristic or machine-learning approaches for solving this problem.

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