Application of a Mathematical Model to an Advertisement Reservation Problem
Television networks provide TV programs free of charge to the public. However, they acquire their revenue by telecasting advertisements in the midst of continuing programs or shows. A key problem faced by the TV networks in Turkey is how to accept and televise the advertisements reserved by a client on a specified advertisement break which we called “Advertisement Reservation Problem” (ARP). The problem is complicated by limited time inventory, by different rating points for different target groups, competition avoidance and the relationship between TV networks and clients. In this study we have developed a mathematical model for advertisement reservation problem and extended this model for some cases encountered in real business life. We have also discussed how these cases affect the decisions of a TV network. Mixed integer linear programming approach is proposed to solve these problems. This approach has been implemented to a case taken from one of the biggest TV networks of Turkey.
[1] Zhang, X., Mathematical Models for the Television Advertising Allocation Problem. IJOR, 1(3), 302-322 (2006).
[2] Alvarado, C., Revenue Management for the Inventory Optimization of Television Azteca. Television Azteca external communication document (2007)
[3] Bollapragada, S., Mallik, H. M., Managing On-air Ad Inventory in Broadcast TV. IIE Transactions, 40 (12), 1107-1123 (2008).
[4] Bollapragada, S., Cheng, H., Phillips, M., Garbiras, M., NBC’s optimization systems increase revenues and productivity. Interfaces, 32 (1), 47-60 (2002).
[5] Bollapragada, S., Garbiras, M., Scheduling commercials on broadcast television. Operations Research, 53 (3), 337-345 (2004).
[6] Kimms, A., Muller-Bungart, M., Revenue management for broadcasting commercials: the channel’s problem of selecting and scheduling the advertisements to be aired. Int. J. of Revenue Management, 1(1), 28 – 44 (2007).
[7] Metheringham, R.A., Measuring the Net Cumulative Coverage of a Print Campaign. J. of Advertising Research, 4, 23-28 (1964).
[8] Kanetkar, V., Weinberg, C.B., Price Sensitivity and Television Advertising Exposures: Some Empirical Findings.Marketing Science, 11(4), 359-371 (1992).
[9] Lodish, L.M., Abraham, M., Kalmenson, S., Livelsberger, J., Lubetkin, B., Richardson, B., Stevens, M.E., How TV Advertising Works: A Meta-Analysis of 389 Real World Cable TV Advertising Experiments. J. of Marketing Research, 32, 125-139 (1995).
[10] Hairong, L., Advertising media, http://www.admedia.org (2005). Accessed November (2011)
[11] Riorden, J., An Introduction to Combinatorial Analysis, John Wiley, New York (1958).
[12] Lee, A.M., Burkart, A.J., Some optimization problems in advertising media planning. Operational Research Quarterly, 11, 113– 122 (1960).
[13] Day, R.L., Linear programming in media selection. J. of Advertising Research, 2, 40– 44 (1962).
[14] Engel, J.F., Warshaw, M.R., Allocating advertising dollars by linear programming. J. of Advertising Research, 4, 42–48 (1964).
[15] Stasch, S.F., Linear programming and space–time considerations in media selection. J. of Advertising Research, 5, 40– 46 (1965).
[16] Brown, D.B., Warshaw, M., Media selection by linear programming. J. of Marketing Research, 2, 83–88 (1965).
[17] Little, J.D.C., Lodish, L.M., A media selection model and its optimization by dynamic programming. Industrial Management Review, 8, 15–23 (1966).
[18] Maffei, R.B., Planning advertising expenditures by dynamic programming methods. Management Technology, 1, 94– 100 (1960).
[19] Aaker, D.A., A probabilistic approach to industrial media selection. J. of Advertising Research, 8, 46–54 (1968).
[20] Zufryden, F.S., Media scheduling: a stochastic dynamic model approach. Management Science, 19, 1395–1406 (1973).
[21] Fruchter, G.E., Kalish, S., Dynamic promotional budgeting and media allocation. European J. of Operational Research, 111,15–27 (1998).
[22] Berkowitz, D., Alaway, A., Souza, G., The impact of differential lag effects on the allocation of advertising budgets across media. J. of Advertising Research, 41 (2), 27–37 (2001).
[23] Mihiotis, A., Tsakiris, I., A mathematical programming study of advertising allocation problem. Applied Mathematics and Computation, 148, 373–379 (2004).
[24] Cetin, E., Esen, S.T., A weapon-target assignment approach to media allocation. Applied Mathematics and Computation, 175, 1266–1275 (2006).
[25] Saha, A., Pal, M., Pal, T. K., Selection of programme slots of television channels for giving advertisement: A graph theoretic approach. Information Sciences, 177 (12), 2480-2492 (2007).
[26] Gensch, D., Shaman, P., Models of competitive television ratings. J. of Marketing Research, 17, 307–315 (1980).
[27] Horen, J., Scheduling of network television programs. Management Science, 2, 354–370 (1980).
[28] Rust, R., Echambadi, N., Scheduling network television programs: a heuristic audience flow approach to maximizing audience share. J. of Advertising, 18, 11–18 (1989).
[29] Talluri, K., van Ryzin, G., The Theory and Practice of Revenue Management, Kluwers, (2004).
[30] Araman, V.F., Popescu, I., Media Revenue Management with Audience Uncertainty: Balancing Upfront and Spot Market Sales. MSOM, 12 (2), 190-212 (2010).
[31] Yano, C., Lee, H.L., Lot sizing and random yields: A review. Operations Research, 43(2), 311-334 (1995).
[32] Grosfeld-Nir, A., Gerchak, Y., Multiple lot sizing in production to order with random yields: Review of recent advances. Annals of Operations Research, 126, 43-69 (2004).
[33] Shih, Optimal inventory policies when stockouts result from defective products. Int. J. of Production Research, 18 (6), 677-685 (1980).
[34] Gerchak, Y., Vickson, R.G., Parlar, M., Periodic Review Production Planning Model with Uncertain Capacity and Uncertain Demand. IIE Transactions. 20 (3), 144-150 (1988).
[35] Bollapragada, S., Morton, T.E., Myopic heuristics for the random yield problem. Operations Research, 47 (5), 713-722 (1999).
[36] Li, Q., Zheng, S., Joint Inventory Replenishment and Pricing Control for Systems with Uncertain Yield and Demand. Operations Research. 54 (4), 696-705 (2006).
[37] Kazaz, B., Production Planning Under Yield and Demand Uncertainty with Yield- Dependent Cost and Price. Manufacturing & Service Operations Management, 6 (3), 209- 224 (2004).