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Using partially observed Markov processes to select optimal termination time of TV shows

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  • Givon, Moshe
  • Grosfeld-Nir, Abraham

Abstract

This paper presents a method for optimal control of a running television show. The problem is formulated as a partially observed Markov decision process (POMDP). A show can be in a "good" state, i.e., it should be continued, or it can be in a "bad" state and therefore it should be changed. The ratings of a show are modeled as a stochastic process that depends on the show's state. An optimal rule for a continue/change decision, which maximizes the expected present value of profits from selling advertising time, is expressed in terms of the prior probability of the show being in the good state. The optimal rule depends on the size of the investment in changing a show, the difference in revenues between a "good" and a "bad" show and the number of time periods remaining until the end of the planning horizon. The application of the method is illustrated with simulated ratings as well as real data.

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  • Givon, Moshe & Grosfeld-Nir, Abraham, 2008. "Using partially observed Markov processes to select optimal termination time of TV shows," Omega, Elsevier, vol. 36(3), pages 477-485, June.
    • Handle: RePEc:eee:jomega:v:36:y:2008:i:3:p:477-485
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    References listed on IDEAS

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    1. Jeffrey H. Horen, 1980. "Scheduling of Network Television Programs," Management Science, INFORMS, vol. 26(4), pages 354-370, April.
    2. Roland T. Rust & Mark I. Alpert, 1984. "An Audience Flow Model of Television Viewing Choice," Marketing Science, INFORMS, vol. 3(2), pages 113-124.
    3. William S. Lovejoy, 1987. "Ordered Solutions for Dynamic Programs," Mathematics of Operations Research, INFORMS, vol. 12(2), pages 269-276, May.
    4. S. Christian Albright, 1979. "Structural Results for Partially Observable Markov Decision Processes," Operations Research, INFORMS, vol. 27(5), pages 1041-1053, October.
    5. Richard D. Smallwood & Edward J. Sondik, 1973. "The Optimal Control of Partially Observable Markov Processes over a Finite Horizon," Operations Research, INFORMS, vol. 21(5), pages 1071-1088, October.
    6. James T. Treharne & Charles R. Sox, 2002. "Adaptive Inventory Control for Nonstationary Demand and Partial Information," Management Science, INFORMS, vol. 48(5), pages 607-624, May.
    7. Abraham Grosfeld-Nir, 1996. "A Two-State Partially Observable Markov Decision Process with Uniformly Distributed Observations," Operations Research, INFORMS, vol. 44(3), pages 458-463, June.
    8. Douglas J. White, 1985. "Real Applications of Markov Decision Processes," Interfaces, INFORMS, vol. 15(6), pages 73-83, December.
    9. George E. Monahan, 1982. "State of the Art---A Survey of Partially Observable Markov Decision Processes: Theory, Models, and Algorithms," Management Science, INFORMS, vol. 28(1), pages 1-16, January.
    10. Daniel E. Lane, 1989. "A Partially Observable Model of Decision Making by Fishermen," Operations Research, INFORMS, vol. 37(2), pages 240-254, April.
    11. James N. Eagle, 1984. "The Optimal Search for a Moving Target When the Search Path Is Constrained," Operations Research, INFORMS, vol. 32(5), pages 1107-1115, October.
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    Cited by:

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    2. Pérez-Gladish, B. & Gonzalez, I. & Bilbao-Terol, A. & Arenas-Parra, M., 2010. "Planning a TV advertising campaign: A crisp multiobjective programming model from fuzzy basic data," Omega, Elsevier, vol. 38(1-2), pages 84-94, February.
    3. Danaher, Peter J. & Dagger, Tracey S. & Smith, Michael S., 2011. "Forecasting television ratings," International Journal of Forecasting, Elsevier, vol. 27(4), pages 1215-1240, October.
    4. Chernonog, Tatyana & Avinadav, Tal, 2016. "A two-state partially observable Markov decision process with three actionsAuthor-Name: Ben-Zvi, Tal," European Journal of Operational Research, Elsevier, vol. 254(3), pages 957-967.
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