Chance Constrained Optimization for Targeted Internet Advertising

We introduce a chance constrained optimization model for the fulfillment of guaranteed display Internet advertising campaigns. The proposed formulation for the allocation of display inventory takes into account the uncertainty of the supply of Internet viewers. We discuss and present theoretical and computational features of the model via Monte Carlo sampling and convex approximations. Theoretical upper and lower bounds are presented along with a numerical substantiation.

[1]  Alexander Shapiro,et al.  Sample Average Approximation Method for Chance Constrained Programming: Theory and Applications , 2009, J. Optimization Theory and Applications.

[2]  Alexander Shapiro,et al.  Convex Approximations of Chance Constrained Programs , 2006, SIAM J. Optim..

[3]  Jason K. Deane,et al.  Scheduling online advertisements to maximize revenue under variable display frequency , 2012 .

[4]  Shabbir Ahmed,et al.  Convex relaxations of chance constrained optimization problems , 2014, Optim. Lett..

[5]  John A. Tomlin,et al.  An entropy approach to unintrusive targeted advertising on the Web , 2000, Comput. Networks.

[6]  Giuseppe Carlo Calafiore,et al.  The scenario approach to robust control design , 2006, IEEE Transactions on Automatic Control.

[7]  Johan Efberg,et al.  YALMIP : A toolbox for modeling and optimization in MATLAB , 2004 .

[8]  John Turner,et al.  The Planning of Guaranteed Targeted Display Advertising , 2012, Oper. Res..

[9]  Jovan Dj. Golic.  Random correlation matrices , 1998, Australas. J Comb..

[10]  Donald Goldfarb,et al.  Second-order cone programming , 2003, Math. Program..

[11]  Md. Tanveer Ahmed,et al.  Optimal contract-sizing in online display advertising for publishers with regret considerations , 2014, Omega.

[12]  Sergei Vassilvitskii,et al.  Inventory Allocation for Online Graphical Display Advertising , 2010, ArXiv.

[13]  J. Lofberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).

[14]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[15]  Susan X. Li.  An insurance and investment portfolio model using chance constrained programming , 1995 .

[16]  James R. Luedtke,et al.  A Sample Approximation Approach for Optimization with Probabilistic Constraints , 2008, SIAM J. Optim..

[17]  Guohe Huang,et al.  An integrated approach for water resources decision making under interactive and compound uncertainties , 2014 .

[18]  Philippe Preux,et al.  Managing advertising campaigns — an approximate planning approach , 2012, Frontiers of Computer Science.

[19]  Antonio Alonso Ayuso,et al.  Introduction to Stochastic Programming , 2009 .

[20]  Sergei Vassilvitskii,et al.  Inventory Allocation for Online Graphical Display Advertising using Multi-objective Optimization , 2012, ICORES.

[21]  B. E. Eckbo,et al.  Appendix , 1826, Epilepsy Research.