A Network Modeling Approach for the Optimization of Internet-Based Advertising Strategies and Pricing with a Quantitative Explanation of Two Paradoxes

Transcription

1 A Network Modelng Approach or the Optmzaton o Internet-Based Advertsng Strateges and Prcng wth a Quanttatve Explanaton o Two Paradoxes Lan Zhao Department o Mathematcs and Computer Scences SUNY/College at Old Westbury, NY568 Anna Nagurney Department o Fnance and Operatons Management Isenberg School o Management Unversty o Massachusetts Amherst. MA0003

2 Hghlghts o ths Research It s the rst attempt to ormulate the determnaton o optmal Internet marketng strateges as a network optmzaton problem, whch allows us to take advantage o network theory n terms o qualtatve analyss and computatons. The results also provde a quanttatve perspectve to explan such paradoxes as: advertsng on more web-stes may cause a declne n the number o clcks and the clck rate.

3 Hghlghts o ths Research Ths research provdes a ormula or the computaton o optmal Internet marketng strateges. It provdes a prcng ndex to suggest how rms should sht rom one prcng scheme to another.

4 Network Modelng has been Used n Numerous Applcatons and Dscplnes: Transportaton Scence and Logstcs Telecommuncatons and Computer Scence Regonal Scence and Economcs Engneerng Fnance Operatons Research and Management Scence

5 Some Lterature on Internet-based Marketng Modelng the Clckstream: Implcatons or webbased advertsng Eorts, by P. Chatterjee, D. L. Homan, and T.P. Novak, 50-54, 003. Advertsng Competton Under Consumers Inerta, Banerjee, B and S. Bandyopadhyay. (003) A Comparson o Onlne and Olne Consumer Brand Loyalty, by Danaher, P., Wlson, I., and R. Davs (003)

6 Assumptons A rm s advertsng on n Internet market places. Response (Amount o clck-through) s an ncreasng, concave uncton o the amount o advertsement exposures.

7 Assumptons Amount o clck-throughs n webste s also mpacted by advertsement exposures on other webstes. r r ( e, e,..., e n ) A rm s objectve s to acheve the maxmum amount o clck-through.

8 The Optmzaton Model Let c,,,n be the unt cost o exposure and C be the advertsng budget. The rm s to Maxmze subject to : e n n r ( e c e 0,,,... n,..., e C n )

9 Let ce, (,...,, n), then s the amount o money assgned to webste. Smple calculus manpulaton can show us that: n the response unctons r ( ) r (,..., ) c are ncreasng c n and concave unctons o, they are ncreasng and concave unctons o e. The non-lnear programmng model s equvalent to:

10 The Network Model Maxmze B( ) n subject to : + 0,,,... n n r ( n+ ) C

11 The Equvalent Network Model The dotted lnk s the dummy lnk that absorbs the budget surplus n+.

12 The Varatonal Inequalty Formulaton B( *) ( *) 0 S { 0, n + C}

13 Ths varatonal nequalty can be solved by an teratve scheme where the uncton n each o the subproblems s separable and quadratc (see Daermos and Sparrow (969), Daermos (980), Zhao and Daermos (99), Nagurney (999)).

14 A Specal-Purpose Algorthm: I B() s a separable quadratc uncton n the sense that B a + b Then the optmal strategy can be ound by procedure:. Sort, wthout lose o generalty, we assume b b b,..., b n ()

15 . Let k Calculate λ k C + k k a b a () Compare wth n () λ k b b λ < b wth pk then Let λ λ k go to (3) p k < p + wth p>k, then let kk+, go to () b b p λ λ k < b p + wth p<k, then let kk-, go to () p k b p +

16 3. 0, * * ;,,... }, max{0, * 0, * ;,,... }, max{0, * > λ λ λ n n n C n a b o n a b

17 When the mpacts o advertsng eorts n webstes are nterrelated, havng more optons o choosng webstes or ads may be worse o than havng ewer optons!

18 An Illustraton o the Paradoxes

19 Example : There are two webstes to choose or advertsng and the budget s $9000. The response unctons on webste and are respectvely: r r e + Optmal Strateges Expendtures Exposures Clck-throughs(n 00s) Ste $ Ste $ e + 0.4e + 0.e +

20 Example : There are three webstes to choose or ads and the budget remans at $9000. The response unctons on each o the stes are respectvely: r 0.000e r r e 0.000e e + 0.e + 0.e e + 0.0e e 0.003e Optmal Strateges Expendtures Exposures Clck-throughs(n 00s) Ste $ Ste $ Ste 3 $ Total clck-throughs are.056 ewer than n Example!

21 Explanaton Usng an addtonal (new) webste causes a change n response, whch can be decomposed nto three parts: () The change n response n old webstes s mpacted by advertsements n the new webste. Ths change may or may not be negatve.

22 Explanaton () The change n response n the old webstes caused by the decrease n assocated advertsng captal s negatve. (3) The response generated n new webste s non-negatve. I tem (3) cannot preval over the sum o () and (), then the use o the new webste or advertsng makes the rm worse-o!

23 Accepted or publcaton n Netnomcs Avalable or download at

24 Future Research The development o network equlbrum models or the modelng o Internet marketng competton. Modelng the mpact o asymmetrc normaton on optmal marketng strateges.

25 For more normaton see:

26 Thank you!!!