Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-11T00:24:44.688Z Has data issue: false hasContentIssue false
  • English
  • Français

Minimization of communication expenditure for seasonal products

Published online by Cambridge University Press:  15 December 2002

Igor Bykadorov ,
Andrea Ellero  and
Elena Moretti
Igor Bykadorov
Affiliation:
Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Science, Acad. Koptyug Prospect 4, Novosibirsk 630090, Russia, and Università Ca'Foscari di Venezia, Italy; bykad@math.nsc.ru, bykadoro@unive.it
Andrea Ellero
Affiliation:
Dipartimento di Matematica Applicata, Università Ca'Foscari di Venezia, Dorsoduro 3825/E, 30123 Venezia, Italy; ellero@unive.it,tomasin@unive.it
Elena Moretti
Affiliation:
Dipartimento di Matematica Applicata, Università Ca'Foscari di Venezia, Dorsoduro 3825/E, 30123 Venezia, Italy; ellero@unive.it,tomasin@unive.it
Get access

Abstract

We consider a firmthat sells seasonal goods. The firm seeks to reach a fixed levelof goodwill at the end of the selling period, with the minimumtotal expenditure in promotional activities. We consider thelinear optimal control problem faced by the firm which can onlycontrol the communication expenditure rate; communication isperformed by means of advertising and sales promotion. Goodwilland sales levels are considered as state variables andword-of-mouth effect and saturation aversion are taken intoaccount. The optimal control problem is addressed by means of theclassical Pontryagin Maximum Principle and the solution can beeasily found solving, in some cases numerically, a system of twonon linear equations. Moreover, a parametric analysis is performedto understand how the total expenditure in communication shouldbe divided between advertising and sales promotion.

Keywords

Optimal controladvertisingsales promotionsseasonal products.
Type
Research Article
Information
RAIRO - Operations Research , Volume 36 , Issue 2 , April 2002 , pp. 109 - 127
Copyright
© EDP Sciences, 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

M.M. Abraham and L.M.Lodish, Fact-Based Strategies for Managing Advertising and Promotion Dollars: Lessons from Single Source Data, Working Paper #89-006. Marketing Department, The Wharton School of the University of Pennsylvania (1989).
A. Buratto and D. Favaretto, Optimal communication mix to maximize brand image, Rapporto No. 95/2001. Dipartimento di Matematica Applicata, Università di Venezia (2001).
Favaretto, D. and Viscolani, B., A single production and advertising control problem with bounded final goodwill. J. Inform. Optim. Sci. 21 (2000) 337-357.
Feichtinger, G., Hartl, R.F. and Sethi, S.P., Dynamic optimal control models in advertising: Recent developments. Management Sci. 40 (1994) 195-226. CrossRef
S. Funari and B. Viscolani, Advertising and congestion management for a museum temporary exhibition. Central Eur. J. Oper. Res. (to appear).
G.L. Lilien, P. Kotler and K.S. Moorthy, Marketing models. Prentice Hall Int., Englewood Cliffs (1992).
Little, J.D.C., Aggregate advertising models: The state of the art. Oper. Res. 27 (1979) 629-667. CrossRef
Naik, P.A., Mantrala, M.K. and Sawyer, A.G., Planning media schedules in the presence of dynamic advertising quality. Marketing Sci. 17 (1998) 214-235. CrossRef
Nerlove, M. and Arrow, K.-J., Optimal advertising policy under dynamic conditions. Economica 29 (1962) 129-142. CrossRef
L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mishchenko, The Matematical Theory of Optimal Processes. Pergamon Press, London (1964).
A. Seierstad and K. Sydsaeter, Optimal Control Theory with Economic Applications. North-Holland, Amsterdam (1987).
K. Spremann, The signaling of quality by reputation, in Optimal Control Theory and Economic Analysis 2, edited by G. Feichtinger. North-Holland, Amsterdam (1985) 235-252.
Vidale, M.L. and Wolfe, H.B., An operations research study for sales response to advertising. Oper. Res. 5 (1957) 370-381. CrossRef