Bykadorov, Igor; Ellero, Andrea; Moretti, Elena Minimization of communication expenditure for seasonal products. (English) Zbl 1062.90022 RAIRO, Oper. Res. 36, No. 2, 109-127 (2002). Summary: We consider a firm that sells seasonal goods. The firm seeks to reach a fixed level of goodwill at the end of the selling period, with the minimum total expenditure in promotional activities. We consider the linear optimal control problem faced by the firm which can only control the communication expenditure rate; communication is performed by means of advertising and sales promotion. Goodwill and sales levels are considered as state variables and word-of-mouth effect and saturation aversion are taken into account. The optimal control problem is addressed by means of the classical Pontryagin maximum principle and the solution can be easily found solving, in some cases numerically, a system of two non linear equations. Moreover, a parametric analysis is performed to understand how the total expenditure in communication should be divided between advertising and sales promotion. Cited in 5 Documents MSC: 90B30 Production models Keywords:optimal control; advertising; sales promotions; seasonal products PDFBibTeX XMLCite \textit{I. Bykadorov} et al., RAIRO, Oper. Res. 36, No. 2, 109--127 (2002; Zbl 1062.90022) Full Text: DOI Numdam Numdam EuDML References: [1] 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 ). [2] A. Buratto and D. Favaretto , Optimal communication mix to maximize brand image , Rapporto No. 95/2001. Dipartimento di Matematica Applicata, Università di Venezia ( 2001 ). [3] D. Favaretto and B. Viscolani , A single production and advertising control problem with bounded final goodwill . J. Inform. Optim. Sci. 21 ( 2000 ) 337 - 357 . MR 1787850 | Zbl 1001.91057 · Zbl 1001.91057 [4] G. Feichtinger , R.F. Hartl and S.P. Sethi , Dynamic optimal control models in advertising: Recent developments . Management Sci. 40 ( 1994 ) 195 - 226 . Zbl 0807.90073 · Zbl 0807.90073 [5] S. Funari and B. Viscolani , Advertising and congestion management for a museum temporary exhibition . Central Eur. J. Oper. Res. (to appear). MR 1924784 | Zbl 1012.90018 · Zbl 1012.90018 [6] G.L. Lilien , P. Kotler and K.S. Moorthy , Marketing models . Prentice Hall Int., Englewood Cliffs ( 1992 ). [7] J.D.C. Little , Aggregate advertising models: The state of the art . Oper. Res. 27 ( 1979 ) 629 - 667 . Zbl 0412.90037 · Zbl 0412.90037 [8] P.A. Naik , M.K. Mantrala and A.G. Sawyer , Planning media schedules in the presence of dynamic advertising quality . Marketing Sci. 17 ( 1998 ) 214 - 235 . [9] M. Nerlove and K.-J. Arrow , Optimal advertising policy under dynamic conditions . Economica 29 ( 1962 ) 129 - 142 . [10] L.S. Pontryagin , V.G. Boltyanskii , R.V. Gamkrelidze and E.F. Mishchenko , The Matematical Theory of Optimal Processes . Pergamon Press, London ( 1964 ). MR 186436 | Zbl 0117.31702 · Zbl 0117.31702 [11] A. Seierstad and K. Sydsaeter , Optimal Control Theory with Economic Applications . North-Holland, Amsterdam ( 1987 ). Zbl 0613.49001 · Zbl 0613.49001 [12] 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 . [13] M.L. Vidale and H.B. Wolfe , An operations research study for sales response to advertising . Oper. Res. 5 ( 1957 ) 370 - 381 . MR 88402 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.