Numerical solution of a conspicuous consumption model with constant control delay

T. Huschto, G. Feichtinger, R.F. Hartl, P.M. Kort, S. Sager, A. Seidl

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We derive optimal pricing strategies for conspicuous consumption products in periods of recession. To that end, we formulate and investigate a two-stage economic optimal control problem that takes uncertainty of the recession period length and delay effects of the pricing strategy into account.

This non-standard optimal control problem is difficult to solve analytically, and solutions depend on the variable model parameters. Therefore, we use a numerical result-driven approach. We propose a structure-exploiting direct method for optimal control to solve this challenging optimization problem. In particular, we discretize the uncertainties in the model formulation by using scenario trees and target the control delays by introduction of slack control functions.

Numerical results illustrate the validity of our approach and show the impact of uncertainties and delay effects on optimal economic strategies. During the recession, delayed optimal prices are higher than the non-delayed ones. In the normal economic period, however, this effect is reversed and optimal prices with a delayed impact are smaller compared to the non-delayed case.
Original languageEnglish
Pages (from-to)1868-1877
JournalAutomatica
Volume47
Issue number9
DOIs
Publication statusPublished - 2011

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Economics
Costs
Uncertainty

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Huschto, T. ; Feichtinger, G. ; Hartl, R.F. ; Kort, P.M. ; Sager, S. ; Seidl, A. / Numerical solution of a conspicuous consumption model with constant control delay. In: Automatica. 2011 ; Vol. 47, No. 9. pp. 1868-1877.
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Huschto, T, Feichtinger, G, Hartl, RF, Kort, PM, Sager, S & Seidl, A 2011, 'Numerical solution of a conspicuous consumption model with constant control delay', Automatica, vol. 47, no. 9, pp. 1868-1877. https://doi.org/10.1016/j.automatica.2011.06.004

Numerical solution of a conspicuous consumption model with constant control delay. / Huschto, T.; Feichtinger, G.; Hartl, R.F.; Kort, P.M.; Sager, S.; Seidl, A.

In: Automatica, Vol. 47, No. 9, 2011, p. 1868-1877.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Huschto, T.

AU - Feichtinger, G.

AU - Hartl, R.F.

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AB - We derive optimal pricing strategies for conspicuous consumption products in periods of recession. To that end, we formulate and investigate a two-stage economic optimal control problem that takes uncertainty of the recession period length and delay effects of the pricing strategy into account.This non-standard optimal control problem is difficult to solve analytically, and solutions depend on the variable model parameters. Therefore, we use a numerical result-driven approach. We propose a structure-exploiting direct method for optimal control to solve this challenging optimization problem. In particular, we discretize the uncertainties in the model formulation by using scenario trees and target the control delays by introduction of slack control functions.Numerical results illustrate the validity of our approach and show the impact of uncertainties and delay effects on optimal economic strategies. During the recession, delayed optimal prices are higher than the non-delayed ones. In the normal economic period, however, this effect is reversed and optimal prices with a delayed impact are smaller compared to the non-delayed case.

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