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G. Feichtinger, T. Huschto, R.F. Hartl, P.M. Kort, S. Sager, A. Seidl:
"Numerical solution of a conspicuous consumption model with constant control delay";
Automatica, 47 (2011), 9; 1868 - 1877.

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.
© 2011 Elsevier Ltd. All rights reserved.

Optimal control; Optimization under uncertainties; Control delays; Economic system; Recession

http://dx.doi.org/10.1016/j.automatica.2011.06.004

Project Head Gustav Feichtinger:
Mehrstufen-Modellierung von Marktstörungen