Title
Numerical solution of a conspicuous consumption model with constant control delay.
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.
Year
DOI
Venue
2011
10.1016/j.automatica.2011.06.004
Automatica
Keywords
Field
DocType
Optimal control,Optimization under uncertainties,Control delays,Economic system,Recession
Conspicuous consumption,Discretization,Direct method,Mathematical optimization,Optimal control,Recession,Control theory,Control delay,Pricing strategies,Optimization problem,Mathematics
Journal
Volume
Issue
ISSN
47
9
0005-1098
Citations 
PageRank 
References 
3
0.48
3
Authors
6
Name
Order
Citations
PageRank
Tony Huschto130.48
Gustav Feichtinger214338.93
Richard F. Hartl31863137.30
Peter M. Kort420544.47
Sebastian Sager514015.01
Andrea Seidl6216.18