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Optimal pattern of technology adoptions under embodiment: A multi‐stage optimal control approach
Author(s) -
Saglam Cagri
Publication year - 2010
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.960
Subject(s) - obsolescence , optimal control , time horizon , horizon , argument (complex analysis) , control (management) , mathematical optimization , computer science , economics , mathematical economics , mathematics , artificial intelligence , business , biochemistry , chemistry , geometry , marketing
By deriving the necessary conditions for a multi‐stage optimal control problem where the endogenous switching instants appear as an argument of the state equation, we analyze the optimal pattern of technology adoptions under embodiment with a finite planning horizon. We show that the optimal pattern of technology adoptions depends crucially on how the growth rate advantage compares to the adjustment and the obsolescence costs inherent to embodiment. We obtain non‐stationary lifetimes for the adopted technologies due to finite planning horizon. We analyze numerically the effects of planning horizon, speed of adjustment to the new technology, growth rate of technology and the impatience rate on the optimal pattern. Copyright © 2010 John Wiley & Sons, Ltd.