Quality & Quantity (2007) 41:1–17 © Springer 2007
Optimizing Location Among Three Countries
Under Exchange Rate Uncertainty: Applying
and CHIN-TSAI LIN
Department of Finance, Yuanpei University, Hsin Chu 30015, Taiwan, R.O.C.
Graduate Institute of Business and Management, Yuanpei University, Hsin Chu 30015,
Abstract. This investigation extends the Batch Process Model [Lin et al. (2002). Journal of
management and system 9: 173–196] from two productive locations between two countries
to establish a decision valuation model for selecting the optimal location of three productive
locations among three countries, respectively. A general form with the ﬁrst order of degree
homothetic production functions is also considered by the rule of decision-making in the
proposed model. The ﬁrm is risk neutral and this study adopts the real options approach for
valuing the behavior of the transferable location among three countries. Furthermore, using
Dynamic programming and Lagrange Multiplies for a continuous-Time Model Optimization
Problem to get a closed form solution of the threshold value, sensitivity analysis, and some
characteristic strategies of the operating method for batch process model among three coun-
tries are sought, providing for another way of thinking.
Key words: batch process, uncertainty of exchange rate, real options
Following the collapse of the Bretton Woods System in 1973, industrialized
nations gradually adopted a system of ﬂoating exchange rates to reduce
government meddling in exchange rates. However, exchange rate uncer-
tainty markedly inﬂuences the cash ﬂow of the exporting manufacturers
and inﬂuences exporters’ choice of a location for their production base.
Most industries use real exchange rates to measure expected remuneration.
The threshold value of the real exchange rate is allowed to become an
important decision-making index by Blonigen (1997) and Tomlin (1998).
Management’s ﬂexibility to respond to altered future market conditions
Author for correspondence: Chin-Tsai Lin, Graduate Institute of Business and
Management, Yuanpei University, Hsin Chu 30015, Taiwan, R.O.C. Tel: 886-3-530-2588;
Fax: 886-3-530-2588; E-mail: firstname.lastname@example.org