Theory and Methodology Fast high precision decision rules for valuing manufacturing ¯exibility Markus Feurstein 1 , Martin Natter * Department of Industrial Information Processing, Vienna University of Economics & Business Administration, Pappenheimgasse 35, A-1200 Vienna, Austria Received 2 March 1998; accepted 20 October 1998 Abstract The valuation of Flexible Manufacturing Systems is one of the most frequently undertaken productivity improve- ment activities. In practice, the introduction of an FMS into industry must be done on the basis of cost justi®cation. Recently developed techniques for the evaluation of the value of ¯exibility typically include the computation of sto- chastic dynamic programs. However, the computational eort of stochastic dynamic programs grows combinatorially and limits application to real world problems. In this contribution we derive fast approximations to the stochastic dynamic program and compare their results to the exact solution. The proposed methods show an excellent worst case behavior (1%) for a wide range of volatility of the underlying stochastic pro®t margins and costs for switching the production mode. The computational eort is reduced by a factor of more than 200. Ó 2000 Elsevier Science B.V. All rights reserved. Keywords: Investment analysis; Flexible manufacturing systems; Dynamic programming; Neural networks 1. Motivation Most investment decisions share three impor- tant characteristics: irreversibilty, uncertainty about future rewards and the timing (Dixit and Pindyck, 1993). Traditionally, the value of an in- vestment is determined by the net present value. Dixit and Pindyck have pointed out that this de- cision rule tends to underestimate the value of a project because it neglects options associated with an investment. Recently, researchers in the ®eld of real options (see, e.g., Trigeorgis, 1995) have de- veloped numerous methodologies that support the calculation of the value of options (e.g., growth options, Taudes, 1998; Pennings, 1998; Kulatilaka and Perotti, 1998). In speci®c cases valuation techniques developed in ®nance can be used directly. However, in most real-world investment decisions, several types of options interact and the underlying stochastic process becomes multivariate (see e.g., Kulatilaka, 1995b; Kulatilaka, 1988). In the case of such general real option pricing problems it seems, European Journal of Operational Research 120 (2000) 108±117 www.elsevier.com/locate/orms * Corresponding author: Tel.: +43-1-31336-5613; fax: +43-1- 31336-5610; e-mail: Martin.Natter@wu-wien.ac.at 1 E-mail: Markus.Feurstein@wu-wien.ac.at 0377-2217/00/$ ± see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 7 - 2 2 1 7 ( 9 8 ) 0 0 3 7 4 - 9