Modeling Strategic Investment Decisions Under Sequential Technological Change

Abstract

Strategic decisions to invest in new equipment are critical not only because of the large initial capital costs incurred but even more importantly because they affect future unit production costs, revenues, and the ability of the firm to perform operations that were not possible earlier. Thus these decisions determine the very competitiveness of the firm. Further, decisions regarding the choice of technology are very expensive to correct if incorrect decisions are identified. These decisions have become increasingly urgent and complex because the state of the art in technology is changing rapidly. However, many models available for evaluating these decisions are either too complex and inefficient or too restrictive in the number, types, and the way appearance of future technologies is modeled. This research attempts to relax some of these restrictions using forecast horizon procedures to model capital investment decisions where any number of technologies may appear in the future with purchase costs and revenues that may vary over time. The appearance of these future technologies are considered uncertain with probabilities that may also vary with time. However, we assume that the order in which they appear is sequential, much like the different generations of microchips for microcomputers. We develop a new approach using nonunique terminal rewards to solve a dynamic programming model of the problem by introducing "converse" difference functions and present an algorithm that is both simple and efficient. Despite the increase in state space from the use of "converse" functions, we show that the computational burden of the algorithm does not increase. Numerical examples are given to illustrate our algorithm. Sensitivity of the optimal decision to changes in probabilities, costs, and revenues are also discussed.strategic investment decisions, equipment replacement, technological change, nonstationary forecasts and costs, forecast horizons

Technology Investment: A Game Theoretic Real Options Approach

“…Thus, the values of these strategies are the same as the value of the strategy "never invest" and therefore they can be ignored for the moment. An equivalent application of this so-called forecast horizon procedure can be found in Nair (1995).…”

“…Of course, this threshold is the option value of waiting. Nair (1995) uses a dynamic programming framework to solve the technology adoption problem for a firm. First the model is solved for a finite planning horizon before which a fixed number of new technologies will arrive.…”

“…In the models of Baldwin (1982), Nair (1995), Rajagopalan (1999), and Balcer and Lippman (1984), a general distribution is used to model the arrival of new technologies. We use a Poisson process to model the technology arrivals.…”

“…In the most advanced models there are multiple new technologies that arrive over time according to a stochastic process. Examples are Balcer and Lippman (1984), Nair (1995), Rajagopalan et al (1998) and Farzin et al (1998) (see also Chapters 2 and 3 of this thesis). These models analyze the investment decision of one firm in isolation, so that the effects of competition are not incorporated.…”

The Effect of Technological Improvement on Capacity Expansion for Uncertain Exponential Demand With Lead Times

“…Their model assumed that the costs associated with the present and future technologies are known, but the appearance times of the future technologies are uncertain. Nair [19] also studied uncertain sequential technological change, which affects the firm's strategic investment decisions. He suggested that the appearance of the future technologies are considered uncertain with probabilities that may vary with time, but the order in which they appear is assumed sequential, such as the different generations of microchips for personal computers.…”