تولید انعطاف پذیر و گزینه های واقعی: یک بازبینی

This paper considers manufacturing flexibility and real options from an industrial engineering/production management perspective. Real options papers are related to different types of manufacturing flexibility in order to show which types that are considered and in what way they are considered. Flexibility types not valued with real options and real options without any corresponding manufacturing flexibility type are identified and discussed

What is flexibility worth to a company? Many managers in the manufacturing industry ask this question, since the investment cost in flexible manufacturing equipment mostly exceeds the investment cost of dedicated equipment. A flexible system gives numerous options to management and these could for example be constituted by the ability to increase or decrease capacity, switch between products and switch between input material. Hence, flexibility gives the management some degrees of freedom to take advantage of outcomes better than expected and simultaneously provide an ability to reduce losses. Such options must of course have a value to companies. Traditionally, in capital budgeting, expected future cash flows have been discounted with a risk-adjusted discount rate. The risk-adjusted rate has for example been estimated with Sharpe-Lintner-Mossin's Capital Asset Pricing Model (CAPM) to handle the effects of the systematic risk in an appropriate way. Other models can also be used to estimate a discount rate but these have the same shortcoming as the CAPM, in that they can not value projects containing flexibility. Thus, other methods have to be used to find the appropriate value of flexibility and one of these is to use option pricing theory. Some big advantages of using option pricing theory are that the complex risk structure of a flexible project is handled more appropriate than in the traditional method mentioned above and that the problem of estimating a risk-adjusted rate is avoided in the most cases. It also gives the possibility to model so-called American options, i.e. options that can be exercised at any point in time during the lifetime of the option, and has thereby another advantage over the traditional method. Since Black and Scholes [1] and Merton [2] presented their work on option pricing theory a lot of application areas, e.g. valuing complex financial securities and valuing companies, have been found. Capital budgeting is another area where option pricing theory has become more and more used, at least by academics. Many authors, see e.g. Trigeoris [3], have used this theory to deal with features and problems associated with valuation of projects containing flexibility which have resulted in a number of papers concerning valuation of so-called real options. This paper will review some of the literature on option pricing theory applied on valuation of manufacturing flexibility, or real options in manufacturing. The paper will relate the real options literature to manufacturing flexibility from an industrial engineering/production management (IE/PM) perspective. As a point of departure from the IE/PM perspective, Sethi and Sethi's [4] survey on manufacturing flexibility is used. Sethi and Sethi proceed from Brown et al. [5] but a number of flexibility types are added and the view of Sethi and Sethi occasionally deviates from that of Browne et al. Gupta and Goyal [6] claim that the definitions of flexibility in Browne et al. are the most comprehensive and use their framework in a survey to classify the literature on manufacturing flexibility. Olhager and West [7] refer to Sethi and Sethi as a literature review on manufacturing flexibility, which covers and systematise the flexibility types linked to flexible manufacturing systems. Hence, the Sethi and Sethi framework based on Browne et al. should be appropriate as a point of departure for a review on and classification of manufacturing flexibility and real options. Using the definitions of Sethi and Sethi, we will consider the value of flexibility • at the basic level, i.e. flexibility of the machine level, • at the system level, i.e. the flexibility of a production system, • at the aggregate level, i.e. the flexibility of a whole manufacturing plant. Sethi and Sethi define a number of flexibility types at each level and these will be used in this paper. Some of the definitions are quite wide and can therefore be interpreted in somewhat different ways. This paper will be structured in the following way. First, a short introduction to option pricing and real options is given. Second, we look at the different levels of flexibility using the Sethi and Sethi framework. Here, we also map the different kinds of flexibility treated in the real option literature to the different types of flexibility as Sethi and Sethi define them. This analysis will highlight the following: This may also be illustrated as in Fig. 1 where the section of the two sets represents the set of real options literature, which can be mapped to flexibility types defined by Sethi and Sethi. The other two sets represent the literature, which cannot be mapped to each other. The literature will be reviewed from an application point of view. Thus, the underlying assumptions and how these affect the solution and impose limitations on the result will be analysed.

In this paper, flexibility in terms of real options are investigated from an industrial engineering and production management perspective. On the one hand the IE/PM literature treats manufacturing flexibility, see e.g. Sethi and Sethi [4], and on the other hand there is some literature on real options. The intersection in Fig. 1 represents the real option papers which can be mapped to flexibility types in the Sethi and Sethi framework and vice versa. There are also real options papers that do not fit in the Sethi and Sethi framework and some types of flexibility that are not treated by any real options papers, which can be illustrated by the sets outside the intersection. Table 1 shows the real options papers that can be related to the flexibility types defined by Sethi and Sethi. As seen in Table 1, there are numerous real option papers that are related to the different types of flexibility. These papers are also described in Section 3. One should keep in mind that most of the real option papers are developed together with restrictive assumptions and that they only consider a specific type of production situation. Sometimes restrictive assumptions are made to enable an analytical solution to the valuation problem but these assumptions are often made at the expense of the applicability of the model. In most of the articles concerning product and process flexibility only two products are considered which partly can be explained by the increased complexity that more products would result in. If one wants to search for a value of having the flexibility to produce more products, numerical methods are preferred to use. In some of the papers in Table 1 more than one type of flexibility are modelled. Multiple options that have interdependencies may require numerical methods in order to value and handle the effects of interdependencies in an appropriate way. As seen in Table 1 some types of flexibility are missing a corresponding real option reference. If the two types at the basic level are considered, two possible answers could be found why these have not been evaluated in the way Sethi and Sethi define them. First, it is hard to find the value of the ability to perform various operations in a machine and move different types efficiently. For example, one relevant question that has to be answered is which underlying stochastic process that affects the value and should be used. Second, it might be of less relevance to value flexibility types at the basic level since they only provide a small contribution to the value of flexibility of a large system or plant. However, they affect the characteristics of flexibility at system and plant level and should be considered. At the system level it is only routing flexibility that misses references. It is hard to evaluate routing flexibility by almost the same reason as above in that the question about which underlying process that should be used still remains. Among the three types at the aggregate level, program flexibility is probably the hardest to evaluate by the same reason as mentioned above. Production flexibility, which is unmarked in Table 1, has strong linkages to product and process flexibility, and the models used to evaluate these should also be applicable to evaluate production flexibility under some circumstances. For example, for a plant, with only one manufacturing system the papers from the system level should be applicable. However, due to the fact that a plant might consist of several systems the models will often be larger and more complex than the models at the system level. This paper also considers real options papers, which are not directly related to any specific type of flexibility but could be related to manufacturing. One group of papers is the so-called wait-to-see options or options to defer investment. Another group is the options to abandon a project for salvage value. These types of flexibility are not explicitly defined within the Sethi and Sethi framework which also shows that Sethi and Sethi do not really consider flexibility on the strategic level. However, these can be of great importance since e.g. manufacturing in a global context is a reality to many companies today and should therefore be considered. Another situation where the option to wait and option to abandon are important and could be very valuable is in large projects-oriented works. Thus, it is clear that the Sethi and Sethi framework is strongly related to and dependent upon manufacturing systems such as flexible manufacturing systems.