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Manufacturing flexibility and real options: A review
Int. J. Production Economics 74 (2001) 213}224
Manufacturing #exibility and real options: A review夽 Jens Bengtsson* Department of Production Economics, IMIE, Linko( ping Institute of Technology, S-581 83, Linko( ping, Sweden
Abstract This paper considers manufacturing #exibility and real options from an industrial engineering/production management perspective. Real options papers are related to di!erent types of manufacturing #exibility 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 #exibility type are identi"ed and discussed. 2001 Elsevier Science B.V. All rights reserved. Keywords: Real options; Manufacturing #exibility; Capital budgeting; Production management
1. Introduction What is #exibility worth to a company? Many managers in the manufacturing industry ask this question, since the investment cost in #exible manufacturing equipment mostly exceeds the investment cost of dedicated equipment. A #exible 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, #exibility 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. 夽 The research is supported by grants from the Swedish Foundation for Strategic Research and Swedish National Board for Industrial and Technical Development. * Corresponding author. Tel.: #46-13281538; fax: #4613288975. E-mail address: [email protected] (J. Bengtsson).
Traditionally, in capital budgeting, expected future cash #ows have been discounted with a riskadjusted discount rate. The risk-adjusted rate has for example been estimated with Sharpe-LintnerMossin's Capital Asset Pricing Model (CAPM) to handle the e!ects 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 #exibility. Thus, other methods have to be used to "nd the appropriate value of #exibility 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 #exible 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.
0925-5273/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 5 2 7 3 ( 0 1 ) 0 0 1 2 8 - 1
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Since Black and Scholes [1] and Merton [2] presented their work on option pricing theory a lot of application areas, e.g. valuing complex "nancial 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. Trigeorgis [3], have used this theory to deal with features and problems associated with valuation of projects containing #exibility 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 #exibility, or real options in manufacturing. The paper will relate the real options literature to manufacturing #exibility 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 #exibility is used. Sethi and Sethi proceed from Brown et al. [5] but a number of #exibility 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 de"nitions of #exibility in Browne et al. are the most comprehensive and use their framework in a survey to classify the literature on manufacturing #exibility. Olhager and West [7] refer to Sethi and Sethi as a literature review on manufacturing #exibility, which covers and systematise the #exibility types linked to #exible 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 classi"cation of manufacturing #exibility and real options. Using the de"nitions of Sethi and Sethi, we will consider the value of #exibility
Some of the de"nitions are quite wide and can therefore be interpreted in somewhat di!erent 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 di!erent levels of #exibility using the Sethi and Sethi framework. Here, we also map the di!erent kinds of #exibility treated in the real option literature to the di!erent types of #exibility as Sethi and Sethi de"ne them. This analysis will highlight the following: (i) The types of #exibility that are treated in the real option literature can be distinguished and clari"ed. (ii) The #exibility types that have not been treated as real options are identi"ed, and can be subject to further research. (iii) The applications of real options may indicate that there are other #exibility types relevant to manufacturing that have not yet been identi"ed by the literature on manufacturing #exibility. 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 #exibility types de"ned 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 a!ect the solution and impose limitations on the result will be analysed.
E at the basic level, i.e. #exibility of the machine level, E at the system level, i.e. the #exibility of a production system, E at the aggregate level, i.e. the #exibility of a whole manufacturing plant. Sethi and Sethi de"ne a number of #exibility types at each level and these will be used in this paper.
Fig. 1. Sets representing di!erent types of #exibility related literature.
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2. Foundations of option pricing and real options 2.1. Introduction to option pricing theory The purpose of this chapter is to give a short introduction to the foundation of option pricing and some option related concepts that are of importance to the following text. A more thorough introduction can be found in Hull [8]. An option gives the holder an opportunity without the corresponding obligation to do something speci"c. Options are derivatives in the sense that they depend on an underlying asset of any kind. Two basic options, on the "nancial markets, are the call option and the put option. The call option gives the holder the opportunity to buy the underlying asset at a predetermined price, the exercise price, at a pre-set date. Since the holder has the opportunity to choose whether to exercise the option or not, it will only be exercised if the value of the underlying asset exceeds the value of the exercise price. Reverse, a put option, which gives the holder the right to sell at a predetermined price, at a pre-set date, will only be exercised if the value of the exercise price exceeds the value of the underlying asset. The value of a call option, C, and the value of a put option, P, at the date of exercise are written as functions of the exercise price, X, and the value of the underlying asset, S and are expressed as in expressions (1) and (2). C"Max [S!X, 0],
(1)
P"Max [X!S, 0].
(2)
The pay-o! at exercise can thereby be illustrated as in Fig. 2. So far, only so-called European options are considered. The feature of European options is that
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they can only be exercised at the date of exercise. On the other hand, there are American options, which can be exercised at any moment, until the date of exercise. The value of an American and an identical European option may di!er but it is beyond the scope of this paper to give a full explanation of the di!erences from a valuation point of view. The foundation of option pricing theory can be found in the classical work by Black and Scholes [1], giving Black and Scholes formula, and Merton [2] which extends the theory. These authors made the break-through and found that the price of options can be derived as if the world is risk-neutral. Thereby, option prices can be derived regardless of risk-preferences of investors and without estimation of any risk-adjusted discount rates. They identify that the payo! from an option can be replicated by a portfolio of positions, either short or long depending on the option, in the underlying asset and in a risk-free asset. To avoid arbitrage opportunities, the value of the portfolio, i.e. positions in the underlying asset and the risk-free asset must have the same value as the option. From this arbitrage argument an expression, i.e. a partial di!erential equation, can be derived, whose solution gives the value of a call option. It can be seen in e.g. Black and Scholes formula that the value of the option, under their assumptions, depends on the current value of the underlying asset, the exercise price, the instantaneous risk-free rate, the variance of return of the underlying asset and the time to exercise. They solve the partial di!erential equation analytically, which results in the famous, closed form, Black and Scholes formula. However, to other types of options it can be hard, or impossible, to "nd an analytical solution to the di!erential equation and in these cases it can be necessary to apply
Fig. 2. Payo! from a call and a put option, respectively.
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numerical methods to estimate the value of the option. In many cases the value of the underlying asset will be a!ected by dividends. For example, in the case of stocks, shareholders will usually get cash payouts, i.e. dividends, from the company, once or a number of times per year. Since dividends are taken from the equity of the "rm, the value of the equity and the stocks will be reduced. Dividends on an underlying asset paid during the lifetime of a call option will reduce its value. In the case of put options, the reverse relationship holds, i.e. the value of a put option increases with the size of the dividends during its lifetime. 2.2. Introduction to real options Since Black, Scholes and Merton presented their work, option pricing has found new areas of applications. Apart from pricing "nancial options the theory is also applicable to options constituted by `real opportunitiesa. In this paper manufacturing #exibility is considered and as the term #exibility claims, one has opportunities but no obligations. Thereby, #exibility can be interpreted as di!erent types of options, but the payo!, in the case of #exibility and real options, is often more complex than the payo! from call and put options. However, in many cases, call and put options can be combined to represent the desired payo!. If we consider a simple case of #exibility, e.g. we have the option to produce if revenue, R, exceeds variable cost,
Fig. 3. Payo! from the option to produce.
cases. Therefore, it is often assumed that markets are complete, i.e. in this case, that the revenues can be replicated by a portfolio of traded assets, a tracking portfolio, whose movements of value are identical to the movements of revenues. In some cases the evolution of the revenues and the tracking portfolio may di!er. This can be adjusted for in a similar manner as dividends are treated in the case of "nancial options. Later in this paper, when di!erent papers are reviewed it will be seen that some valuation models cannot handle dividends and this also includes the case when the evolution of the underlying asset, e.g. demand, pro"t etc., di!ers from that of the tracking portfolio. 3. Flexibility and real options 3.1. Flexibility and real options at the basic level Flexibility at the basic level of the Sethi and Sethi [4] framework includes machine #exibility, material handling system #exibility and operation #exibility. Sethi and Sethi de"ne these as follows: E Machine #exibility refers to the various types of operations that the machine can perform without requiring a prohibitive e!ort in switching from one operation to another. E Material handling system #exibility is the ability to move di!erent part types e$ciently for proper positioning and processing through the manufacturing facility it serves. E Operation #exibility of a part refers to its ability to be produced in di!erent ways i.e. a sequence of operations can either be interchanged or substituted with each other.
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Kulatilaka [9] can be used to evaluate a special case of operation #exibility. Here, one machine, a #exible manufacturing system, provides di!erent modes to produce one product, which then are ready to be sold. This places this article in the borderland between basic and system level or in the extreme case, the aggregate level, if one machine carries out all production in the plant. Kulatilaka considers the case when the product can be produced in two di!erent modes. Switching costs from one mode to another are taken into respect but capacity constraints are not considered. The mode that is the most pro"table is partly dependent on output price, which is uncertain, but is also dependent on switching cost. However, output price can be interchanged for demand, exchange rate etc. as the uncertain underlying asset. When the value of the #exible machine is calculated it can be compared to the value of a non-#exible machine to evaluate the operating #exibility. Kulatilaka uses stochastic dynamic programming considering e.g. switching cost in an appropriate way. With this valuation approach the e!ects from a current switch on all future production scenarios is considered. These e!ects from so-called compound or interrelated options are considered later in this paper. In Kulatilaka, actions such as abandoning the machine, waiting to invest and temporarily shutting down production are also considered but these are not treated here. The model used in Kulatilaka [9] is more thoroughly explained in Kulatilaka [10]. Kulatilaka [10] describes a general model, allowing for valuing di!erent kinds of #exibility such as the #exibility types mentioned above but also expansion #exibility and process/product #exibility in the two-product case. However, the underlying valuation model for valuing these types of #exibility is essentially the same. 3.2. Flexibility and real options at the system level Flexibility at the system level concerns #exibility of the whole manufacturing system and will be dependent on the #exibility types at the basic level. Sethi and Sethi [4] de"ne "ve #exibility types at the system level and these are process, product, routing, volume and expansion #exibility.
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3.2.1. Process yexibility Sethi and Sethi's de"nition is that process #exibility of a manufacturing system relates to the set of part types that the system can produce without major set-ups, i.e. only small or in"nitesimal set-up costs are allowed. Process #exibility can be seen as an operational #exibility or short-term #exibility and is strongly dependent on machine #exibility due to the importance of the characteristics of the machine. One of the e!ects of process #exibility is that it enables reduced batch sizes and inventory costs. Margrabe [11] considers the general option to exchange one risky asset for another. This paper was in the "rst hand developed for pricing of "nancial securities but could also be applicable to some simple two-products real option valuation problems. The option can be valued using an analytical formula both for European and American options. In a process #exible context Margrabe's model can be used for valuing the opportunity to mutually exchange from producing one product to another when e.g. prices or pro"ts of the products are uncertain. Margrabe does not handle any capacity constraints, set-up cost or any dividends and is thereby of limited use in real life problems. McDonald and Siegel [12] extend Margrabe to include dividends in the case of European options and Carr [13] considers the American exchange option with dividends. Triantis and Hodder [14] develop a model, which evaluates investments in process #exible equipment where pro"t margins are uncertain, switching between products is free of charge and production decisions are taken at pre-set points in time. The model allows for downward sloping demand curves, capacity constraints and several products can be produced during a period. Production decisions, regarding the quantity of each product, are made to obtain the maximum value of the manufacturing program in the beginning of each period. Triantis and Hodder show that a complex closed form analytical formula can be found in the two-product case using Lagrange optimisation and an equivalent martingale valuation approach. However, if more products are added a Monte Carlo simulation is preferred to evaluate the options since complexity increases rapidly. Triantis
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and Hodder also point out that the drift and variance parameters in their model can be time varying to model e.g. di!erent stages of the life cycle of a product. The assumption concerning switching cost can also be relaxed to include this cost, see Triantis [15], but adds a great deal of complexity. Triantis [15] also develops a model under perfect competition, no switching cost and when the marginal pro"t contribution is uncertain. The model also considers temporarily shutdowns of operation and reopening, which are free of charge, and capacity constraints. However, in this model only one product can be produced during a period. Triantis shows that in the two product case a closed form solution can be found. Andreou [16] evaluates a process #exible manufacturing system producing two di!erent products without any switching cost. The system consists of two dedicated machines and one #exible machine. The model treats capacity constraints and it is assumed that no back-order takes place. Andreou sketches seven di!erent scenarios representing different states of the relationship between actual demand of each product and available capacity. Each scenario occurs with a corresponding probability and in the case of demand for both products, and limited capacity, the most pro"table will be produced in the "rst place. The probabilities are dependent on the bivariate distribution of demand of the two products. Scenarios with an option content are then interpreted in terms of option pay-o!. The pay-o! is depending on the variable pro"ts from two products where the variable pro"ts are the underlying asset and follow geometric Brownian motions. The scenarios containing options can then be valued using McDonald and Siegel [12]. If more products were added or if a more complex production set-up would be used the complexity and the number of scenarios would increase and a numerical valuation approach may be required.
3.2.2. Product yexibility Sethi and Sethi [4] de"ne product #exibility as the ease with which new parts can be added or substituted for existing parts. In contrast to process #exibility these additions and substitutions always lead to set-up cost, however not excessively large.
This also means that the papers listed below could be mapped to process #exibility if the set-up cost would be zero. Product #exibility allows e.g. the company to be responsive to the market by enabling it to bring newly designed products quickly to the market. In Stulz [17] the European option on the maximum of two risky assets with a "xed exercise price is evaluated. This paper is originally developed for "nancial applications but can also be used in some simple real option applications. For example, in a product #exible context it can be used to "nd the value of having the mutually exclusive opportunity to produce two products when pro"ts are uncertain and costs are equal and "xed. This means that only one product can be produced during a period. Stulz [17] is solved using analytical formulas but does not consider capacity constraints or any dividend pay out and are thereby of limited use in most real life situations. Johnson [18] extends Stulz to include several risky assets, i.e. there are several mutually exclusive products that can be produced. Stulz and Johnson can only be used to analyse the value of one switch since several switches with corresponding switching cost may result in interdependencies. In this case, other valuation methods are required which also will be discussed later. Triantis [15] develops two models, which evaluate a product #exible manufacturing system under somewhat di!erent circumstances. The "rst model assumes uncertain prices and equal marginal costs. Both models assume symmetric set-up costs, that only one product is produced during a period and both can be solved analytically in the two-product case. The "rst model evaluates product #exibility over an in"nite horizon where switching might occur at any point in time. Thereby, the option to switch has almost the same features as an American option except from that this option can be exercised more than once. In this model the option to abandon is also considered giving the opportunity to abandon the system if prices are too low. This reduces the lifetime of the project from in"nite to "nite in most cases since it will not be optimal to hold it to in"nity. The second model evaluates product #exibility when switching takes place at di!erent pre-speci"ed points in time. Thereby, the characteristics of the options will be European-like
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with compound features. In this model it is assumed that the price of one of the two products is uncertain, that the production costs might di!er between the products and the lifetime is "nite. However, more products will increase complexity and it might thereby be preferable to use numerical methods. Kamrad and Ernst [19] consider valuation of multiproduct agreements where demand, delivery schedule, and output prices are known since sales are contractually "xed. Uncertainty appears in the output yield and in the prices of inputs, e.g. raw material. Capacity of production and inventory are constrained and except from valuing the agreement, optimal production and inventory guidelines will also be found which also result in a more extensive operations research model. The model considers set-up cost and only one product type is produced during a period. Supplies of the other products have to be covered by inventory during this period. No analytical solution has been found for valuation purposes. Therefore, Kamrad and Ernst use a numerical lattice approach to model risk-neutral prices and stochastic dynamic programming to estimate the value of the production agreements in the case of three inputs and two outputs. 3.2.3. Routing yexibility Sethi and Sethi [4] de"ne routing #exibility of a manufacturing system as its ability to produce a part by alternate routes through the system. Routing #exibility allows for e$cient scheduling of parts by better balancing of machine loads. No way of evaluation is developed and this #exibility type is the only one at the system level, which lacks a corresponding real option. 3.2.4. Volume yexibility Sethi and Sethi [4] de"ne volume #exibility of a manufacturing system as its ability to be operated pro"tably at di!erent overall output levels. Volume #exibility permits the factory to adjust production upwards or downwards within wide limits and can be seen as an operational or short-term #exibility. Tannous [20] builds a model to evaluate volume #exible equipment when demand is uncertain,
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which then is used to "nd the optimal level of investment in volume #exibility. Tannous considers a closed system where the level of #exibility is dependent on the relationship between #exible and non-#exible equipment. The characteristic of the #exible equipment is that the production rate can be adjusted to respond to #uctuations in demand. However, adjustments can only be made within some limits, which are given by e.g. the machine. Investment in #exible equipment increases the level of #exibility and widens the limits of the whole system. The value of the cash #ow from each year of the lifetime of the system is then calculated, using basically Black and Scholes formula. Tannous' model also handles the e!ect of having an inventory. The model as it is formulated is likely having restricted use since it requires that the equipment should be quite similar in that they perform the same tasks and that they directly a!ect the total output rate. Bengtsson [21] considers the value of having the option to hire personnel on short contracts when demand of a product or aggregated demand is uncertain, i.e. one source of uncertainty is considered. This type of option gives "rms the opportunity, but not the obligation, to hire personnel and if demand is su$ciently high they will utilise this opportunity, otherwise not. The option will have di!erent characteristics depending on the duration of the contract and the frequency of the "rm's decision making during the time of an ongoing contract. In Bengtsson a contract, which last for three months and where production decisions are made every month, is considered. In this case the value of the option is not only depending on demand at the hiring date but also on the value of the subsequent production options. The production option is based on a similar idea as McDonald and Siegel [12] that one does not utilise extra personnel if demand is not high enough. As the contract is formulated in Bengtsson this results in so-called compound options, which will be considered later in the paper and numerical methods may have to be used to value the options. 3.2.5. Expansion yexibility Sethi and Sethi [4] de"ne expansion #exibility of a manufacturing system as the ease with which its
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capacity and capability can be increased when needed. Expansion #exibility is important to "rms with growth strategies, such as ventures into new markets, and can be considered as long-term or strategic #exibility. Trigeorgis [3] considers the option to expand when an investment decision is made and where the underlying value of the project is uncertain. These options are appropriate when e.g. a "rm is able to increase the value of an ongoing project by an additional investment. In a production context these could be exempli"ed by the opportunity to buy more production capacity, increase sales and thereby increase the value of the project. This option will only be exercised if the value of the project after exercise exceeds the value of the additional investment cost and the current value of the project. If it is not exercised the value of the project will remain the same. If the option is European it could be valued using basically Black and Scholes formula but if the option is American, other numerical methods may be required. Pindyck [22] does not explicitly address the problem of valuing expansion #exibility. Instead, capacity choice and expansion are examined in order to maximise the value of the "rm when investments are irreversible and demand is uncertain. Pindyck looks at the value of the marginal capacity, which has to exceed the sum of the purchasing cost, the installation cost and the value of the option to invest in the marginal capacity for an investment to take place. Pindyck derives a decision rule telling whether to invest or not, which e.g. is dependent on current demand and actual capacity. He and Pindyck [23] use the same approach as Pindyck [22] but extend the analysis to include #exible capacity and compare this to the situation when only dedicated equipment is used. 3.3. Flexibility and real options at the aggregate level Flexibility at the aggregated level concerns #exibility at the plant level. Sethi and Sethi [4] identify and de"ne three types of #exibility at the aggregate level and these are program #exibility, production #exibility and market #exibility. According to Sethi
and Sethi they are de"ned as E Program #exibility is the ability of the system to run virtually untended for a long enough period. E Production #exibility is the universe of part types that the manufacturing system can produce without adding major capital equipment. E Market #exibility is the ease with which the manufacturing system can adapt to a changing market environment. Program #exibility has linkages to process and routing #exibility and enables reduced throughput time by having e.g. reduced set-up time. Production #exibility has linkages to process, routing and product #exibility. In contrast to product #exibility, production #exibility allows for considerable set-ups without adding major capital equipment. Production #exibility allows the "rm to compete in a market where new products are frequently demanded and can be considered as long-term #exibility. Market #exibility has linkages to product, volume and expansion #exibility. Market #exibility is necessary when environment changes because of rapid technological innovations, changes in customer tastes, short product life cycles, uncertainty in sources of supply, etc. and is important to the survival of a "rm in an environment that is constantly in #ux. All of these #exibility types have linkages to other types of #exibility. Therefore it would be appropriate to use the real option models from the system level to deal with the problem to evaluate both production and market #exibility. However, Sethi and Sethi's de"nitions are wide and there are some types of market #exibility described in the real option literature which are not directly related to any type at the system level and some of these papers are brie#y considered below. 3.3.1. Option to temporarily shut down McDonald and Siegel [12] consider investments where there is an option to temporarily shut down without any costs when unit output price is less than unit variable cost. Thereby, an investment can be seen as a portfolio of European call options on the contribution margins of each period, respectively. For each period there is a corresponding option, which is exercised if the contribution margin of the
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period exceeds zero. The gross present value of the investment can be found by valuing each of these options individually and add them together. The option should be restricted to the one product case or the several products case with equal unit prices and equal unit variable costs. If shutdowns would cost, this would lead to interdependencies between options of di!erent periods and this can lead to a requirement for numerical methods. 3.3.2. Option to abandon Margrabe [11], earlier considered under process #exibility in this paper, can also be used for valuing the option to permanent abandon for salvage value. If the project and salvage values are uncertain and no dividend, or pay out, takes place Margrabe's analytical expressions can be used. This type of option can be seen as an American put option on the value of the project with a stochastic exercise price, represented by the salvage value. The assumption regarding that no dividends are allowed may possibly limit the practical use of this option. However, in the case of dividends the valuation model of Carr [13] may be used. Myers and Majd [24] evaluate the option to permanent abandon for its salvage value, or the value of alternative use, when the gross present value of the project is uncertain. Abandonment takes place if gross present value is below salvage value. This option has the same features as an American put option and is solved using numerical methods due to that dividends are allowed. Myers and Majd also extend the option to include the case when salvage value is stochastic resulting in a similar problem as in Margrabe, however, dividends are not allowed in the latter. 3.3.3. Compound options and interdependencies Most of the projects in real life are not restricted to only one type of #exibility or real option. Instead, an investment opportunity might consist of the options to wait, switch and abandon, which are also treated in some of the papers presented earlier. Often, there are interdependencies or compound e!ects between options in the meaning that the exercise of an option gives numerous of new options. The value of a prior option is, therefore, a!ected by the value of subsequent options. From
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a valuation point of view this means that the di!erent types of option cannot be seen and valued, as they were individual. Instead of considering and evaluating only one option at a time, all options have to be evaluated together at the same time. This will often lead to that analytical expression cannot be found and numerical techniques have to be used instead. Trigeorgis [25] considers valuation of a generic investment with the option to defer, switch use, expand, contract and abandon. Using a numerical method, from Trigeorgis [26], it is shown that the value of a collection of options generally deviates from the sum of the values of each individual option. Trigeorgis [25] shows that the incremental value of an additional option when other options are present is generally less than the value of the options in isolation. The incremental value also tends to decline, as more options are present. Kulatilaka [27] evaluates interdependent options, in this case wait-to-invest, expand and shutdown option, using the model in Kulatilaka [10] and shows that the value of a collection of option is less than the sum of individual options. Brennan and Schwartz [28] consider interdependent options in a valuation of a mine. In this case output prices of commodity are uncertain and the options to open, close, reopen and abandon are considered.
4. Real option papers outside the Sethi and Sethi framework If one consider the real option literature that has some point in contact to manufacturing it will appear that some of them cannot be mapped to types of #exibility in the Sethi and Sethi [4] framework. However, these can play an important role in application and valuation of real options. Below, some of these papers are considered and grouped together to show di!erent categories. 4.1. Option to defer investment The option to defer, or the option to wait, has been considered in numerous papers. This type of option concerns the value of waiting before an investment takes place, thereby giving the
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opportunity to take advantages of future information and can be very valuable in big project such as mining and oil exploration. McDonald and Siegel [29] consider the valuation of a perpetual investment opportunity in irreversible projects. The project cannot be used for other purposes, the present value of future cash #ow is uncertain and the cost of investment is considered as either uncertain or certain. There is an analytical solution to this option when lifetime is perpetual but, however, in more realistic cases is not an investment opportunity perpetual and in these cases numerical methods are required. Majd and Pindyck [24] examine the option to delay irreversible construction in a project where a series of outlays must be made sequentially. Production cannot proceed faster than at a rate k, the project produces no intermediate cash #ow until it is complete and the market value of the "nished project is uncertain during the whole construction phase. Majd and Pindyck claim that these options can be valuable in industries such as aircraft industry, mining or plant building where the market value of the investment is uncertain during the whole construction phase. There exists no analytical solution to this problem and therefore numerical solution methods are required.
5. Concluding remarks In this paper, #exibility 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 #exibility, 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 #exibility types in the Sethi and Sethi framework and vice versa. There are also real options papers that do not "t in the Sethi and Sethi framework and some types of #exibility 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 #exibility types de"ned by Sethi and Sethi.
As seen in Table 1, there are numerous real option papers that are related to the di!erent types of #exibility. 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 speci"c 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 #exibility 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 #exibility to produce more products, numerical methods are preferred to use. In some of the papers in Table 1 more than one type of #exibility are modelled. Multiple options that have interdependencies may require numerical methods in order to value and handle the e!ects of interdependencies in an appropriate way. As seen in Table 1 some types of #exibility 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 de"ne them. First, it is hard to "nd the value of the ability to perform various operations in a machine and move di!erent types e$ciently. For example, one relevant question that has to be answered is which underlying stochastic process that a!ects the value and should be used. Second, it might be of less relevance to value #exibility types at the basic level since they only provide a small contribution to the value of #exibility of a large system or plant. However, they a!ect the characteristics of #exibility at system and plant level and should be considered. At the system level it is only routing #exibility that misses references. It is hard to evaluate routing #exibility 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 #exibility is probably the hardest to evaluate by the same reason as mentioned above. Production #exibility, which is unmarked in Table 1,
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Table 1 Real options articles mapped to #exibility types according to Sethi and Sethi's [4] framework Level
Type of #exibility
Real option papers
Basic
Machine Material handling system Operation
* * Kulatilaka [9] Kulatilaka [10]
System
Process
Margrabe [11] McDonald and Siegel [12] Triantis and Hodder [14] Andreou [16] Carr [13] Stulz [17] Johnson [18] Triantis [15] Kamrad and Ernst [19] Kulatilaka [10] * Tannous [20] Bengtsson [21] Trigeorgis [3] Pindyck [22] He and Pindyck [23] Kulatilaka [10]
Product
Routing Volume Expansion
Aggregate
Program Production Market
has strong linkages to product and process #exibility, and the models used to evaluate these should also be applicable to evaluate production #exibility 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 speci"c type of #exibility but could be related to manufacturing. One group of papers is the so-called wait-to-see options or options to defer investment. Another
* * Brennan and Schwartz [28] Margrabe [11] McDonald and Siegel [12] Myers and Majd [30] Kulatilaka [10] Carr [13]
group is the options to abandon a project for salvage value. These types of #exibility are not explicitly de"ned within the Sethi and Sethi framework which also shows that Sethi and Sethi do not really consider #exibility 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 #exible manufacturing systems.
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References [1] F. Black, M. Scholes, The pricing of option and corporate liabilities, Journal of Political Economy 81 (1973) 637}654. [2] R.C. Merton, Theory of rational option pricing, Bell Journal of Economic and Management Science 4 (1973) 141}183. [3] L. Trigeorgis, Real Options: Managerial Flexibility and Strategy in Resource Allocation, The MIT Press, Cambridge, MA, 1996. [4] A.K. Sethi, S.P. Sethi, Flexibility in manufacturing: A survey, The International Journal of Flexible Manufacturing Systems 2 (1990) 289}328. [5] J. Browne, D. Dubois, K. Rathmill, S.P. Sethi, K.E. Stecke, Classi"cation of #exible manufacturing systems, The FMS Magazine 2 (2) (1984) 114}117. [6] Y.P. Gupta, G. Goyal, Flexibility of manufacturing systems: Concepts and measurements, European Journal of Operational Research 43 (1989) 119}135. [7] J. Olhager, B.M. West, The house of #exibility: using the QFD approach to deploy manufacturing #exibility, Working Paper, WP-259, Department of Production Economics, LinkoK ping Institute of Technology, 1999. [8] J.C. Hull, Options Futures and Other Derivatives, 4th Edition, Prentice Hall Inc., Englewood Cli!s, NJ, 2000. [9] N. Kulatilaka, Valuing the #exibility of #exible manufacturing system, IEEE Transactions on Engineering Management 35 (4) (1988) 250}257. [10] N. Kulatilaka, The value of #exibility: A general model of real options, in: L. Trigeorgis (Ed.), Real Options in Capital Investment: Models, Strategies, and Application, Praeger, New York, 1995. [11] W. Margrabe, The value of an option to exchange one asset for another, Journal of Finance 33 (1) (1978) 177}186. [12] R. McDonald, D. Siegel, Investment and the valuation of "rms when there is an option to shut down, International Economic Review 26 (2) (1985) 331}349. [13] P. Carr, The valuation of American exchange options with application to real options, in: L. Trigeorgis (Ed.), Real Options in Capital Investment: Models, Strategies, and Application, Praeger, New York, 1995. [14] A. Triantis, J. Hodder, Valuing #exibility as a complex option, The Journal of Finance 45 (2) (1990) 549}565. [15] A. Triantis, Contingent claims valuation of #exible production systems, Ph.D. Dissertation, Stanford, 1988. [16] S.A. Andreou, A capital budgeting model for product-mix #exibility, Journal of Manufacturing and Operations Management 3 (1990) 5}23.
[17] R.M. Stulz, Options on the minimum or maximum of two risky assets: Analysis and application, Journal of Financial Economics 10 (2) (1982) 161}185. [18] H. Johnson, Options on the maximum or the minimum of several assets, Journal of Financial and Quantitative Analysis 22 (3) (1987) 277}283. [19] B. Kamrad, R. Ernst, Multiproduct manufacturing with stochastic input prices and output yield uncertainty, in: L. Trigeorgis (Ed.), Real Options in Capital Investment: Models, Strategies, and Application, Praeger, New York, 1995. [20] G.F. Tannous, Capital budgeting for volume #exible equipment, Decision Sciences 27 (2) (1996) 157}184. [21] J. Bengtsson, The value of manufacturing #exibility: Real options in practice, working paper, WP 262, Department of Production Economics, LinkoK ping Institute of Technology, 1999. [22] R.S. Pindyck, Irreversible investment, capacity choice, and the value of the "rm, The American Economic Review 78 (5) (1988) 969}985. [23] H. He, R.S. Pindyck, Investment in #exible production capacity, Journal of Dynamics and Control 16 (1992) 575}599. [24] S. Majd, R.S. Pindyck, Time to build, option value, and investment decisions, Journal of Financial Economics 18 (1) (1987) 7}27. [25] L. Trigeorgis, The nature of option interactions and the valuation of investments with multiple real options, Journal of Financial and Quantitative Analysis 28 (1) (1993) 1}20. [26] L. Trigeorgis, A log-transformed binomial numerical analysis method for valuing complex multi-option investment, Journal of Financial and Quantitative Analysis 26 (3) (1991) 309}326. [27] N. Kulatilaka, Operating #exibilities in capital budgeting: substitutability and complementarity in real options, in: L. Trigeorgis (Ed.), Real Options in Capital Investment: Models, Strategies, and Application, Praeger, New York, 1995b. [28] M. Brennan, E. Schwartz, Evaluating natural resource investments, Journal of Business 58 (2) (1985) 135}157. [29] R. McDonald, D. Siegel, The value of waiting to invest, Quarterly Journal of Economics 101 (1986) 707}727. [30] S.C. Myers, S. Majd, Abandonment value and project life, Advances in Futures and Options Research 4 (1990) 1}21.
Manufacturing #exibility and real options: A review夽 Jens Bengtsson* Department of Production Economics, IMIE, Linko( ping Institute of Technology, S-581 83, Linko( ping, Sweden
Abstract This paper considers manufacturing #exibility and real options from an industrial engineering/production management perspective. Real options papers are related to di!erent types of manufacturing #exibility 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 #exibility type are identi"ed and discussed. 2001 Elsevier Science B.V. All rights reserved. Keywords: Real options; Manufacturing #exibility; Capital budgeting; Production management
1. Introduction What is #exibility worth to a company? Many managers in the manufacturing industry ask this question, since the investment cost in #exible manufacturing equipment mostly exceeds the investment cost of dedicated equipment. A #exible 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, #exibility 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. 夽 The research is supported by grants from the Swedish Foundation for Strategic Research and Swedish National Board for Industrial and Technical Development. * Corresponding author. Tel.: #46-13281538; fax: #4613288975. E-mail address: [email protected] (J. Bengtsson).
Traditionally, in capital budgeting, expected future cash #ows have been discounted with a riskadjusted discount rate. The risk-adjusted rate has for example been estimated with Sharpe-LintnerMossin's Capital Asset Pricing Model (CAPM) to handle the e!ects 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 #exibility. Thus, other methods have to be used to "nd the appropriate value of #exibility 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 #exible 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.
0925-5273/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 5 2 7 3 ( 0 1 ) 0 0 1 2 8 - 1
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Since Black and Scholes [1] and Merton [2] presented their work on option pricing theory a lot of application areas, e.g. valuing complex "nancial 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. Trigeorgis [3], have used this theory to deal with features and problems associated with valuation of projects containing #exibility 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 #exibility, or real options in manufacturing. The paper will relate the real options literature to manufacturing #exibility 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 #exibility is used. Sethi and Sethi proceed from Brown et al. [5] but a number of #exibility 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 de"nitions of #exibility in Browne et al. are the most comprehensive and use their framework in a survey to classify the literature on manufacturing #exibility. Olhager and West [7] refer to Sethi and Sethi as a literature review on manufacturing #exibility, which covers and systematise the #exibility types linked to #exible 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 classi"cation of manufacturing #exibility and real options. Using the de"nitions of Sethi and Sethi, we will consider the value of #exibility
Some of the de"nitions are quite wide and can therefore be interpreted in somewhat di!erent 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 di!erent levels of #exibility using the Sethi and Sethi framework. Here, we also map the di!erent kinds of #exibility treated in the real option literature to the di!erent types of #exibility as Sethi and Sethi de"ne them. This analysis will highlight the following: (i) The types of #exibility that are treated in the real option literature can be distinguished and clari"ed. (ii) The #exibility types that have not been treated as real options are identi"ed, and can be subject to further research. (iii) The applications of real options may indicate that there are other #exibility types relevant to manufacturing that have not yet been identi"ed by the literature on manufacturing #exibility. 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 #exibility types de"ned 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 a!ect the solution and impose limitations on the result will be analysed.
E at the basic level, i.e. #exibility of the machine level, E at the system level, i.e. the #exibility of a production system, E at the aggregate level, i.e. the #exibility of a whole manufacturing plant. Sethi and Sethi de"ne a number of #exibility types at each level and these will be used in this paper.
Fig. 1. Sets representing di!erent types of #exibility related literature.
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2. Foundations of option pricing and real options 2.1. Introduction to option pricing theory The purpose of this chapter is to give a short introduction to the foundation of option pricing and some option related concepts that are of importance to the following text. A more thorough introduction can be found in Hull [8]. An option gives the holder an opportunity without the corresponding obligation to do something speci"c. Options are derivatives in the sense that they depend on an underlying asset of any kind. Two basic options, on the "nancial markets, are the call option and the put option. The call option gives the holder the opportunity to buy the underlying asset at a predetermined price, the exercise price, at a pre-set date. Since the holder has the opportunity to choose whether to exercise the option or not, it will only be exercised if the value of the underlying asset exceeds the value of the exercise price. Reverse, a put option, which gives the holder the right to sell at a predetermined price, at a pre-set date, will only be exercised if the value of the exercise price exceeds the value of the underlying asset. The value of a call option, C, and the value of a put option, P, at the date of exercise are written as functions of the exercise price, X, and the value of the underlying asset, S and are expressed as in expressions (1) and (2). C"Max [S!X, 0],
(1)
P"Max [X!S, 0].
(2)
The pay-o! at exercise can thereby be illustrated as in Fig. 2. So far, only so-called European options are considered. The feature of European options is that
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they can only be exercised at the date of exercise. On the other hand, there are American options, which can be exercised at any moment, until the date of exercise. The value of an American and an identical European option may di!er but it is beyond the scope of this paper to give a full explanation of the di!erences from a valuation point of view. The foundation of option pricing theory can be found in the classical work by Black and Scholes [1], giving Black and Scholes formula, and Merton [2] which extends the theory. These authors made the break-through and found that the price of options can be derived as if the world is risk-neutral. Thereby, option prices can be derived regardless of risk-preferences of investors and without estimation of any risk-adjusted discount rates. They identify that the payo! from an option can be replicated by a portfolio of positions, either short or long depending on the option, in the underlying asset and in a risk-free asset. To avoid arbitrage opportunities, the value of the portfolio, i.e. positions in the underlying asset and the risk-free asset must have the same value as the option. From this arbitrage argument an expression, i.e. a partial di!erential equation, can be derived, whose solution gives the value of a call option. It can be seen in e.g. Black and Scholes formula that the value of the option, under their assumptions, depends on the current value of the underlying asset, the exercise price, the instantaneous risk-free rate, the variance of return of the underlying asset and the time to exercise. They solve the partial di!erential equation analytically, which results in the famous, closed form, Black and Scholes formula. However, to other types of options it can be hard, or impossible, to "nd an analytical solution to the di!erential equation and in these cases it can be necessary to apply
Fig. 2. Payo! from a call and a put option, respectively.
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numerical methods to estimate the value of the option. In many cases the value of the underlying asset will be a!ected by dividends. For example, in the case of stocks, shareholders will usually get cash payouts, i.e. dividends, from the company, once or a number of times per year. Since dividends are taken from the equity of the "rm, the value of the equity and the stocks will be reduced. Dividends on an underlying asset paid during the lifetime of a call option will reduce its value. In the case of put options, the reverse relationship holds, i.e. the value of a put option increases with the size of the dividends during its lifetime. 2.2. Introduction to real options Since Black, Scholes and Merton presented their work, option pricing has found new areas of applications. Apart from pricing "nancial options the theory is also applicable to options constituted by `real opportunitiesa. In this paper manufacturing #exibility is considered and as the term #exibility claims, one has opportunities but no obligations. Thereby, #exibility can be interpreted as di!erent types of options, but the payo!, in the case of #exibility and real options, is often more complex than the payo! from call and put options. However, in many cases, call and put options can be combined to represent the desired payo!. If we consider a simple case of #exibility, e.g. we have the option to produce if revenue, R, exceeds variable cost,
Fig. 3. Payo! from the option to produce.
cases. Therefore, it is often assumed that markets are complete, i.e. in this case, that the revenues can be replicated by a portfolio of traded assets, a tracking portfolio, whose movements of value are identical to the movements of revenues. In some cases the evolution of the revenues and the tracking portfolio may di!er. This can be adjusted for in a similar manner as dividends are treated in the case of "nancial options. Later in this paper, when di!erent papers are reviewed it will be seen that some valuation models cannot handle dividends and this also includes the case when the evolution of the underlying asset, e.g. demand, pro"t etc., di!ers from that of the tracking portfolio. 3. Flexibility and real options 3.1. Flexibility and real options at the basic level Flexibility at the basic level of the Sethi and Sethi [4] framework includes machine #exibility, material handling system #exibility and operation #exibility. Sethi and Sethi de"ne these as follows: E Machine #exibility refers to the various types of operations that the machine can perform without requiring a prohibitive e!ort in switching from one operation to another. E Material handling system #exibility is the ability to move di!erent part types e$ciently for proper positioning and processing through the manufacturing facility it serves. E Operation #exibility of a part refers to its ability to be produced in di!erent ways i.e. a sequence of operations can either be interchanged or substituted with each other.
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Kulatilaka [9] can be used to evaluate a special case of operation #exibility. Here, one machine, a #exible manufacturing system, provides di!erent modes to produce one product, which then are ready to be sold. This places this article in the borderland between basic and system level or in the extreme case, the aggregate level, if one machine carries out all production in the plant. Kulatilaka considers the case when the product can be produced in two di!erent modes. Switching costs from one mode to another are taken into respect but capacity constraints are not considered. The mode that is the most pro"table is partly dependent on output price, which is uncertain, but is also dependent on switching cost. However, output price can be interchanged for demand, exchange rate etc. as the uncertain underlying asset. When the value of the #exible machine is calculated it can be compared to the value of a non-#exible machine to evaluate the operating #exibility. Kulatilaka uses stochastic dynamic programming considering e.g. switching cost in an appropriate way. With this valuation approach the e!ects from a current switch on all future production scenarios is considered. These e!ects from so-called compound or interrelated options are considered later in this paper. In Kulatilaka, actions such as abandoning the machine, waiting to invest and temporarily shutting down production are also considered but these are not treated here. The model used in Kulatilaka [9] is more thoroughly explained in Kulatilaka [10]. Kulatilaka [10] describes a general model, allowing for valuing di!erent kinds of #exibility such as the #exibility types mentioned above but also expansion #exibility and process/product #exibility in the two-product case. However, the underlying valuation model for valuing these types of #exibility is essentially the same. 3.2. Flexibility and real options at the system level Flexibility at the system level concerns #exibility of the whole manufacturing system and will be dependent on the #exibility types at the basic level. Sethi and Sethi [4] de"ne "ve #exibility types at the system level and these are process, product, routing, volume and expansion #exibility.
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3.2.1. Process yexibility Sethi and Sethi's de"nition is that process #exibility of a manufacturing system relates to the set of part types that the system can produce without major set-ups, i.e. only small or in"nitesimal set-up costs are allowed. Process #exibility can be seen as an operational #exibility or short-term #exibility and is strongly dependent on machine #exibility due to the importance of the characteristics of the machine. One of the e!ects of process #exibility is that it enables reduced batch sizes and inventory costs. Margrabe [11] considers the general option to exchange one risky asset for another. This paper was in the "rst hand developed for pricing of "nancial securities but could also be applicable to some simple two-products real option valuation problems. The option can be valued using an analytical formula both for European and American options. In a process #exible context Margrabe's model can be used for valuing the opportunity to mutually exchange from producing one product to another when e.g. prices or pro"ts of the products are uncertain. Margrabe does not handle any capacity constraints, set-up cost or any dividends and is thereby of limited use in real life problems. McDonald and Siegel [12] extend Margrabe to include dividends in the case of European options and Carr [13] considers the American exchange option with dividends. Triantis and Hodder [14] develop a model, which evaluates investments in process #exible equipment where pro"t margins are uncertain, switching between products is free of charge and production decisions are taken at pre-set points in time. The model allows for downward sloping demand curves, capacity constraints and several products can be produced during a period. Production decisions, regarding the quantity of each product, are made to obtain the maximum value of the manufacturing program in the beginning of each period. Triantis and Hodder show that a complex closed form analytical formula can be found in the two-product case using Lagrange optimisation and an equivalent martingale valuation approach. However, if more products are added a Monte Carlo simulation is preferred to evaluate the options since complexity increases rapidly. Triantis
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and Hodder also point out that the drift and variance parameters in their model can be time varying to model e.g. di!erent stages of the life cycle of a product. The assumption concerning switching cost can also be relaxed to include this cost, see Triantis [15], but adds a great deal of complexity. Triantis [15] also develops a model under perfect competition, no switching cost and when the marginal pro"t contribution is uncertain. The model also considers temporarily shutdowns of operation and reopening, which are free of charge, and capacity constraints. However, in this model only one product can be produced during a period. Triantis shows that in the two product case a closed form solution can be found. Andreou [16] evaluates a process #exible manufacturing system producing two di!erent products without any switching cost. The system consists of two dedicated machines and one #exible machine. The model treats capacity constraints and it is assumed that no back-order takes place. Andreou sketches seven di!erent scenarios representing different states of the relationship between actual demand of each product and available capacity. Each scenario occurs with a corresponding probability and in the case of demand for both products, and limited capacity, the most pro"table will be produced in the "rst place. The probabilities are dependent on the bivariate distribution of demand of the two products. Scenarios with an option content are then interpreted in terms of option pay-o!. The pay-o! is depending on the variable pro"ts from two products where the variable pro"ts are the underlying asset and follow geometric Brownian motions. The scenarios containing options can then be valued using McDonald and Siegel [12]. If more products were added or if a more complex production set-up would be used the complexity and the number of scenarios would increase and a numerical valuation approach may be required.
3.2.2. Product yexibility Sethi and Sethi [4] de"ne product #exibility as the ease with which new parts can be added or substituted for existing parts. In contrast to process #exibility these additions and substitutions always lead to set-up cost, however not excessively large.
This also means that the papers listed below could be mapped to process #exibility if the set-up cost would be zero. Product #exibility allows e.g. the company to be responsive to the market by enabling it to bring newly designed products quickly to the market. In Stulz [17] the European option on the maximum of two risky assets with a "xed exercise price is evaluated. This paper is originally developed for "nancial applications but can also be used in some simple real option applications. For example, in a product #exible context it can be used to "nd the value of having the mutually exclusive opportunity to produce two products when pro"ts are uncertain and costs are equal and "xed. This means that only one product can be produced during a period. Stulz [17] is solved using analytical formulas but does not consider capacity constraints or any dividend pay out and are thereby of limited use in most real life situations. Johnson [18] extends Stulz to include several risky assets, i.e. there are several mutually exclusive products that can be produced. Stulz and Johnson can only be used to analyse the value of one switch since several switches with corresponding switching cost may result in interdependencies. In this case, other valuation methods are required which also will be discussed later. Triantis [15] develops two models, which evaluate a product #exible manufacturing system under somewhat di!erent circumstances. The "rst model assumes uncertain prices and equal marginal costs. Both models assume symmetric set-up costs, that only one product is produced during a period and both can be solved analytically in the two-product case. The "rst model evaluates product #exibility over an in"nite horizon where switching might occur at any point in time. Thereby, the option to switch has almost the same features as an American option except from that this option can be exercised more than once. In this model the option to abandon is also considered giving the opportunity to abandon the system if prices are too low. This reduces the lifetime of the project from in"nite to "nite in most cases since it will not be optimal to hold it to in"nity. The second model evaluates product #exibility when switching takes place at di!erent pre-speci"ed points in time. Thereby, the characteristics of the options will be European-like
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with compound features. In this model it is assumed that the price of one of the two products is uncertain, that the production costs might di!er between the products and the lifetime is "nite. However, more products will increase complexity and it might thereby be preferable to use numerical methods. Kamrad and Ernst [19] consider valuation of multiproduct agreements where demand, delivery schedule, and output prices are known since sales are contractually "xed. Uncertainty appears in the output yield and in the prices of inputs, e.g. raw material. Capacity of production and inventory are constrained and except from valuing the agreement, optimal production and inventory guidelines will also be found which also result in a more extensive operations research model. The model considers set-up cost and only one product type is produced during a period. Supplies of the other products have to be covered by inventory during this period. No analytical solution has been found for valuation purposes. Therefore, Kamrad and Ernst use a numerical lattice approach to model risk-neutral prices and stochastic dynamic programming to estimate the value of the production agreements in the case of three inputs and two outputs. 3.2.3. Routing yexibility Sethi and Sethi [4] de"ne routing #exibility of a manufacturing system as its ability to produce a part by alternate routes through the system. Routing #exibility allows for e$cient scheduling of parts by better balancing of machine loads. No way of evaluation is developed and this #exibility type is the only one at the system level, which lacks a corresponding real option. 3.2.4. Volume yexibility Sethi and Sethi [4] de"ne volume #exibility of a manufacturing system as its ability to be operated pro"tably at di!erent overall output levels. Volume #exibility permits the factory to adjust production upwards or downwards within wide limits and can be seen as an operational or short-term #exibility. Tannous [20] builds a model to evaluate volume #exible equipment when demand is uncertain,
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which then is used to "nd the optimal level of investment in volume #exibility. Tannous considers a closed system where the level of #exibility is dependent on the relationship between #exible and non-#exible equipment. The characteristic of the #exible equipment is that the production rate can be adjusted to respond to #uctuations in demand. However, adjustments can only be made within some limits, which are given by e.g. the machine. Investment in #exible equipment increases the level of #exibility and widens the limits of the whole system. The value of the cash #ow from each year of the lifetime of the system is then calculated, using basically Black and Scholes formula. Tannous' model also handles the e!ect of having an inventory. The model as it is formulated is likely having restricted use since it requires that the equipment should be quite similar in that they perform the same tasks and that they directly a!ect the total output rate. Bengtsson [21] considers the value of having the option to hire personnel on short contracts when demand of a product or aggregated demand is uncertain, i.e. one source of uncertainty is considered. This type of option gives "rms the opportunity, but not the obligation, to hire personnel and if demand is su$ciently high they will utilise this opportunity, otherwise not. The option will have di!erent characteristics depending on the duration of the contract and the frequency of the "rm's decision making during the time of an ongoing contract. In Bengtsson a contract, which last for three months and where production decisions are made every month, is considered. In this case the value of the option is not only depending on demand at the hiring date but also on the value of the subsequent production options. The production option is based on a similar idea as McDonald and Siegel [12] that one does not utilise extra personnel if demand is not high enough. As the contract is formulated in Bengtsson this results in so-called compound options, which will be considered later in the paper and numerical methods may have to be used to value the options. 3.2.5. Expansion yexibility Sethi and Sethi [4] de"ne expansion #exibility of a manufacturing system as the ease with which its
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capacity and capability can be increased when needed. Expansion #exibility is important to "rms with growth strategies, such as ventures into new markets, and can be considered as long-term or strategic #exibility. Trigeorgis [3] considers the option to expand when an investment decision is made and where the underlying value of the project is uncertain. These options are appropriate when e.g. a "rm is able to increase the value of an ongoing project by an additional investment. In a production context these could be exempli"ed by the opportunity to buy more production capacity, increase sales and thereby increase the value of the project. This option will only be exercised if the value of the project after exercise exceeds the value of the additional investment cost and the current value of the project. If it is not exercised the value of the project will remain the same. If the option is European it could be valued using basically Black and Scholes formula but if the option is American, other numerical methods may be required. Pindyck [22] does not explicitly address the problem of valuing expansion #exibility. Instead, capacity choice and expansion are examined in order to maximise the value of the "rm when investments are irreversible and demand is uncertain. Pindyck looks at the value of the marginal capacity, which has to exceed the sum of the purchasing cost, the installation cost and the value of the option to invest in the marginal capacity for an investment to take place. Pindyck derives a decision rule telling whether to invest or not, which e.g. is dependent on current demand and actual capacity. He and Pindyck [23] use the same approach as Pindyck [22] but extend the analysis to include #exible capacity and compare this to the situation when only dedicated equipment is used. 3.3. Flexibility and real options at the aggregate level Flexibility at the aggregated level concerns #exibility at the plant level. Sethi and Sethi [4] identify and de"ne three types of #exibility at the aggregate level and these are program #exibility, production #exibility and market #exibility. According to Sethi
and Sethi they are de"ned as E Program #exibility is the ability of the system to run virtually untended for a long enough period. E Production #exibility is the universe of part types that the manufacturing system can produce without adding major capital equipment. E Market #exibility is the ease with which the manufacturing system can adapt to a changing market environment. Program #exibility has linkages to process and routing #exibility and enables reduced throughput time by having e.g. reduced set-up time. Production #exibility has linkages to process, routing and product #exibility. In contrast to product #exibility, production #exibility allows for considerable set-ups without adding major capital equipment. Production #exibility allows the "rm to compete in a market where new products are frequently demanded and can be considered as long-term #exibility. Market #exibility has linkages to product, volume and expansion #exibility. Market #exibility is necessary when environment changes because of rapid technological innovations, changes in customer tastes, short product life cycles, uncertainty in sources of supply, etc. and is important to the survival of a "rm in an environment that is constantly in #ux. All of these #exibility types have linkages to other types of #exibility. Therefore it would be appropriate to use the real option models from the system level to deal with the problem to evaluate both production and market #exibility. However, Sethi and Sethi's de"nitions are wide and there are some types of market #exibility described in the real option literature which are not directly related to any type at the system level and some of these papers are brie#y considered below. 3.3.1. Option to temporarily shut down McDonald and Siegel [12] consider investments where there is an option to temporarily shut down without any costs when unit output price is less than unit variable cost. Thereby, an investment can be seen as a portfolio of European call options on the contribution margins of each period, respectively. For each period there is a corresponding option, which is exercised if the contribution margin of the
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period exceeds zero. The gross present value of the investment can be found by valuing each of these options individually and add them together. The option should be restricted to the one product case or the several products case with equal unit prices and equal unit variable costs. If shutdowns would cost, this would lead to interdependencies between options of di!erent periods and this can lead to a requirement for numerical methods. 3.3.2. Option to abandon Margrabe [11], earlier considered under process #exibility in this paper, can also be used for valuing the option to permanent abandon for salvage value. If the project and salvage values are uncertain and no dividend, or pay out, takes place Margrabe's analytical expressions can be used. This type of option can be seen as an American put option on the value of the project with a stochastic exercise price, represented by the salvage value. The assumption regarding that no dividends are allowed may possibly limit the practical use of this option. However, in the case of dividends the valuation model of Carr [13] may be used. Myers and Majd [24] evaluate the option to permanent abandon for its salvage value, or the value of alternative use, when the gross present value of the project is uncertain. Abandonment takes place if gross present value is below salvage value. This option has the same features as an American put option and is solved using numerical methods due to that dividends are allowed. Myers and Majd also extend the option to include the case when salvage value is stochastic resulting in a similar problem as in Margrabe, however, dividends are not allowed in the latter. 3.3.3. Compound options and interdependencies Most of the projects in real life are not restricted to only one type of #exibility or real option. Instead, an investment opportunity might consist of the options to wait, switch and abandon, which are also treated in some of the papers presented earlier. Often, there are interdependencies or compound e!ects between options in the meaning that the exercise of an option gives numerous of new options. The value of a prior option is, therefore, a!ected by the value of subsequent options. From
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a valuation point of view this means that the di!erent types of option cannot be seen and valued, as they were individual. Instead of considering and evaluating only one option at a time, all options have to be evaluated together at the same time. This will often lead to that analytical expression cannot be found and numerical techniques have to be used instead. Trigeorgis [25] considers valuation of a generic investment with the option to defer, switch use, expand, contract and abandon. Using a numerical method, from Trigeorgis [26], it is shown that the value of a collection of options generally deviates from the sum of the values of each individual option. Trigeorgis [25] shows that the incremental value of an additional option when other options are present is generally less than the value of the options in isolation. The incremental value also tends to decline, as more options are present. Kulatilaka [27] evaluates interdependent options, in this case wait-to-invest, expand and shutdown option, using the model in Kulatilaka [10] and shows that the value of a collection of option is less than the sum of individual options. Brennan and Schwartz [28] consider interdependent options in a valuation of a mine. In this case output prices of commodity are uncertain and the options to open, close, reopen and abandon are considered.
4. Real option papers outside the Sethi and Sethi framework If one consider the real option literature that has some point in contact to manufacturing it will appear that some of them cannot be mapped to types of #exibility in the Sethi and Sethi [4] framework. However, these can play an important role in application and valuation of real options. Below, some of these papers are considered and grouped together to show di!erent categories. 4.1. Option to defer investment The option to defer, or the option to wait, has been considered in numerous papers. This type of option concerns the value of waiting before an investment takes place, thereby giving the
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opportunity to take advantages of future information and can be very valuable in big project such as mining and oil exploration. McDonald and Siegel [29] consider the valuation of a perpetual investment opportunity in irreversible projects. The project cannot be used for other purposes, the present value of future cash #ow is uncertain and the cost of investment is considered as either uncertain or certain. There is an analytical solution to this option when lifetime is perpetual but, however, in more realistic cases is not an investment opportunity perpetual and in these cases numerical methods are required. Majd and Pindyck [24] examine the option to delay irreversible construction in a project where a series of outlays must be made sequentially. Production cannot proceed faster than at a rate k, the project produces no intermediate cash #ow until it is complete and the market value of the "nished project is uncertain during the whole construction phase. Majd and Pindyck claim that these options can be valuable in industries such as aircraft industry, mining or plant building where the market value of the investment is uncertain during the whole construction phase. There exists no analytical solution to this problem and therefore numerical solution methods are required.
5. Concluding remarks In this paper, #exibility 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 #exibility, 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 #exibility types in the Sethi and Sethi framework and vice versa. There are also real options papers that do not "t in the Sethi and Sethi framework and some types of #exibility 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 #exibility types de"ned by Sethi and Sethi.
As seen in Table 1, there are numerous real option papers that are related to the di!erent types of #exibility. 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 speci"c 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 #exibility 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 #exibility to produce more products, numerical methods are preferred to use. In some of the papers in Table 1 more than one type of #exibility are modelled. Multiple options that have interdependencies may require numerical methods in order to value and handle the e!ects of interdependencies in an appropriate way. As seen in Table 1 some types of #exibility 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 de"ne them. First, it is hard to "nd the value of the ability to perform various operations in a machine and move di!erent types e$ciently. For example, one relevant question that has to be answered is which underlying stochastic process that a!ects the value and should be used. Second, it might be of less relevance to value #exibility types at the basic level since they only provide a small contribution to the value of #exibility of a large system or plant. However, they a!ect the characteristics of #exibility at system and plant level and should be considered. At the system level it is only routing #exibility that misses references. It is hard to evaluate routing #exibility 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 #exibility is probably the hardest to evaluate by the same reason as mentioned above. Production #exibility, which is unmarked in Table 1,
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Table 1 Real options articles mapped to #exibility types according to Sethi and Sethi's [4] framework Level
Type of #exibility
Real option papers
Basic
Machine Material handling system Operation
* * Kulatilaka [9] Kulatilaka [10]
System
Process
Margrabe [11] McDonald and Siegel [12] Triantis and Hodder [14] Andreou [16] Carr [13] Stulz [17] Johnson [18] Triantis [15] Kamrad and Ernst [19] Kulatilaka [10] * Tannous [20] Bengtsson [21] Trigeorgis [3] Pindyck [22] He and Pindyck [23] Kulatilaka [10]
Product
Routing Volume Expansion
Aggregate
Program Production Market
has strong linkages to product and process #exibility, and the models used to evaluate these should also be applicable to evaluate production #exibility 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 speci"c type of #exibility but could be related to manufacturing. One group of papers is the so-called wait-to-see options or options to defer investment. Another
* * Brennan and Schwartz [28] Margrabe [11] McDonald and Siegel [12] Myers and Majd [30] Kulatilaka [10] Carr [13]
group is the options to abandon a project for salvage value. These types of #exibility are not explicitly de"ned within the Sethi and Sethi framework which also shows that Sethi and Sethi do not really consider #exibility 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 #exible manufacturing systems.
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