Evaluating the Expansion Flexibility of Manufacturing Systems in
Uncertain Environments
Roberta Pellegrino
Dipartimento di Ingegneria Meccanica e Gestionale, Politecnico di Bari, Viale Japigia 182,
70126, Bari, Italy, email: r.pellegrino@poliba.it
Extended abstract
Today having the agility to react to changes in market conditions is one of the keys to success
in dynamic and uncertain manufacturing environments.
Manufacturing flexibility is an important part of a firm’s competitive strength. Flexibility of a
system can be defined as “its adaptability to a wide range of possible environments that it may
encounter. A flexible system must be capable of changing in order to deal with a changing
environment.” (Sethi and Sethi, 1990). Flexibility in manufacturing systems can be of
different types: machine, material handling, operation, process, product, routing, volume,
expansion, program, production, and market flexibility. Acquiring this flexibility has a cost.
In fact, the investment in flexible manufacturing equipment is generally major than the
investment in dedicated equipment. But, on the other hand, a flexible system allows managers
to cope with uncertainty and to do future actions in response to market changes. “Flexibility
gives the management some degrees of freedom to take advantage of outcomes better than
expected and simultaneously provide an ability to reduce losses” (Bengtsson, 2001). This is
often very valuable for the firm. The problem is: how valuable is this flexibility? How much
money is a firm disposed to spend in order to have this flexibility? To answer these questions,
an appropriate methodology able to take into account these characteristics has to be used.
Traditional techniques, in fact, are not suitable for evaluating such kinds of flexible
manufacturing system investments. They assume that management makes an irrevocable
decision on the basis of its future market expectations. Therefore, they assume that the
“deterministic” cash flows are known with certainty at initial time. Then, they are discounted
with a given discount rate (discounted cash flow – DCF – methodology). This is enough
correct in absence of uncertainty, but when managers have the possibility to change their
initial decision for reacting to new information from market and, therefore, to improve the
value of the project, traditional discounted cash flow methodology assumptions are too heavy.
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Thus, other more suitable methods to value this flexibility have been proposed in literature;
some are based on real options, others do not directly use options theory (Kulatilaka, 1988;
Kumar, 1995; He and Pindyck, 1989; Karsak and Ozogul, 2005; Trigeorgis, 1996).
In the present paper the author focuses on one kind of manufacturing flexibility: the
expansion flexibility. “Expansion flexibility of a manufacturing system is the ease with which
its capacity and capability can be increased when needed” (Sethi and Sethi, 1990). This kind
of investment can be viewed as consisting of two investment phases (Kumar, 1995). The first
(“primary investment”) is the initial price paid to acquire flexible system. The second
(“secondary investment”) represents the additional investment required at a later date in order
to use flexibility provided by the system. This investment will be made if there are the market
conditions (that require the capacity increase) and if it is convenient. As Sethi and Sethi
(1990) state, expansion flexibility can be achieved in several ways, such as, for example, by
having modular manufacturing system, building small production units, acquiring
multipurpose machinery, having a high level of automation that can facilitate mounting
additional shifts, providing infrastructure to support growth. From a real options perspective,
the initial investment to acquire this option (that is, the investment needed to have flexible
system) corresponds to the option price or premium, while the secondary investment to make
for expanding the system capacity is the strike or exercise price. As said above, capital
expenditure required for flexible system are generally higher than dedicated production
systems, and the potential future costs and benefits - that could result from exercising the
option - are difficult to value with accuracy at initial time. This is particularly true in presence
of a high level of uncertainty, when it is difficult to foresee if the option will be exercised or
not.
For this reason, this kind of investments requires a correct evaluation tool. The possible
secondary investment (for the capacity increase) and the resulting benefits have to be taken
into account during the evaluation of the initial investment (that is, when managers have to
decide if to invest or not and choose among investment alternatives). Approaches based on
option theory have been developed in order to do this (Kumar, 1995; Karsak and Ozogul,
2005).
In this paper, the author adopts an approach based on Monte Carlo method (already tested in
another – more simple – production context (Costantino and Pellegrino, 2007)). Unlike the
traditional techniques, Monte Carlo simulation is able to take several different (theoretically
endless) uncertainty sources into account in the evaluation. It assigns a probability
distribution (derived by the managers’ experience) to each uncertain or variable model input.
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On the contrary of traditional methodologies, this can give a (probabilistic) result also when
the system complexity does not have closed-form solutions. The traditional techniques
proposed in literature for valuating real options have their roots in financial world, such as
Black-Scholes’ (1973) model modifies by Merton in 1973, Boyle’s (1977) model for
European options, binomial model presented by Cox, Ross and Rubinstein (1979), Least
Squares Monte Carlo approach (LSM) proposed by Longstaff and Schwartz (2001), and
others. The “financial origin” of these methods often limits their application in real world
cases (Lander and Pinches, 1998), especially when the uncertainty sources increase. In fact,
they assume that only one (or, however, few) parameter is affected by uncertainty, the others
are generally deterministic.
This paper presents a quantitative model based on Monte Carlo technique in order to value the
option of capacity expansion. Managers have to decide at initial time if to invest in a flexible
manufacturing system (with the possibility to increase capacity in the future) or in dedicated
system. In other words, the firm has to value if it is convenient to spend additional money to
acquire expansion flexibility. Managers have foreseen that an increase of the current demand
for final product could happen with a certain probability. Thus, the developed model
considers if this event happens. In a positive case, it values if it is really convenient to expand
production capacity according to the actual production costs and selling price. In other terms,
the model values if the benefits resulting from the capacity expansion (that is, the exercise of
the option) are major than the costs to do this.
The input parameters of the model are described with adequate probability distributions (on
the basis of the managers’ expectations), such as the probability that a demand increase
happens, or the value of this increase. Then, the differential benefits and costs between a
flexible system and a dedicated one are considered. An illustrative case shows the model
working and its results by using the Crystal Ball software. With enough repetitions, it is
possible to obtain a probability distribution of benefits/costs associated to this expansion
option. This way, managers can assess the probability to have a positive result and the extent
of probabilistic differential benefits against an initial certain expenditure for acquiring this
flexibility. This tool could be an interesting guide for managers in order to value this kind of
investment in uncertain environments. It is clear that the value of this option increases with
increasing uncertainty, and it has no value when there is no uncertainty.
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