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1. Introduction
To face
the increasing globalization of markets and the constraints of changing
economic and technological environments, organizations use information
technology as an instrument of competitiveness. In particular, software
systems play increasingly important roles in supporting organization’s
business and decision-making processes. Nevertheless, the development of
such systems is difficult and costly because of uncertainty and risk
inherent in software engineering. (Dakhli 1998) and (Toffolon 1996) have
stressed that high maintenance costs and poor quality of software
systems result from uncertainty inherent in stakeholders’ requirements.
Uncertain events are random events with unknown probability of
occurrence. They must be distinguished from risky events, which are
random with known probability distribution. As noticed by (Boehm 1991),
(Charette 1989), and (Karolak 1996), analysis of software engineering
uncertainties and risks is a tedious task. On the one hand, because
software engineering has many dimensions (Toffolon 1999). On the other
hand, the great number of methods, technologies and tools proposed in
order to support the software production process often worsen
difficulties encountered during uncertainties and risks analysis.
Finally, such difficulties are related to the attributes of
organizations operational and business processes supported by software
systems. These processes reflect the conflicting interests and points of
view of stakeholders concerned with software systems. Consequently,
uncertainty reduction, and risk management are among the most critical
activities in software engineering. Uncertainty reduction consists in
transforming uncertain events into risky events. There are two kinds of
uncertainties related to software systems development and use. Technical
uncertainty is endogenous to the decision process and refers to the
unknowns involved in developing software artifacts: time, effort and
technologies required,... Economic uncertainty is exogenous to the
decision process and refers to unexpected events beyond the direct
control of the organization: political events, changes in interest
rates,...Software informative prototyping is among the most important
instruments of technical uncertainty reduction. Software informative
prototyping is an iterative approach to development of a working model
of a software system in order to learn about its true requirements. Such
a working model is called software informative prototype. In particular,
software informative prototyping makes it possible to provide
information necessary to allow the choice of the most appropriate
computer solutions, technologies, methods and tools to build the
software products meeting the organization’s requirements. Such an
information permits reducing the problems of communication and
incomprehension between the software project stakeholders. For instance,
software informative prototyping makes it possible to obtain precise
details on the users needs and can be used to evaluate the impacts of an
architecture model, a process, or a new technology on the universe of
discourse. However, software informative prototyping is costly and
incurs an irreversible investment in limited resources whose level
depends on the quantity of required information and whose profitability
is dubious. By another way, information obtained through software
informative prototyping may result in more complex software, additional
development and maintenance costs, and higher risks of failure. So, it
is necessary to evaluate informative prototyping before building
informative prototypes. In particular, informative prototyping
evaluation consists in solving two main problems related to the
determination of the optimal implementation date and the optimal number
of iterations of an informative prototype. In this paper, we propose a
decision-oriented framework to manage software informative prototyping
process, based on economic decision theory and option-pricing theory
(Hull 1993). This framework assumes that software informative
prototyping is undertaken in order to help decision-makers choosing the
most appropriate among many alternative computer solutions to an
organizational problem. The remainder of the paper is organized as
follows. In section 2, we present the most important related work.
Section 3 describes an approach to determine the relevant states of the
nature associated with many alternative computer solutions to an
organizational problem. In section 4, we present an approach to
determine on the one hand, the value of information issued from software
informative prototyping and on the other hand, the optimal number of
iterations during the informative prototyping process. In section 5, we
apply the option-pricing theory to define an evaluation approach which
helps determining the optimal implementation date of informative
prototypes. Such an approach improves the technique presented in section
4. Implications for research and practice are discussed in section 6.
2. Related
work
The main work about software
prototyping evaluation is due to B.W. Boehm (Boehm 1981). This author
proposed an approach of software informative prototyping, based on the
economic decision theory. Certainly, many aspects of this evaluation
approach are interesting, in particular because of its theoretical
basis. Nevertheless, Boehm’s approach presents three shortcomings.
Firstly, it rests on a too general definition of prototyping. In other
words, no classification of informative prototyping is used by this
approach. This results in neglecting many aspects of informative
prototyping during the evaluation process. In particular software
prototyping non-monetary aspects (organizational aspects, human aspects,
...) are not taken into account by the Boehm’s evaluation approach.
Secondly, it is based on the paretian cost/benefit analysis i.e. on the
classical Net Present Value technique (NPV) which consists in:
·
computing
the expectation of the present value of the investment decision
benefits,
·
computing
the expectation of the present value of the investment decision costs,
·
computing
the NPV i.e. the difference between the first and the second
quantities ;
·
observing
the following decision rule : « the investment is carried out only if
the NPV is positive ».
This decision
rule is not optimal even if all the aspects (including organizational
and human) of prototyping costs and benefits are taken into account.
Indeed, it is built on the faulty assumption that two possibilities are
available: invest now or never. So, in order to get additional
information by software informative prototyping, the software project
manager has to choose between two exclusive decisions: invest
immediately in the implementation of an informative prototype, or not
invest at all. In many cases, the immediate investment in informative
prototyping does not correspond to an optimal decision. This is true in
particular for organizations where a software system is already
operational and informative prototype relates to a new computer solution
involving an important technical or design change. For instance, the
organizational actors involved in the software development and use
processes can obtain, after a short waiting time, further information
without any prototyping. The irreversible nature of investment in the
software prototyping development process justifies, in many cases, the
« wait and see » strategy. Finally, Boehm’s evaluation approach is
applicable only in the case of a single uncertainty period. In other
words, software informative prototyping and the related design decisions
must be made in this period, with regard to the information provided by
the prototype. This hypothesis is not realistic since, most of the time,
the decisions resulting from software prototyping are made after several
periods necessary to obtain more information by other means.
By another way, (Chalasani et
al. 1997) have proposed an evaluation approach of software informative
prototyping based upon the option-pricing theory which integrates the
timing of informative prototyping decisions and design decisions within
a single framework. This approach improves Boehm’s work through taking
into account the flexibility of being able to postpone the informative
prototyping and design decisions. In particular, (Chalasani et al. 1997)
argue that, on the one hand, this flexibility is analogous to the
flexibility of exercise of financial options and on the other hand,
flexibility’s value is the value of the corresponding financial option.
Nevertheless, the framework proposed by (Chalasani et al. 1997) doesn’t
consider software informative prototyping benefits and thus doesn’t
provide instruments to evaluate these benefits. Moreover, this framework
doesn’t take into account the iterative nature of software informative
prototyping. The approach presented in this paper deals with these two
aspects of software informative prototyping but doesn’t study
relationships between informative prototyping and design decisions. The
evaluation approach we propose in this paper aims to cope with the
shortcomings of frameworks cited previously in two different ways. On
the one hand, our approach uses the software dimensions theory (Toffolon
1999) to determine with a good approximation the set of relevant states
of the nature simultaneously with their probability distribution.
Benefits of software informative prototyping are evaluated on the basis
of this knowledge. The principal advantage of this technique consists in
taking into account all the aspects of software prototyping during the
evaluation process. On the other hand, we use the option-pricing theory
to evaluate software informative prototyping as an irreversible
investment, which could be deferred. This improves the NPV rule, which
consider that software informative prototyping, corresponds to
now-or-never decisions. The description of the software informative
prototyping evaluation approach we propose in this paper takes place in
three steps:
1.
First, we
use the software dimensions theory to determine the states of the nature
associated with the alternative computer solutions;
2.
Thereafter,
we propose an approach to determine the value of information issued from
software informative prototyping;
3.
Finally, we
provide an evaluation instrument, based on the option-pricing theory,
which helps decision-makers in determining the optimal timing of
software informative prototyping decisions.
3. Determination
of the states of the nature
The determination of the
states of the nature associated with a computer solution or a design
decision is a difficult task. Indeed, the states of the nature must
reflect interactions between the computer solution and the organization
concerned with this solution. Many well-known models of organization
show the complexity of these interactions. For example, H. J. Leavitt
(Leavitt 1963) (Stohr et al. 1992) views organization as an interaction
between six main components: structure, task, people, production
technology, information technology, and environment. By another way, the
economic agency theory (Alchian et al. 1972) analyzes an organization as
a nexus of contracts among self-interested individuals. Each agency
contract links a principal (entrepreneur) and agents (employees) in
order to perform some service. The economic agency theory rests upon the
following assumption: each agent maximizes its proper utility and pays
no regard to the welfare of the principal or non-pecuniary virtues. Our
approach uses the software dimensions to define with a good
approximation the set of relevant states of the nature simultaneously
with their probability distribution. Software dimensions has been
determined on the basis of a deep analysis of the links between the
software crisis and organizations, i.e. the interrelations between all
organizational components (structural, tasks, individual, technical),
environment and information technology. These ten dimensions concern
altogether the software process and the artifacts produced by this
process. The process dimensions (cost dimension, delay dimension,
technical dimension, communication dimension and organizational
dimension) and the product’s dimensions (functional dimension, human
dimension, economic dimension, organizational dimension and temporal
dimension) demonstrate that a same software may reflect many different
realities. These realities depend on the organizational, social and
economic contexts of its use and exploitation. The determination of the
states of the nature technique consists firstly, to characterize each
software dimension ()
by a set of attributes ()
and secondly, to associate with each alternative solution
one
predicate per
software dimension ().
is
a random variable defined as follows :
·
=2
if takes
into account all the dimension’s attributes,
·
=1
if takes
into account only a part of the dimension’s attributes,
·
=0
if doesn’t
take into account any dimension’s attribute.
We suppose that :
·
,
·
,
·
.
where .
A state of the nature is
defined as one value of the random matrix ,
which rows correspond to the alternative solutions and columns
correspond to software dimensions. So there are
possible
states of the nature. For example, if a decision-maker is concerned with
three dimensions and has to choose between two alternative solutions,
then there are states
of the nature. Difficulties generated by such a high number of states of
the nature makes necessary the identification of those states of the
nature which really hold. Classification of the software dimensions is a
technology, which permits choosing the most important dimensions. It
consists to assign a weight to each software dimension on the basis of
the importance of this dimension in the development of a set of software
products to satisfy user’s needs. Software dimensions whose weights are
negligible must be excluded from the field of analysis. As weights
depend on the information amount hold by decision-maker, estimating
these weights may be improved by using prototyping to reduce uncertainty
and get more information about dimensions role in the implementation of
a software solution. The probability that a state of the nature
is
true is
4.
The value of information provided by informative
prototyping
Software informative
prototyping can be used to get additional information about the payoff
of each alternative solution, or about the relative importance of its
attributes. In particular, it makes it possible to reduce uncertainties
related to the probabilities of realization of the various states of the
nature associated with these solutions. The information provided by an
informative prototype relates to the software product, the development
process, and the interaction between the software product and the
environment where it is implemented and used. Nevertheless, the quantity
of information sought depends on the one hand, on the organization’s
priorities and on the other hand, on the amount that can be invested in
software informative prototyping. So, the software informative
prototyping process must be managed. We think that the determination of
the optimal number of iterations is an adequate technique to control
this process. This technique is based on the evaluation of the
information brought by software informative prototyping under
uncertainty.
1.
Notations
and basic assumptions
Let
be
a set of alternative solutions to a software engineering problem,
a
set of states of the nature associated with and
the
payoff of the alternative solution under
the state of the nature .
is
interpreted as a cost if it is negative and as a benefit if it is
positive, =0
means that the alternative solution is
neutral under the state of the nature .
We denote the
development cost of an informative prototype and
an
estimate of the “a priori” probability distribution of the random vector
(,
" ).
Since cannot
be known with certainty, we assume that an estimate of
is
known. is
a vector of subjective probabilities which depends on the information
held by the decision-makers. In the same way, we assume that the payoff
of
an alternative solution under
the state of the nature is
known. So, the average payoff of the alternative solution
is :
.
The decision rule consists
in choosing the alternative solution whose
average payoff is
maximum. So, the maximum expected payoff is .
The above decision rule depends
on the average payoff of each alternative solution. That means that the
states of the nature and their distribution of probabilities, as well as
the payoff of each alternative solution under a given state of the
nature, are known. The states of the nature associated with each
alternative solution are determined according to the method described in
section 3. The distribution of probabilities of the states of the nature
and the payoff of each alternative solution under a given state of the
nature are estimated by the decision-makers. These estimates depend on
the decision-makers experience and can be improved by informative
prototyping.
2.
The
software informative prototyping optimal number of iterations
If the software informative
prototyping development process provides perfect information on which
state of the nature will hold, the decision-maker will be able to choose
the alternative solution which payoff under a given state of the nature
is maximum. In that case, expected payoff is .
So, the value of perfect information i.e. the benefit of prototyping is:.
Nevertheless, since software informative prototype is an outline of the
final software system, the information it produces is not perfect. So,
instead of an exact response on the true state of the nature associated
with an alternative computer solution, software informative prototyping
provides a set of probabilistic results at
the qth iteration. Let
be
an estimate provided by the decision-maker of the conditional
probability of the result under
the state of the nature and
the
matrix of the conditional probabilities whose lines correspond to the
results provided by software informative prototyping and the columns
correspond to the states of the nature. Thus, the distribution of
probability of the random vector is
defined
as follows: .
Consequently, we obtain a
matrix of
“a posteriori” probabilities whose line provides
the “a posteriori” probability distribution of the random vector
given
informative prototyping result .
So, .
Given the distribution of « a priori » probabilities
of
the random vector ,
the information produced by software informative prototyping is
evaluated according to the following algorithm:
1.
Identify
the results of
software informative prototyping;
2.
Estimate
the matrix such
that ;
3.
Determine
the distribution of probabilities of
the random vector ;
4.
Compute the
matrix of “a posteriori” probabilities
such
that ;
5.
For each
result provided
by software informative prototyping, compute the average payoff
of
the alternative solution at
the qth iteration. Given software
informative prototyping result ,
choose the alternative solution whose average payoff at the qth
iteration is maximum. In this case, the expected payoff is
.
6.
Compute the
value of information provided by software informative prototyping
.
denotes
the cost of software informative prototyping at the
iteration
and is such that .
Consequently, the software informative prototyping process can be
controlled according to the following decision rule: once the
iteration
completed, a version
of informative prototype is developed if .
If ,
the optimal number of iterations during the informative prototyping
process is q.
5.
An
option based software informative prototyping evaluation approach
(Dixit et al. 1995) define
investment as “the act of incurring an immediate cost in the expectation
of future rewards”. Investments in information technology are, in
general, uncertain and irreversible i.e. if the business doesn’t
succeed, the money spent can’t be recovered. Since the early 80’s, it
has been noticed that the neoclassical analysis of investment decisions,
based on the NPV, appears to be incorrect as soon as the investment
decision is irreversible or uncertain. They stressed the value of
waiting to invest and noted that one of the major characteristics of
investment is the delay between the investment decision and its
implementation. This delay is related to the decision process
characteristics, the needs for information about the investment, or the
gathering of the financing funds necessary to undertake the investment
spending. By neglecting uncertainty, risks and irreversibility inherent
in investment process, the neoclassical NPV approach assumes that only
two decisions are possible: invest now or never.
1.
The option-pricing models
The option-pricing theory
provides a more realistic approach to analyze irreversible investment
decisions under uncertainty. Indeed, an irreversible investment can be
compared to a financial call option. An option is a contract between two
parties whereby the option holder has the right but not the obligation
to perform a specified transaction with the option issuer. There are two
fundamental categories of options: puts and calls. An European call
(put) option on some underlying asset gives its holder the right to buy
(sell) the asset for an agreed price (the strike price), at a fixed
expiration date. An American option is an option that may be exercised
by the option holder at a fixed price (the strike price) on or before a
certain expiration date. So, making an irreversible investment is
equivalent to exercising a call option. As noticed by (Sick 1995),
(Nichols 1994) (Trigeorgis 1995) and (Trigeorgis 1996), the investment
opportunity in information technology option available to an
organization is a “real option” consisting in flexibility a manager has
for making decisions about real assets (in contrast to shares of stock).
A real options approach is an extension of the financial option theory
to options on real (non-financial) assets. Consequently, for each
irreversible investment, the decision-maker has four strategies: invest
now, abandon the investment, defer the investment, or invest to get more
information.
The real options theory is
applicable to evaluate design decisions made during the software
development process since these decisions are, in general, irreversible
and uncertain. In particular, since software informative prototyping
requires an irreversible and uncertain investment in limited resources
whose level depends on the quantity of required information, it
corresponds to a call option that can be exercised by the software
developer. The evaluation approach described in this section aims at
providing a “call option-based” answer to the following question related
to software informative prototyping: when to develop an informative
prototype?
The Black-Scholes model (Black
et al. 1973) and the Cox, Ross and Rubinstein binomial model (Cox et al.
1979) are among the most important models used to evaluate options
strategies. Nevertheless, only the binomial model is appropriate to
accurately evaluate American options. Indeed, it is possible with this
model to check at every point in an option’s life for the possibility of
exercising this option before the expiration date. In that order, the
binomial model breaks down the time to expiration T into
potentially a very large number of time intervals, or steps. A tree of
asset prices is initially produced working forward from the present to
the expiration date. The binomial model is based upon the following
assumption: at each step, the asset price moves up or down with a
specific probability and by an amount calculated using volatility, time
to expiration date and risk free rate. The tree corresponds to all the
possible paths that asset price could take during the option life.
2. An
option-oriented evaluation approach
As noticed previously, software
informative prototyping is associated with an American call option which
can be exercised at any time before the expiration date T ()
determined according to the computer project attributes and the
organization’s constraints and priorities. Therefore, there are T+1
possible software informative prototyping dates 0, 1, 2,..., T.
Money is assumed to be borrowed or lent at the same risk free rate r.
This assumption is realistic since while applying the binomial model, an
agent is either lending or borrowing money. The strike price Cp
of this call option is the cost of software informative prototype
development. The software informative prototyping payoff at date is
denoted .
The probability qt that software informative
prototyping takes place at date t is assumed to be given. The
probability distribution associated with the vector is
denoted .
We assume that the payoff is
non-random. As noticed in the previous section, is
computed according to the following formula:.
In this formula, the index t denotes the software informative
prototyping date. Let ()
be the s-algebra determined by information available before t.
The random variable is -measurable
i.e. it depends only on information provided by .
Since software informative prototyping is analogous to an American call
option, its value payoff at time t is which
is worth at
the present time (t=0). To determine the optimal date to exercise
the software informative prototyping call option, we use the concept of
“stopping time”. A stopping time n is a random variable taking integral
values in the range [0,T], such that for each t Î {0,
1, 2,..., T}, c{n=t} is -measurable.
For each A Î ,
the random variable cA is defined as: .
The stopping time concept
permits describing any American call option exercise strategy.
Furthermore, according to (Hull 1993), given the information up to time
t, the expected present value at time t from exercising the call
option associated with software informative prototyping is .
Let L(t,T) be the set of all the stopping times taking values in
the range [t,T]. Therefore, at time t, the optimal time of
software informative prototyping is:
.
Consequently, if then
software informative prototyping is never undertaken ().
3.
Software
informative prototyping control
The option-pricing theory may
be used to control software informative prototyping through determining
on the one hand, the optimal number of iterations and on the other hand,
the optimal date to undertake a new iteration of the software
informative prototyping process. We recall that the cost of the qth
iteration is denoted ().
Investment associated with the qth
iteration of software informative prototyping is irreversible and
uncertain. According to the Bounded Rationality Principle (Simon 1983),
such an investment may be postponed or not undertaken at all in
particular when decision-makers consider that information provided by
the first (q-1) software prototyping iterations is “satisfycing”.
Consequently, undertaking the (q+1)th iteration of
software informative prototyping may be analyzed as a American call
option. The strike price of this call option is .
According to the previous paragraph results, if the present date is t,
the first software informative prototyping iteration takes place at .
In the following, we use the expression to
denote ,
and the expression to
denote ("
n³1).
Therefore, the second iteration of software informative prototyping is
undertaken at .
More generally, the optimal time of the qth
iteration is which
is computed according to the following algorithm:
a)
Compute.
b)
The optimal number of
software informative prototyping iterations is
.
6.
Implications for
research and practice
The option-pricing theory
is a powerful tool which permit taking into account the flexibility of
being able to postpone the informative prototyping. The value inherent
in such a flexibility represents the opportunity cost of investing in
software informative prototyping i.e. the cost of loosing the
opportunity of being able to decide when to prototype. The framework
described in this paper provides instruments to control –under delay and
budget constraints- two main aspects of software informative prototyping
related to the determination of the optimal start time and the optimal
number of iterations. According to this framework, software informative
prototyping is associated with a decision-making process based upon on
the one hand, the value of information produced and on the other hand,
the value of flexibility of postponing iterations. Such a
decision-making process has three main advantages. Firstly, it makes it
possible to manage software informative prototyping like a project whose
outputs are information reducing uncertainty. Secondly, it permits
decision-makers taking into account organizational learning during
software informative prototyping. Indeed, option-pricing models provide
decision-makers with instruments to determine the right timing, the
scaling-up or abandonment of iterations as the organization learns
during the period preceding the expiration date of the call option
associated with software informative prototyping. Finally, by taking
into account the delay and budget constraints, the decision-making
process permits avoiding the gold-plating problem resulting from
software informative prototyping. Nevertheless, the practical use of the
proposed framework depends on how accurate are approximation of states
of the nature and estimates of payoffs associated with alternative
computer solutions. In that way, we think that the use of the software
dimensions may be helpful. Indeed, a computer solution may be
characterized by the software dimensions. To take into account the
organization’s constraints and priorities, the software dimensions are
associated with a vector of weights and each dimension is described by a
vector of weighted attributes. We denote the
vector of software dimensions weights, the
vector of attributes of the dimension l ()
and the
vector of weights associated with these attributes. Let be
the contribution of attribute of
dimension l to the computer solution under
the state of the nature .
Then the payoff of
the computer solution under
the state of the nature may
be computed according to the following formula: .
By another
way, the use of this framework in practice may be hard since
option-pricing models theoretical basics and assumptions are often not
well-known to IS decision-makers. Nevertheless, as stressed by (Benaroch
et al. 1999), the difficulties encountered while using option-pricing
models don’t result in greater challenges than when NPV-based
traditional techniques are used.
Since
software informative prototyping is usually undertaken within a software
project, the framework proposed in this paper should be generalized at
three levels. On the one hand, decision to invest in informative
prototyping and decision to invest in development of software systems
are linked and analogous to American call options. Analyzing these
decisions as nested call options seems to be an appropriate way to
complete the proposed framework. On the other hand, impacts of
informative prototyping on the probabilities of events are taken into
account only in an implicit way by our approach. So, an explicit formal
expression of the probability distributions seems to be necessary.
Finally, information provided by software informative prototyping may
result in more complex and costly software systems. Evaluation of
complexity resulting from software informative prototyping should
improve the decision-making process based upon the framework proposed in
this paper.
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