Quantitative methods in marketing 239
scheduling and controlling in all functions of
management. For a number of reasons, this
technique is particularly applicable for use in
marketing management. First, marketing man-
agement, by definition, involves the co-ordina-
tion of many other functions and activities:
advertising; distribution; selling; market
research; product research and development.
Second, much of the work in marketing can be
of a project nature (for example, new product
launch, organization of a sales promotion,
setting up of a new distribution system).
CPA is based on the assumption that some
of the activities of a marketing project are in a
concurrent relationship and take place simulta-
neously. The advantages to be gained from CPA
in marketing are similar to those obtained in
other functions, except that the centrality of the
marketing function, particularly in some con-
sumer goods firms, increases its desirability.
There are a large number of possible
applications of PERT and CPM: for new
product launch (Robertson, 1970); distribution;
planning (LaLonde and Headon, 1973); sales
negotiations; and purchasing (Bird et al., 1973);
launching a marketing company/project/
department; sales promotions; conference
organization; advertising campaigns; new store
openings; realigning sales territories, etc.
Budnicket al. (1977) proposed using net-
work planning for product development, while
others suggest the use of the CPM to co-ordinate
and plan the hundreds of activities which must
be carried out prior to commercialization of a
new product. Johansson and Redinger (1979)
used path analysis to formulate an advertising–
sales relationship of a hairspray product.
Chaos theory
Chaos theory has the potential to contribute
valuable insights into the nature of complex
systems in the business world. As is often the
case with the introduction of a new manage-
ment metaphor, ‘chaos’ is now being ‘dis-
covered’ at all levels of managerial activity
(Stacey, 1993).
What is chaos theory?
Chaos theory can be compactly defined as ‘the
qualitative study of unstable aperiodic behav-
iour in deterministic non-linear dynamical sys-
tems’ (Kellert, 1993, p. 2). A researcher can often
define a system of interest by representing its
important variables and their interrelationships
by a set of equations. A system (or, more
technically, its equations) is dynamical when
the equations are capable of describing changes
in the values of system variables from one point
in time to another. Non-linear terms involve
complicated functions of the system variables
such as: yt+ 1 = xtyt.
Chaos theorists have discovered that even
simple non-linear sets of equations can produce
complex aperiodic behaviour. The most famil-
iar example is the logistic equation of the form:
xt+1=rxt(1 –xt), where xlies between 0 and 1.
This system is deterministic in the sense that no
stochastic or chance elements are involved.
Figure 9.8 depicts the behaviour of this system
for varying levels of r.
At values of r< 2, iterating over the logistic
equation will result in the system stabilizing at
x= 0 (Figure 9.8a). Between r= 2 and r= 3, the
system reaches equilibrium at progressively
higher values of x(Figure 9.8b). At around r= 3,
the system is seen to bifurcate into two values.
The steady-state value of xalternates period-
ically between two values (Figure 9.8c). As r
continues to increase, it continues to increase in
periodicity, alternating between 2, then 4, 8 and
16 points. When ris approximately 3.7, another
qualitative change occurs – the system becomes
chaotic. The output ranges over a seemingly
infinite (non-repeating) range of xvalues (Fig-
ure 9.8d).
Chaotic systems are also unstable, exhibit-
ing a sensitive dependence on initial
conditions.
The Lyapunov exponent is a mathemat-
ically precise measure of the degree of sensitive
dependence on initial conditions. The Lyapu-
nov exponent takes the one-dimensional form
e^ t. If < 0, then the initial differences will