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PROBLEM FORMULATION 541

analyze more complex problems and to identify an optimal sequence of decisions,
referred to as an optimal decision strategy. Sensitivity analysis shows how changes in
various aspects of the problem affect the recommended decision alternative.

13.1 Problem Formulation

The first step in the decision analysis process is problem formulation. We begin with
a verbal statement of the problem. We then identify the decision alternatives, the
uncertain future events, referred to as chance events and the consequences associ-
ated with each decision alternative and each chance event outcome. Let us begin by
considering a construction project of the Planning and Development Council (PDC)
in Oman.
The PDC is a government agency tasked with supporting the development of the
Oman economy. One of PDC’s key strategies is to support the diversification of the
economy away from a reliance on oil. One of the initiatives under consideration is
the construction of a new business complex. The complex will be located near the
international airport and will consist of a number of purpose-built business units.
Each unit will be equipped to the highest standards in terms of facilities, telecoms,
parking, etc. It is expected that local businesses wishing to expand will be attracted
to the complex as will overseas companies who wish to establish a base in Oman.
The business units will be available on a first-come-first-served basis either on a
long-term lease arrangement or for outright purchase.
Whilst the main purpose of the new complex is to attract new businesses, PDC is
also expected to maximize the financial return on the project (through the income
generated from leases or from sales). However, PDC is facing some uncertainty
particularly in relation to the expected demand for units in the complex. When
asked about the possible demand for the units, PDC’s president acknowledged a
wide range of possibilities, but decided that it would be adequate to consider two
possible chance event outcomes: a strong demand and a weak demand.
In decision analysis, the possible outcomes for a chance event are referred to as
the states of nature. The states of nature are defined so that one and only one of the
possible states of nature will occur. For the PDC problem, the chance event con-
cerning the demand for the units has two states of nature:
s 1 ¼ strong demand for the units
s 2 ¼ weak demand for the units
As a result of this uncertainty, PDC has commissioned three alternative plans for the
complex:
d 1 ¼ to build a small complex of 30 business units
d 2 ¼ to build a medium-sized complex of 60 units
d 3 ¼ to build a large complex of 90 units
These are the decision alternatives for PDC and the situation facing PDC is typical.
It must first choose between these decision alternatives (size of the complex), then it
must wait to see which state of nature occurs (demand for the units) and then it will
see the consequence occurring (the financial return made from the decision given
the state of nature).

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