stages in problem solving

1. Stages in problem solving
in Quantitative Techniques
and Business Management
by Dr.Ammara Omer Khakwani

2. Any reasoning that uses
numbers is quantitative.
Any reasoning that does not use
numbers, but is based on
judgment and opinions, is
qualitative.

3. Stages in problem solving
Models form a key part of the broader decision-making process. (see Figure 1.2).
1) Identify a problem. Describe the details of the problem and its context. At the
end of this stage, managers should have a clear understanding of the problem
they are tackling and the requirements of their solution.
This might include:
(a) Initial investigation – to look at operations, identify difficulties and
recognize that there is a problem.
(b) Defining the problem – to add details to the initial investigation, saying
exactly what the problem is (and not just its symptoms), its context,
scope, boundaries and any other relevant details.
(c) Setting objectives – to identify the decision makers, their aims,
improvement they want, effects on the organization, and measures
OF success.
(d) Identifying variables, possible alternatives and courses of action.
(e) Planning the work – showing how to tackle the problem, schedule
activities,design timetables and check resources.

4. 2)Analyse the problem. At the end of this stage, managers should have a clear
understanding of their options and the consequences. For this they might:
(a) Consider different approaches to solving the problem.
(b) Check work done on similar problems and see if they can use the same
approach.
(c) Study the problem more closely and refine the details.
(d) Identify the key variables and relationships between them.
(e) Build a model of the problem and test its accuracy.
(f ) Collect data needed by the model and analyse it.
(g) Run more tests on the model and data to make sure that they are working
properly, are accurate and describe the real conditions.
(h) Experiment with the model to find results in different circumstances
and under different conditions.
(i) Analyse the results, making sure that they are accurate and consistent.

5. 3) Make decisions. This is where managers
consider the results from analyses, review all
the circumstances and make their decisions.
This has three steps to:
(a) Compare solutions, looking at all aspects of
their performance.
(b) Find solutions that best meet the decision
makers’ objectives.
(c) Identify and agree the best overall solution.

6. 4) Implement the decisions.
At this point managers turn ideas into practice, moving from ‘we
should do this’ to actually doing it. For this they:
(a) Check that the proposed solution really works and is an
improvement.
(b) Plan details of the implementation.
(c) Change operations to introduce new ways of doing things.

7. The main features of a model are as follows:
1. It is a representation of reality.
2. It is simplified, with only relevant details
included.
3. Properties in reality are represented by other
properties in the model.

8. WORKED EXAMPLE 1.1
An automatic ticket machine only accepts pound
coins. The numbers of tickets it gives are:
£1 – 1 ticket, £2 – 3 tickets, £3 – 4 tickets,
£4 – 5 tickets, £5 – 7 tickets
How can you get the cheapest tickets?
Solution
You can do a simple calculation to find the best
value for money. You know that:
o £1 gives 1 ticket, so each ticket costs £1/1 = £1
o £2 gives 3 tickets, so each ticket costs £2/3 = £0.67
o £3 gives 4 tickets, so each ticket costs £3/4 = £0.75
o £4 gives 5 tickets, so each ticket costs £4/5 = £0.80
o £5 gives 7 tickets, so each ticket costs £5/7 = £0.71
Buying three tickets for £2 clearly gives the lowest
cost per ticket.

9. WORKED EXAMPLE 1.2
The policy of Benchmark Global Consultants is to employ one consultant for
every 10 clients on their books. Last month they had 125 clients. How many
consultants should they employ?
Solution
A purely quantitative analysis suggests employing 125/10 = 12.5
consultants. They could employ part time staff, but this may not be
feasible, particularly if the number of clients keeps changing.
Realistically the company could round the number of consultants
to either 12 or 13. The best decision depends on a range of
qualitative factors – such as expected changes to client numbers,
amount of work sent by each client, attitudes of consultants, type
of business, planned staff departures, recruitment, training,
seasonal trends, and so on. Managers must review all the available
information– both quantitative and qualitative – before making
their decision.

10. CASE STUDY
Patrick Chua is the senior vice-president of RPF Global, a firm of financial
consultants with offices in major cities around the Pacific Rim. He outlines
his use of quantitative ideas as follows. ‘Most of my work is communicating
with managers in companies and government offices. I am certainly not a
mathematician, and am often confused by figures – but I use quantitative
ideas all the time. When I talk to a board of directors, they won’t be
impressed if I say, “This project is quite good; if all goes well you should
make a profit at some point in the future.” They want me to spell things out
clearly and say, “You can expect a 20% return over the next two years.” My
clients look for a competitive advantage in a fast-moving world. They make
difficult decisions. Quantitative methods help us make better decisions – and
they help explain and communicate these decisions. Quantitative methods
allow us to:
look logically and objectively at a problem;
measure key variables and the results in calculations;
analyze a problem and look for practical

11. solutions;
• compare alternative solutions and identify the best;
• compare performance across different operations,
• companies and times;
• explain the options and alternatives;
• support or defend a particular decision;
• overcome subjective and biased opinions.
Quantitative methods are an essential part of any business.
Without them, we just could not survive!’
Source: Chua P., personal correspondence, 2006; Chua P., talk
to Eastern Business Forum, Hong Kong, 2005.

12. Then a symbolic model for the amount of value added tax payable is:
VAT = rate × sales
where the symbol ‘VAT’ in the model represents the amount of tax paid in reality, and the
symbols ‘rate’ and ‘sales’ represent the actual rate of VAT and value of sales. If a
company sells a product for £300 a unit, a model of its income is:
income = number of units sold × selling price = number of units sold × 300
We can extend the model by finding the profit when it costs £200 to make each unit:
profit = number of units sold × (selling price − cost)
or
profit = number of units sold × (300 − 200) = number of units sold × 100
This equation is our model.

13. BG Group (BGG) is an international energy group with a turnover of around $6
billion a year. Its main business is the supply of natural gas. This is a ‘clean’ fuel,
and because the worldwide demand for energy is growing, sales are expected to rise
significantly over the next 10 years. To meet this demand BGG has to continually
find and develop new reserves. National governments generally regard gas fields as
a vital strategic resource, so they keep tight control over them. To develop a field,
governments divide it into blocks and invite energy companies to bid for exploration
rights. BGG, along with every other energy company, has to decide whether to bid
for exploration rights in available blocks, and how much to bid. These are
important decisions that are characterised by high costs (typically hundreds of
millions of dollars), long lead times (typically five years before a project starts
earning money), limited lifetime (as there is a finite amount of gas available) and
complex tax and contractual arrangements. BGG considers many factors in each
decision. Firstly, there are qualitative factors, particularly BGG’s rigorous ethical
guidelines and business principles. These are important in showing how

14. Example:_
BG Group does business and what it stands for – and how it deals with issues
such as gas finds in sensitive environments, conflict zones, or areas where
indigenous peoples are contesting land rights. Other qualitative questions concern
the availability of alternative projects, structure of the company’s long-term
portfolio of fields, partnerships, effect on share value, and so on. Secondly, there
are quantitative factors. These focus on two issues:
1) Risks – where geologists look at the chances of finding gas and the likely size
of discoveries, engineers look at potential difficulties with production, health
and safety look at safety and environmental risks, and economists look at
likely demand, prices and commercial risks.
2) Return from the project, starting with the basic
formula:
net cash flow = revenue − costs − taxes
Managers review the results from both qualitative and quantitative analyses
before making any decision.
Sources: BG Annual Reports and websites www.bg-group.com and
www.thetimes100.co.uk.

15. Exercise
Q.1.1What are the benefits of quantitative methods?
Q.1.2 Do quantitative analyses make the best decisions?
Q.1.3 Managers must be good mathematicians. Do you think this is
true?
Q.1.4 Why has the use of quantitative methods by managers
increased in the past 20 years?

16. 1.5) Why do managers use models?
1.6 )What are the stages in solving a problem?
1.7 )Where do quantitative models fit into this approach?
1.8) Is there only one correct way to tackle a problem?

17. Answers of Questions
1.1_ They allow clear, precise and objective measures of features, calculations using
these, and rational analysis of problems.
1.2_ No – managers make decisions.
1.3_ No – but they must be aware of the types of analysis available,understand the
underlying principles, recognise the assumptions and limitations, do some analyses
themselves, have intelligent discussions with experts, and interpret the results.
1.4 _There are several reasons for this, including availability of computers, improving
software, fiercer competition forcing better decisions, new quantitative methods,
good experiences with earlier analyses, better education of managers, and so on.
1.5 To develop solutions for problems, allow experimentation without risk to actual
operations, allow experiments that would not be possible in reality, check the
consequences of decisions, see how sensitive operations are to change, and so on.
1.6 We describe four stages: identifying a problem, analysing it, making decisions and
implementing the results.
1.7 Generally in the analysis stage.

18. 1.8 No – we can use any approach that efficiently gets a good answer.
1.9 No – you can get a feel for the numbers without doing the detailed calculations.
1.10 Because they are widely available, they use standard formats that are familiar
and easy to use, and you do not have to learn how to use a new program for each
problem.