Introduction to operations research

1     Objectives

·        To be able to

·        define operations research, describe the historical - development of O.R.,

·        explain the services offered by an operations researcher, and

·        describe the major steps involved in solving an O.R. problem.

2     The Problem of Defining O.R.

Most definitions emphasise the use of techniques of several disciplines (statistics, accounting, computer science, etc.) to assist management in improving its decision making .  For example:

By the term decision making we mean selecting from a set of alternatives - it is making a choice.  The decision making process (or problem solving) refers to the entire sequence of steps from identifying a problem through to its solution.

2.1     The History of OR

As technology has developed, industrial organisations have become more complex.  The owner/manager has been replaced by specialised components in an organisation - production, finance, personnel, marketing, research and development.

Early assistance in the production area was provided by Frederick W. Taylor[4], Frank and Lillian Gilbreth[5] and Gantt[6] in the field of industrial engineering with time and motion studies, work simplification and plant layout.  Henri Fayol[7] attempted to extend the management principles to administration without success.  The time was not ripe for such a concept.

The period of World War II saw the military management in the United Kingdom call on a team of scientists (under the management of Professor P.M.S. Blackett in 1939) to study strategic and tactical problems associated with air and land defence.  The name operations research was apparently coined because the team was dealing with research into military operations.  In the United States similar groups were formed in 1942 by the military management with applications to logistic problems, flight pattern determination, sea mining planning and effective utilisation of electronics equipment.

Following the war, industrial managers turned to O.R. to aid in coordinating the individual goals of the specialised activities of the organisations which were sometimes not consistent with the overall goals. Clearly this was stimulated by the availability of digital computers.  In 1950, O.R. became a recognised profession with the founding of the Operations Research Society of Great Britain.  In 1953, the Operations Research Society of America was formed and within a year a similar group, The Institute of Management Science was founded.  In Australia, there is an active group - The Australian Society of Operations Research (ASOR) - with Chapter organisations in most capital cities and a number of regional centres.

In the early 1960's universities commenced programmes in O.R. and new O.R. publications developed.  O.R. had become a recognised academic pursuit. Computer power and availability increased, enabling analysts of O.R. to find employment almost everywhere in industry and more recently in the study of non-industrial social systems, for example, fire control, hospital organisation, community planning, pollution control and police work.

2.2     Operational Research Methodology

The scientific method has evolved out of the practical experience of many scientists - astronomers, chemists, physicists, biologists etc.  Sir Francis Bacon has generally been credited with being the first to formally describe the method nearly four hundred years ago.  The steps an O.R. analyst takes, once the existence of a problem is suspected, are detailed below.

2.2.1     Formulate the problem

This means identifying the components of the decision problem.  First, who has the authority and/or major responsibility for control of the system (and who in fact is controlling the system)?  It may require a thorough systems analysis at this stage to identify the decision-makers and their inter-relationships.

Second, identify the available actions and consequent outcomes and establish the decision-makers' preferences for the outcomes.  Identify the sources of uncertainty which make it clear how the preferred outcome can be directly achieved.  Sources of data and information that might be used to reduce or eliminate the uncertainties are sought at this stage.

2.2.2     Construct a model

A model is simply a representation of the system.  Models are of three general kinds:

·      Iconic -  physical one-to-one representations, for example, maps or scale models;

·      Analogue - representation of one physical system by another, for example, electronic circuitry to represent an hydraulic system; and

·      Symbolic - mathematical, for instance, representation of a system by a set of equations.

It is the third model which is most frequently used in operations research, and it is usually prescriptive in that it contains:

(i)                  the outcomes, or more generally, the probability of each outcome as a function of the available actions;

(ii)                a function of the outcomes which measures the preference for the outcomes; and

(iii)               the criterion of choice to be used in selecting the best action.

A model containing only (i) is a descriptive model only.  With (ii) and (iii) the researcher may proceed to:

2.2.3     Solve the model

This is the mathematical solution.  Sometimes existing mathematical techniques are inadequate so that a `deterministic' solution cannot be obtained and the analyst must obtain an approximate solution either by heuristic or simulation methods.

·      Heuristic methods commence with an initial solution to the model and utilise rules to successively improve the solution.

·      Simulation models imitate the behaviour of the model over a period of time and measurements are made on the simulated system.

Solution of the model is not the final step because the operations researcher must assess the reliability of the model.

2.2.4     Validate the model

Does the model adequately predict the behaviour of the system that it is supposed to represent?  It may not be possible to test validity for a new system except through the construction of a simulation model, but validation may use past data or require the collection of new data.

2.2.5     Establish controls over the solution

The model is based on a number of assumptions and estimates.  If these cease to hold, then the solution may not be the best solution.  Sensitivity Analysis determines how sensitive the optimal solution is to certain parameters in the model.  We must set up a system for detecting changes before we:

2.2.6     Implement the solution

The mathematical solution must be translated into directives for action and communicated adequately to operating personnel.  This will be more effective if the operators have been involved in the development of the plan from the first stage.  Cases have been reported where a great deal of otherwise good work by an O.R. team was sabotaged by the people affected by a changed system they did not understand and hence did not want.

2.3     Use of Quantitative Methods in Organisations

 

Frequency of Use - percent

Method

Not at all

Sometimes

Often

Economic Analysis

 3

25

72

Statistical Analysis

 6

27

67

Simulation

15

35

50

Linear Programming

27

50

23

Inventory Control Theory

34

45

21

PERT/CPM

41

38

21

Mathematical Programming

55

34

11

Search Techniques

60

35

 5

Queueing Theory

63

31

 6

Game Theory

84

14

 2

 

A 1977 survey of non-academic members of the Operations Research Society of America (ORSA) and The Institute of Management Science (TIMS) found that many methods were very frequently used.  (See Table 1.)  Another question explored the results obtained from using the techniques.  (See Table 2.)  Not surprisingly the methods which consistently produced the most favourable results were also the ones which are most frequently used.

Table 1: How frequently Quantitative Methods are used.

Table 2: User Satisfaction with Quantitative Methods.

 

Percent of users who evaluate methods as

Method

Poor

Fair

Good

Uncertain

Economic Analysis

1

20

78

1

Statistical Analysis

1

17

80

2

Simulation

3

20

73

4

Linear Programming

14

28

49

9

Inventory Control Theory

9

36

51

4

PERT/CPM

10

40

47

3

Mathematical Programming

7

33

56

5

Search Techniques

6

33

56

5

Queueing Theory

7

24

60

9

Game Theory

21

31

26

22

Source:  Gallagher, C.  A., and Watson, H.  J., Quantitative Methods for Business Decisions, (McGraw-Hill, 1985).  Survey carried out by H. J. Watson and J. M.  Baecher.

It’s about time that this research was updated.  Anyone game enough!


[1]  Saaty, T.L., (1959), Mathematical Methods of Operations Research, McGraw-Hill.

[2] Wagner, H.M., (1975), Principles of Operations Research, 2nd ed., Prentice-Hall.

[3] Ackoff, R.L. & Sasieni, . (1968), Fundamentals of Operations Research, Wiley.

[4] Taylor, F.W., (1911), The Principles of Scientific Management, Harper, New York,  reprinted by Norton (1967) (RMIT/CTRL 658 T241)

[5] Gilbreth F. & Gilbreth, L., publications from 1980-1917 reprinted in The Writing of the Gilbreths, ed. W.R. Spiegel & C.E. Myers, (1953), R.D. Irwin, Homewood Ill.                                                                                                                       (RMIT/CTRL 658.5 G466)

[6] Gantt, H.L. various works circa 1916 reprinted in Gantt o Management: Guide for Today’s Executive, 1961, New York American Management Association                                                                                                                  (RMIT/CTRL 658 G211)

[7] Fayol, H., (1930), Industrial and General Administration, Pitman, London reprinted by the New York Institute of Electrical and Electronics Engineers, C1984,                                                                                                                                    RMIT/CTRL 658 F285