A basic training in Operations Research offers diverse and varied career opportunities providing an ideal route for students with a mathematical or scientific background to enter a career in business. Much Operations Research work is done under a variety of different names; for example, members of ASOR, including recent graduates are able to apply their OR training in one or more of the following areas:
Graduates generally obtain rewarding and challenging jobs.
PROFILE OF AN OPERATIONS RESEARCH ANALYST
The OR analyst applies scientific method to problems concerning the management of systems of people, machines, materials and money in industry, business government and defence. He or she conducts logical analysis of management problems in collaboration with management with a view to understanding the system behind that problem, so that the system may be made to work in a manner which eliminates the problem.
The analyst will strive to define the objectives and constraints of the system in quantitative terms and will generally develop a mathematical model which includes chance and risk factors. The analyst often operates as an agent of change within the system and must therefore develop interpersonal skills and be able to work with management as part of an interdisciplinary team.
Standard OR techniques such as Linear Programming, Critical Path Analysis, Simulation, Statistical Decision Theory, Queueing Theory and Inventory Control Theory may be used. Specialist work may be in the production, marketing or financial planning areas.
OR work can be with any one of a large number of industries, including oil, chemicals, steel, manufacturing, the railways, electricity generation, agriculture, the airlines, banking, insurance and many other fields including defence, medical and welfare services.
DOES OR HOLD A FUTURE FOR YOU?
If you do decide to follow a career in Operations Research your future is very much in your own hands. Initiative, flair and creativity are just as necessary as integrity, ability and hard work. It is a profession which is rapidly developing.
Most OR projects are handled by small project teams and in your early years you might be a junior member of such a team. However, it would be unusual if during this period, you did not also have some projects of your own. Many young graduates become project leaders within two years. It is really up to you. Quite often you may be working on several projects at the same time, in a different project team in each case.
The ideal OR analyst needs to be able to identify the right problem to solve, collect the relevant data, construct a model of the system often using a computer, and seek a solution that people in the real world can live with. Finally they may need to "sell" their solution to management.
Generally, you would be able to move around as many different organisations employ OR personnel. It is not unusual for OR graduates to gain experience in other countries and they are frequently required to travel within large firms or government departments. This is certainly true if you join a consulting firm.
WHAT IS OPERATIONS RESEARCH
Operations Research is concerned with analysing complex problems and helping decision makers work out the best means of achieving some objective or objectives.
Thus Operations Research requires an enquiring mind capable of asking probing questions to help clarify the decision makers objective. Within a business organisation the primary objective will often be either:
- Maximising profits, or
- Minimising costs
This may seem simple, but to come up with a good solution to a problem it it necessary to identify ail of the factors which contribute to costs or profit and that is not so easy. In many situations, more than one objective is set, and these will typically be in conflict.
Further, Operations Research is not only used in business: in other applications the real challenge of the work is often concerned with quantifying objectives which cannot be expressed in financial terms.
Any proposed solution to a problem must be practicable and take account of any constraints which limit the range of possible actions. Thus a systematic approach is needed to identify all aspects of a problem and analytical ability to work out how the different parts of the problem situation are related to each other. Finally, the analysis must take account of risk and uncertainty.
HOW OPERATIONS RESEARCH IS CARRIED OUT
Most OR starts with a problem, which does not necessarily mean something has gone wrong or is about to go wrong. It could just be that a decision has to be made or that the person or group responsible for some activity believes it could be carried out better: that there is scope for improvement. From that start, there are a number of more or less standard steps to the conduct of the investigation.
Obtain as complete a picture as possible of the situation being investigated and identify how all the people involved see the problem or decision. Then identify alternative courses of action which are available to solve the problem or improve the operation. Not infrequently, the problem definition will lead to a quite different view of a problem or of the scope of a decision from that originally reported.
Specification of Objectives
Develop a clear statement of the goal or purpose of the organisation or activity being studies. This is a crucial step, and never easy. Do not assume that there will always be one person who will immediately give you a clear, unambiguous statement of a single objective. Part of the problem will usually be that different people are responsible for different aspects of an activity, and that each sees the objectives in a different light. So, the OR analyst will need to talk to all the people concerned and collect all their views on the goals and objectives of the activity, identifying any conflicts between different objectives and then trying to find some means of resolving these conflicts and constructing an overall measure of performance. Sometimes, on reflection, the overall objective can be specified as the best compromise; in other cases it is not so easy to see how to balance one objective against another.
Identification of Constraints
Find the features of a problem or activity which limit the range of possible options, or alternative courses of action. We have already mentioned budgetary constraints - limitations on the amount of money available to spend on an activity. With manufacturing problems, there will usually be constraints associated with plant capacity and quality requirements. Sometimes, when there is more than one objective, some of the objectives can be converted into constraints by specifying minimum acceptable levels of performance. Sometimes, the constraints are found not to be as absolute as was believed, then the OR specialist can contribute by demonstrating how to relieve such limitations.
Once all of the characteristics of the problem have been identified, the next difficult task is to accurately quantify all items. The search for complete, correct data is a difficult, but an essential task if a valid result is to follow.
Before a model can be used as a decision tool it must be validated. This is usually carried out by demonstrating that the model can accurately represent the known prior behaviour of the system.
Evaluating The Alternatives
Find how the alternatives measure up against the objectives. If there is a single easily measurable objective such as cost or profit and a finite list of alternatives this can be straight-forward. However, objectives like human well-being are not so easy to quantify, so such cases can require a lot of careful thought and judgement.
Selecting The Best Solution
Choosing the alternative which measures up best against the objectives. If the analysis comes up with a single overall objective which is acceptable to all people concerned the choice many follow simply from the previous step. However, if there are several objectives which are difficult to combine into a single overall objective, then the analyst can produce a short list of good alternatives which look good against one of the objectives and not too bad against the others. Thus often the solution will involve compromise amongst conflicting or competing objectives.
Getting the people responsible for the problem or activity to act on the recommended solution, or - if there is not a single recommended solution - to use the results of your analysis to make a well informed decision. Indeed, being able to favourably influence the framework of decisions is often of greater long term value than getting a particular recommendation accepted.
While it is always nice to find that a proposed "solution" to a problem works in practice, it does not always work out that way. OR work cannot truly be said to be complete until it has been demonstrated that the implementation achieved a satisfactory improvement in performance.
OPERATIONS RESEARCH AND MATHEMATICS
Much Operations Research makes use of mathematical concepts, but from what you have already read in this booklet it will be clear that Operations Research is more than just mathematics. Sometimes the mathematics is just addition, subtraction and multiplication, while other projects use more advanced mathematics and a computer is required for the computations. However, even when a computer is used, the basic mathematical concepts are often quite straight-forward, but would take far too long if done by hand.
Similar mathematical methods can be used for many problems with a common mathematical structure and this has led to the development of some standard OR TECHNIQUES.
The inter-related activities in a complex situation (say, a construction project) are represented by arrows on a diagram. The diagram shows the logical relationships between activities, and, once it has been drawn it is fairly simple to determine the "critical path': that sequence of activities which determines the total duration of the project.
One of the earliest developed and most widely used OR techniques. One of the main applications is in planning manufacturing activities. The elements of a linear programming problem are:
- Quantity of each product to produce
- Quantity each raw material to buy
- Market demand for the products, plant
- Capacity and product quality
- Objective function:
- A mathematical formula which expresses the objective say profit, as a function of all the variables.
The technique is called linear programming because it can only be applied if the objective function is a linear function and the constraints are linear equations or inequalities.
Stock Control Theory
Another standard OR application, which includes a mathematical method for finding the best compromise between the periodic cost of ordering or producing an item and the cost of carrying stock. The natural preference of a production manager may be to choose long production runs so as to spread set-up costs over a larger number of units, while an accountant may want to have short production runs so as to minimise the costs of holding stock. Stock control theory provides a method of selecting a quantity which minimises the sum of these two costs, and the formula can be developed using fairly simple calculus.
Is not so much an OR technique as an aspect of mathematics which forms an essential part of the background training of an O. R. analyst. There is a lot of uncertainty associated with most real life problems, so the OR analyst needs some knowledge of statistics to be able to handle that uncertainty in a rational manner. However, what is often needed is not so much a knowledge of specific statistical techniques as a general ability to think in statistical terms.
The mathematical basis of all of the above techniques can be understood by someone with a good grounding in High School mathematics. However, real problems tend to be bigger, messier and more complex than text book problems and therefore an operations research analyst needs to:
- exercise judgement and creativity in adapting standard techniques to accommodate all aspects of a real problem.
- use a computer to handle the sheer volume of often repetitive calculation.
- have qualities of perseverance and patience to see a big project, through to successful completion.
The available techniques, of which the above are a few examples, is constantly growing. Thus this is an active, evolving field of study offering opportunities for the enterprising person.
THE HUMAN SIDE OF OPERATIONS RESEARCH
Having explained something of the connection between Operations Research and Mathematics, it is important to emphasise the human side of Operations Research. As mentioned in the general description a very important part of OR is concerned with talking to people about a problem; getting them to describe the objectives and constraints. This requires a lot of personal skills:-
- ESTABLISHING THE RIGHT SORT OF FRIENDLY BUT BUSINESS LIKE ATMOSPHERE IN WHICH TO CONDUCT YOUR DISCUSSIONS.
- COMMUNICATING CLEARLY THE PURPOSE OF YOUR INVESTIGATION.
- LISTENING CAREFULLY AND ATTENTIVELY, SO THAT YOU PICK UP THE CORRECT EMPHASIS OF WHAT THE OTHER PERSON IS SAYING AND THINGS WHICH ARE IMPLIED BUT NOT SAID DIRECTLY.
- JUDGEMENT IN BEING ABLE TO ESTABLISH THE TRUTH WHEN YOU GET CONFLICTING ACCOUNTS OF THE SAME "FACTS" FROM DIFFERENT PEOPLE, THUS AVOIDING JUMPING TO PREMATURE OR ONE-SIDED CONCLUSIONS.
- WILLINGNESS TO LEARN THE TECHNICALITIES OF FIELDS ENTIRELY NEW TO YOU, SO THAT YOU CAN UNDERSTAND WHAT IS REALLY HAPPENING.
- ABILITY TO ACCEPT AND DEAL WITH INPUTS THAT ARE VAGUE, UNCERTAIN OR UNQUANTIFIABLE.
- SENSITIVITY TO THE FEELINGS OF PEOPLE WHO MAY BE RESISTANT TO OR FEEL THREATENED BY YOUR INVESTIGATION OR RECOMMENDATIONS.
- HELPING TO BUILD CONSENSUS AMONG A DIVERSE GROUP OF PEOPLE AS THE BASIS FOR EFFECTIVEIMPLEMENTATION.
Integer Programming At School
Every school is run on a master time-table. The pupils see only parts that affect them - the times, subjects and teachers and rooms. The teachers see a different time-table, with classes, subjects and rooms. Consider a school of say 1 000 pupils in about 40 classes ranging from year 7 to year 12, with about 80 staff and nearly sixty rooms counting special laboratories etc. Then think how you would allocate teachers and classes to rooms to maintain adequate supervision of all classes, to avoid clashes over rooms, to observe the working conditions for teaching staff, but primarily to provide a properly balanced teaching programme.
If this objective of a "balanced teaching programme" can be specified in the appropriate quantitative terms the problem can be represented as a linear programme with all of the requirements of avoiding clashes over rooms and so on as constraints. However, it is a special type of linear programme, an Integer Programme with variables required to be integers: a classroom at a given time has to be allocated to one class or another; it can not be allocated half to one class and half to another.
Linear Programming For Refinery Planning
Shell Australia operates two refineries, one at Geelong and the other at Clyde in the Sydney metropolitan area. The major inputs to these refineries are (-rude oil from Bass Strait and crude oil imported from Indonesia and the Middle East. The crude oil goes through a number of processes such as fractional distillation, which separates out the light components from the thicker heavier oils; cracking, which breaks down the heavy constituents of the crude oil into lighter components'. reforming which changes the chemical structure of other components in order to meet product specifications; and desulphurising which removes sulphur from the product in order to meet environmental and quality requirements. That list is far from complete, so it will be evident that an oil refinery is a very complex affair which can be operated with considerable variation mix of crude oil inputs. However, the job of the refinery economist is to work out the best way to run the refinery to decide how much of each crude to run through the distiller at each refinery: how much of the heavier fractions to run through the cracker, and so on, in order to find the most profitable way of meeting the expected market demand for:
- kerosine (for jet aircraft)
- fuel oil (for industry)
- lubricating oil and other products.
Up to about 25 years ago all of this had to be planned on the basis of experience and trial and error calculations, but now Shell (and other major oil companies) use linear programming to solve this problem. This is possible because profit can be expressed as a linear objective function and linear equations or inequalities can be used to represent all of the constraints concerning:-
- the available quantities of different crude oils
- quality requirements for each product
- market demand for each product
- Two of the biggest advantages of using LP are:-
- When circumstances change significantly it is possible to produce a revised refinery plan much faster than previously.
- The linear programme can be used to investigate the impact of anticipated future changes and to check that a proposed expansion of one part of a refinery gives a suitable overall improvement.
Production Scheduling In A Shoe Factory
When shoes are made in a factory the manufacture of each type and size of shoe requires the use of a number of machines. The different types of shoes are made in batches of several hundred and each type of machine has to be adjusted or "set up" for each batch of shoes. At any given time there will be a number of types and sizes which need to be made in the immediate future and a decision has to be made as to the sequence in which the different batches pass from machine to machine. Any sequence chosen is likely to mean that for some of the available time some of the machines and operators will be idle. Hence, it is desirable to choose a sequence which minimises this idle time.
The problem was tackled for a Victorian shoe manufacturer by two students as a project which formed part of the final year OR course at an Institute of Technology.
The problem they studied is illustrated by the following example:-
Consider eight batches of shoes of types A, B, C, D, E, F, G and H which must pass through four sections during manufacturing with the following times required (in minutes) for 600 shoes of each type in each section,
Section A B C D E F G H Buffing Department 32 66 40 67 44 75 97 54 Sewing Department 13 8 78 220 49 99 65 94 Trachong Section 107 144 28 197 80 80 80 119
For this example, the sequence A B E C H F D G gives the best sequence being 241 mins quicker than the sequence B G H D C E A F.
A number of mathematical procedures (or algorithms) have been developed for choosing "good" sequences for the above type of problem. Such methods need to be flexible so as to take account of complications such as rush orders from the sales department. Accordingly, algorithms with weighting factors to help force some batches through early in the sequence have been developed.
Referring to the example again, a further complication is that each batch (eg. 600 shoes of type A) can be divided into several sub-batches.
eg, A1: 400 shoes of type A; A2: 200 shoes of type A
However, the reduction in idle time from splitting up batches must be balanced against the extra time spent re-adjusting machines between the increased number of batches.
No-one has yet developed a method to give the best solution in every case. However, common sense algorithms have been developed which tend to give "good" solutions most of the time.
Forecasting And Control In Insurance
National Mutual reviewed its rule for the calculation of asset book values. Put simply the book value of an asset is the value shown in the official records of the company. The problem in determining book value arises from the fact that over a period of time the market value of an asset (what it could actually be sold for) will differ from the purchase price. Accordingly, the company wants to revise the book value of an asset so as to keep it in line with movements in market value. However, any revision must allow for future variations in market value and take account of the possibility of downward movements. For instance, if a building has an abnormally high market value at the moment but may not be sold for another fifteen years, then it should not receive a huge immediate boost in book value. The book value can be viewed as representing the underlying trend in the market value.
Setting an accurate book value is particularly critical in Life Insurance because of the need to balance current income against the uncertain liability for future claims. Too high a book may mean the granting of excessive bonuses, depleting reserves to a level where claims cannot be met. Too low a book value could mean disadvantaging present policy holders and being uncompetitive.
Against the above background, the OR problem set by National Mutual's Management was to devise a rule for calculating book value subject to the following constraints:-
- Book value must not exceed market value less the expense of selling
- Book value should not have to decrease
- It is desirable for book value not to fall below 85% of market value
- For assets with a stable market value pattern, book value should be as close to market value as 'safely' possible where safety is measured in terms of 1. and 2.
- It is desirable that the release of profit (ie, annual change in book value) should be fairly constant when adjusted for inflation.
The starting point of the OR analysis was a recognition that the problem was connected with the forecasting of future movements in market value. However, while book value must follow the trend in market value it had to be held sufficiently below the trend in market value to satisfy condition 2. A mathematical technique known as exponential smoothing has these properties and was shown to give good results, but for some assets it was not possible to satisfy both constraints (2) and (3).
PROFILE OF PEOPLE WHO STARTED THEIR CAREERS IN OR
The following traces the career of some of the people who have featured as young practitioners in earlier aditions of this career information.
Gayle graduated from an Institute of Technology where she studied Operations Research, Statistics and Computing. Her final year Project, concerning a survey of patient needs in a large metropolitan hospital won her a prize in the Victorian Chapter of ASOR's student conference. Since graduating, she has worked as an Industrial Engineer for a manufacturing company where her projects have included
- Evaluation of palletising by robots;
- Evaluation of plant and labour requirements of an automatic production line.
All of that was 16 years ago. In the intervening years Gayle has spent most of her time in Marketing roles, initially with the same manufacturing company (first as Customer Relations Manager and then as a Product Manager) and more recently with a department store. She is currently Marketing Specialist Women's Fashions responsible for a $6m advertising budget.
Discussing her move out of OR into Marketing, Gayle observed that the company chose her for the job in Customer Relations because they needed an analytical person to fix up the systems. And the story goes on: Gayle described her current role in Women's Fashions as operating in a production environment and added that if advertisements are not ready in time the consequence would be blank pages in magazines. In this context, Gayle has found critical path thinking to be of great value when setting priorities: doing first those things that have to be done to enable other people to meet her deadlines.
Among the other advantages she listed for the OR background in her Marketing roles were:
- General analytical skills;
- Problem definition and problem resolution skills;
- Holistic thinking.
After completing a degree in Mathematics and Physics, Harry did a one year postgraduate course in OR at a university. He then joined the Operations Research Department of an oil company where he has undertaken a variety of projects including
- Development of a financial model for economic evaluation of new LPG sites;
- Construction of a sector planning model for exploration activities;
- Optimisation of a distribution network.
Harry sees the Operations Research Department as providing interesting work and the opportunity to gain exposure to a wide range of the company's activities.
16 years later Harry is still with the same oil company and in the meantime has worked in the Corporate Treasury and a number of Marketing jobs (in both Oil Products and Coal) as well as two stints in Planning roles. He is currently Planning Manager for Upstream Oil and Natural Gas.
Among the advantages he listed for the OR background in his Marketing roles were:
- The ability to analyse more deeply;
- Better understanding of the financial drivers of the business;
- Better appreciation of the importance of problem definition;
- Better understanding of the dealer's financial situation and the impact of Marketing decisions on the dealer.
Harry has found the combination of OR training and commercial experience to be an ideal preparation for his planning roles. Like Gayle, he emphasised the importance of critical path thinking when setting priorities.
After completing an honours degree in Pure Mathematics, Rowan joined the OR department of a large mutual life office. His early projects concerned the development of small models and algorithms in the actuarial and financial areas and he was also involved in the continuing development and use of a large corporate model.
After 3 years, he transferred to the Resources Investment area, assisting in the management of existing investments and developing models to support decisions on new investments. Interestingly, he finds more scope for applying classical OR in the investment division than when he was in the OR department.
15 years ago Rowan left the insurance company to join a stock-broker where he worked in a number of research roles including that of setting up a "Quant Group" specialising in things like portfolio design, optimisation, arbitrage and portfolio trading. To support analysis and trading the Quant Group established expertise in databases and real time processing. This effort was highly regarded and lead to a desire to transfer these techologies to the whole of the business. Rowan became Head of IT and focussed on the transformation of front and back offices architectures, always with an OR type approach rather than traditional IT. More recently, Rowan decided he wanted to get back into the business side of stock-broking and moved to another broker to set up a margin lending business. This role provides an interesting mix of problems, to which his OR and analytical background is well suited..
Among the advantages he listed for his OR background were:
- The modelling approach;
- Systems thinking: focus on inputs and outputs rather than activity;
- Recognition that there sometimes isn't a solution: it is not possible to do what is asked for;
- Pragmatic approach: solution doesn't have to be optimal to be good.
Finally, like Gayle and Harry, Rowan emphasised the importance of critical path thinking when planning his work and setting priorities.
Profile of Young Practitioners
After completing a Ph.D. in Operations Research, Susanne joined the research and development department of a worldwide mining organisation. The section that she works in applies mathematical and numerical techniques to a wide range of mining and mineral processing problems. The sections particular interests include process optimisation and control, computational fluid dynamics, statistical analysis and steady state or dynamic modelling.
Project work has given Susanne a great opportunity to travel around Australia. Work to date has primarily focussed on developing novel approaches both stochastic and deterministic, for understanding the complex systems that constitutes a mining operation. In particular, OR technique has been applied in the following areas:
- Equipment and resource scheduling (e.g. decision support systems).
- Whole of business analysis (e.g. establishing drivers for process throughput and quality variability, identifying key leverage points to optimise capital investment).
Andreas obtained a Bachelor of Science majoring in Applied Mathematics from the University of Western Australia and then completed a PhD on the topic of convex network optimisation at the same institution. He then joined CSIRO as part of an operations research group.
In the first four years of working with CSIRO, Andreas has worked on a wide variety of projects including simulating a remand centre, several rostering projects, scheduling of a coal terminal, vehicle scheduling, and production planning.
As well as the above projects for industry, Andreas has been able to continue research and publishing in academic journals while working for CSIRO on topics such as hub location and scheduling.
Whilst completing a BSc in CS/OR Bruce started an IT consultancy, predominantly supplying PC based management reporting software to clients in the licensing industry. Later working closely with colleagues in management consulting, the work moved more towards analytical projects for financial services companies.
Now nearing completion of a PhD in integer programming, Bruce has joined forces with an ex-management consultant. This company now largely tackles problems such as product pricing, demand forecasting and targeting of direct marketing campaigns with Australian banks and insurers being the major clients.
The heavily used components of the companies analytical toolkit include several techniques for predictive modelling (classification trees, multiple regression, nueral nets) as well as global and local search techniques for Unconstrained "almost convex" nonlinear optimisation.
EDUCATION FOR OPERATIONS RESEARCH
There are many routes to becoming an Operations Research Analyst but most start with a degree in a numerate discipline, be it mathematics, science, engineering or economics. Many undergraduate courses in these disciplines provide a substantial training in Operations Research techniques and methodology. Some very similar subjects are offered under the titles Quantitative Methods, Management Science, Operations Management. Someone following this route into Operations Research would probably want to round out their training, possibly after a few years work experience, with a more generalist post-graduate course in management covering subjects such as organisational behaviour, marketing, economics, law, accounting and finance.
Alternatively, a prospective OR analyst can take a more traditional first degree in mathematics or science, followed by a specialist postgraduate course in Operations Research or even a generalist post graduate qualification such as an M.B.A. which permits specialisation in Operations Research.
A course providing a good grounding in OR would include; Mathematics, Operations Research, Statistics and Computer Programming subjects as well as subjects in techniques and methodology. Some background knowledge of Accountancy, Economics and Behavioural Science would be of additional benefit.
Various courses are available at universities and institutes of technology including some courses which specialise in Operations Research.
EMPLOYMENT IN OPERATIONS RESEARCH
Many large firms have groups of OR analysts (commonly 4 to 12 people). These are located in the steel, mining, oil, gas, chemicals, paper and engineering industries; airlines, railways, banking and insurance. Within the public sector, OR analysts are also employed in health, education and electricity supply. Not all of these people have the formal title of Operations Research Analyst and may be located in departments such as Industrial Engineering, Management Services or Corporate Research.
THE AUSTRALIAN SOCIETY FOR OPERATIONS RESEARCH INC. ASOR Caters for all who are interested in, and are concerned about, Operations Research, and in particular for such person who are resident in Australia. ASOR operates as a professional society through Meetings, Conferences, Publications etc. Many of the Members have affiliations with other similar societies that serve their particular discipline. Accordingly, the ASOR strives to set very moderate subscription levels in order to foster this multi-discipline character.
The society operates Branches in most States of Australia, and its activities are organised through Chapters in each of the capitals and also at Newcastle and Wollongong.
ASOR is affiliated with I.F.ORS. (International Federations of Operations Research Societies) and members are made aware of conferences, special interest groups and recent publications.
For further information contact your local chapters or write to AS0R, GPO Box 1048H, Melbourne 3001, Australia