OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following conditions.
A full list of the topics available in OR-Notes can be found here.
In recent years a number of approaches to problems which have come to be labelled collectively as "soft OR" have appeared. Many of these approaches have their origins in the United Kingdom.
By contrast the classical OR techniques such as linear programming, integer programming, etc are labelled collectively as "hard OR".
Hard OR is used here in the sense that traditional/classical OR techniques are:
Any doubts that arise over the value of hard OR are not to do with the correctness of the techniques themselves, but to do with their applicability (i.e. the number/variety of real-world problems to which they can be successfully applied).
Soft OR, by contrast, is:
Doubts that arise over the value of soft OR concern both the correctness of the techniques/approaches, as well as their applicability (i.e. the number/variety of real-world problems to which they can be successfully applied).
Soft OR is still relatively controversial. In many respects soft OR has taken on some of the attributes of a religion:
With respect to this last point belief in soft OR appears to be founded on relatively few applications. This is in sharp contrast to the many success stories reported over the years for hard OR.
By and large hard OR has avoided some of the religious excesses of soft OR although some recent hard OR techniques (such as tabu search) have unfortunately taken on some of these characteristics. Genetic algorithms, a technique from computer science that is also now being applied in OR, also has some of these religious characteristics.
As an acknowledged hard OR person myself I hope to present here a clear, fair, but critical, view of a number of soft OR techniques, namely:
Note here that a collective generic name for these particular soft OR approaches is problem structuring methods.
For more information about these problem structuring methods see J. Rosenhead (editor) Rational analysis for a problematic world: problem structuring methods for complexity, uncertainty and conflict. (John Wiley, 1989) [ISBN 0-471-92285-4 (hardback) or 0-471-92286-2 (paperback)]
Before going on to consider each of the three problem structuring methods (PSM's for short) in detail it will be helpful if we first outline what they have in common. Probably the main characteristic of such methods is that, to a greater or lesser extent, their primary focus is on:
and their secondary focus is on:
This is in sharp contrast to traditional hard OR approaches which are geared to understanding the problem and developing the best answer to it. Or to phrase it another way in hard OR the primary focus is on:
and the secondary focus (if at all) is on:
You can clearly see here how in problem structuring methods the focus has been reversed from that of hard OR.
Although it is plain that both issues: THE PEOPLE INVOLVED WITH THE PROBLEM; and THE PROBLEM need to be considered the focus adopted can lead to some distinct differences.
For example if my primary focus is on THE PEOPLE INVOLVED WITH THE PROBLEM I could regard myself as a success if I can get them to better understand the issues that they face and agree on a course of action. The fact that this course of action may be an absolutely disastrous one from the point of view of THE PROBLEM is somewhat irrelevant.
Indeed one of my main criticisms of soft OR is that this kind of subjective assessment "they all agreed on the way forward and were committed to it" is taken as proof of the worth of an approach. Such self-validation/assessment is simply not an intellectually valid way to show the worth of an approach.
That said, I do believe that approaches that help people to better understand problems have value.
As an overview problem structuring methods:
To achieve this such methods typically use a consultant (external person) whose role is:
The consultant does not need to possess any special knowledge about the problem, i.e. they do not need to be an expert in the problem area. However they are often expert in the particular problem structuring method being applied.
Such methods try to capture the group's perception of the problem:
Words are used as they are believed to be the natural currency of problem definition/discussion/solution (compare hard OR which uses mathematics). The use of pictures/diagrams helps to structure the group's perception of the problem and enables discussion/debate to be less personal.
Such methods help the members of the group:
Problem structuring methods involve the use of a number of words with specific meanings, as below.
As mentioned above we consider here three problem structuring methods:
To try and illustrate these methods we will apply each of them to the following example problem.
Crime is a real problem in this country. We are spending more and more on locking up increasing numbers of people in prisons, yet crime seems to go on rising. Many of those in prison are there for reasons connected with medical problems (e.g. drug addiction, mental illness), yet when they come out these problems are unresolved and so they go straight back to crime. Perhaps the answer is longer prison sentences.
SODA elicits information from members of the group using individual interviews. Such information is represented on cognitive maps. These show:
By concept here we typically mean a short phrase capturing some idea. This idea should be an action-oriented idea, that is intended to suggest an option for changing the situation. Often the negative (reverse) of the concept is also introduced.
For example, in talking about our crime example above, a concept used may be "more prisoners" with the negative concept being "less prisoners"
To ease concept representation we use three dots to separate positive and negative concepts so that we can capture both concepts in "more prisoners...less prisoners" This is read as "more prisoners rather than less prisoners", i.e. "more prisoners as opposed to less prisoners". As a shorthand we sometimes omit the negative concept and write "more prisoners..." so that the second concept is implied as the negative of "more prisoners".
Concepts are linked by arrows, with the direction of the arrow being such that concepts representing options lead to concepts representing outcomes. A negative sign associated with an arrow indicates that if the first phrase of the first concept applies, then the second phrase of the second concept also applies.
represents the views that more prisoners links to less crime and longer prison sentences do not reform criminals.
Concepts in maps are generally either:
Strategic options, sometimes called strategic directions, are options which have no other options above them in the map.
In SODA cognitive maps are first produced for each individual by interviewing them in a relatively unstructured "free-flowing" way to try to elicit their thought processes about the problem under discussion and what they think is important about the problem. Such maps often contain 40 to 100 concepts and may also help each individual to refine their thinking.
As an example we show below a small map based on our crime example given above. You can see that the goals (at the top of the map) are "less crime" and "reform criminals" and we have a number of options available, e.g. "more medical care in prisons"
In the above the strategic options are "more medical care in prisons..." and "longer prison sentences...".
Note here that the map may show contradictory information. Just as people's ideas and thinking are often contradictory so may the map be. Note too that it is hard/difficult to reproduce the thoughts and beliefs of a person in a simple two-dimensional diagram.
Another map for an individual talking about the same problem might be:
Once individual maps have been produced they need to be merged into a single map, initially often containing several hundred concepts. In doing this:
For example we might merge our two individual maps above to get:
In order to make this map manageable in problems larger than our simple example considered here:
This merged overview map (and the individual cluster maps) serves as a focus for discussion at a workshop involving:
As for all problem structuring methods the aim of SODA is to achieve understanding/agreement within the group.
More about cognitive mapping can be found here.
More about software to help apply SODA can be found here.
SSM operates by defining systems of purposeful activity (the root definition), building models of a number of relevant systems, and comparing these models to the real world action going on, in order to structure a debate focusing on the differences. That debate should lead the group of people involved in the process to see their way to possible changes and to motivate these people to carry out these changes.
There are seven stages in the SSM process, but they are not necessarily followed in a linear fashion. Diagrammatically these stages are:
Below we expand on each of the stages in SSM in greater detail
Stages 1 and 2: Finding out
This stage entails entering the problem situation and identifying within it:
Stage 3: Developing root definitions
SSM requires one or more root definitions to be stated. These are sentences which describe the ideal system (or subsystems within the overall system).
To ensure that appropriate elements of the system are captured in a root definition it should be possible to deduce from the root definition answers to the following questions:
C who are the customers/victims/beneficiaries of the system? A who are the actors/participants in the system? T what is transformed by this system, what inputs are transformed into what outputs? W Weltanschauung is a German word for which the usual translation is worldview. It is helpful to consider it as the stock of images in our head, put there by our origins, upbringing and experience of the world. We use these images to help us make sense of the world and they normally go unquestioned. So what is the worldview underlying the system? O who is the owner of the system, who has the power to stop the system? E what are the environmental constraints that cannot be altered and which need to be considered?
These questions are collectively referred to using the CATWOE mnemonic:
C customer A actors T transformation process W Weltanschauung O owner E environmental constraints
Hence you should be clear here that the root definition and CATWOE are linked together.
So taking our crime example a possible root definition could be:
The prison system is a system for ensuring convicted criminals (prisoners) serve their sentences in humane conditions, receive appropriate medical care, are given opportunities to obtain training and learn skills, and are released back into society at the end of their sentence with appropriate support so that they reform from their life of crime.
Checking this root definition against CATWOE to ensure it is appropriate we have:
C customer - society A actors - prisoners and prison staff T transformation process - need for convicted criminals to be locked away from society to need being met W Weltanschauung - desire to reform criminals and prevent future crime O owner - government E environmental constraints - criminals exist
Note that it may be possible to derive alternative answers for one or more of these CATWOE elements from a root definition. For example the transformation above could be from unreformed criminals to reformed criminals.
The root definition and CATWOE have at their centre the transformation process (the T in CATWOE): what does the system defined by this root definition do? This can be seen diagrammatically as:
Input --> Transformation --> Output
The Input can be physical or abstract. However the Output must be of the same type as the Input. In our example above we actually had two transformations, one physical (unreformed criminals to reformed criminals) and one abstract (need for convicted criminals to be locked away from society to need being met).
There are two types of root definitions:
Stage 4: Building conceptual models
In SSM a model is a diagram of activities with links connecting them. It:
x ---> y
is equivalent to saying activity y is dependent on activity x having been carried out
The model should contain a monitoring and control subsystem which monitors:
where in building the model the measures used for these controls need to be determined.
The process of developing root definitions and models can be followed to expand subsections of the overall model (i.e. they can be developed for an individual activity/activities in the main model built). Models encompassing the initial root definition can also be built.
With respect to our root definition given above some activities could be:
and we could link them as shown in the conceptual model below:
With regard to the monitoring and control subsystem, not shown in the above model for simplicity, this should address:
Stage 5: Comparing models with the real world
This stage involves comparing the models that have been developed with the real world. The most systematic way to do this is by ordered questions, namely for each and every activity and link in the model ask the questions:
This stage is designed to provide structure and substance to an organised debate about improving the current situation.
With reference to our model above for example we might identify that we are not making sufficient effort to carry out the activity
Of the three soft OR approaches considered here SSM is (in my view) the most powerful/applicable. Thinking clearly and logically about what constitutes an ideal system and then comparing it to the real world can plainly yield insights and ideas that might enable us to make the real world a little more like our ideal world.
Stage 6: Identifying changes
This stage involves identifying changes that could be made to the real world system, changes that appear, to those participating in the SSM process, as worth trying. The changes need to be systematically desirable and culturally feasible.
With reference to our model above for example we might identify putting more resources into medical assessment/care of prisoners as a change to be made.
Stage 7: Taking action
This stage involves putting into practice the most appropriate changes identified in the previous stage.
SC identifies four modes of decision-making activity:
with the facilitator identifying when to switch between modes, which are not followed in a linear fashion, but are switched between as appropriate.
A key theme underlying SC is the identification of uncertainty areas.
SC identifies three types of uncertainty:
The easiest way to think of the difference between UV and UR is that UV relates to the situation where you discuss/consult within your own organisation and UR relates to the situation where you need to discuss/consult outside your own organisation.
Throughout the strategic choice process:
In the last mode listed above, the choosing mode, these uncertainty areas are addressed in the context of proposed decisions.
In the shaping mode decision areas are identified as questions. These are simply areas where alternative courses of action are possible (i.e. a choice is possible). These decision areas are then presented on a decision graph, where:
For our crime example one possible decision graph is shown below.
Once the decision graph has been drawn, areas of problem focus, consisting of three or four decision areas need to be identified. The areas chosen are generally those which are important, urgent and/or connected.
For our crime example above we will have one problem focus based on the areas:
With regard to uncertainty we will have just one factor in our uncertainty list, namely:
In the designing mode we take each problem focus in turn and:
For our crime example with the problem focus based on the areas:
We have the options in each of these decision areas of:
Incompatibilities between options in this example are shown below, where a link in that option graph indicates two options (in different problem areas) are (in our judgement) incompatible. Note here that this contrasts with the meaning of the lines in the decision graph above - there lines indicated areas that were connected and needed to be considered together - here lines indicate incompatibilities.
With 3 options in one decision area and 2 in the other two there are 3(2)(2) = 12 possible decision schemes, although some of these will not be feasible as they involve incompatible options.
These 12 schemes are listed below:
build more prisons? impose longer increase rewards sentences? for informing? no no no yes no no yes yes yes yes - five more no no yes no no yes yes yes yes - ten more no no yes no no yes yes yes
Checking each of these schemes we find that for this example these are just three possible feasible decision schemes (labelled A, B and C below) which are:
Scheme build more prisons? impose longer increase rewards sentences? for informing? A no no no B yes - five more yes yes C yes - ten more yes yes
With regard to uncertainty our uncertainty list, after addition of two more factors, becomes:
In the comparing mode we compare each of the feasible decision schemes. This is done by:
The values chosen can be monetary sums or values chosen from some scale (e.g. rank on a scale from 1 to 10).
Based on this assignment of values particular schemes may be selected for closer analysis, either individually or as members of a shortlist. A common approach is to compare, in a pairwise fashion, all members of the shortlist. In this pairwise comparison the uncertainty areas are explicitly considered to identify those uncertainty areas relating to the schemes being compared.
For our crime example we could compare our feasible decision schemes (three in this case) with respect to the comparison areas of:
We present these numbers below:
Scheme Capital Running Government Public cost cost acceptability acceptability A 0 0 3 5 B 200 40 5 3 C 400 75 9 1
Selecting schemes A (no more prisons, no longer sentences and no increased rewards for informing) and B (five more prisons, longer sentences and increased rewards for informing) for pairwise comparison we have:
Scheme A Scheme B Capital cost 0 200 Running cost 0 40 Government acceptability 3 5 Public acceptability 5 3
Recalling the uncertainty list:
the only relevant uncertainties for this pairwise comparison of schemes A and B relate to scheme B (five more prisons, longer sentences and increased rewards for informing) and are:
These uncertainty areas are hence ones that will need attention if we are to make a choice between these two schemes. Recall here that all feasible decision schemes, three in this example, are mutually exclusive by the way they were constructed and so, at the end of the process, a choice of just one of them can be made.
In the choosing mode a commitment package (i.e. what we are proposing to do) is decided upon (or more than one package for submission to higher authorities). A commitment package is guided by the preferred feasible decision scheme and consists of:
With respect to our crime example if we assume scheme B (five more prisons, longer sentences and increased rewards for informing) for which the relevant uncertainty areas are
is the preferred feasible decision scheme then the commitment package might be:
Note that the actual decision scheme that we choose may be altered by the results of the explorations. For example if our explorations reveal there are no sites available for five prisons.
Software to assist in applying strategic choice can be found here.
Problem structuring methods undoubtedly have a role to play in decision-making. However at this stage in their evolution much remains to be done before they can find wider acceptance. In particular:
I would remark here that in reading to research what has been presented here I often thought that people in this area seem to write in a manner which obscures (at length!) the underlying basics of the methods they are trying to propose. Coming from a hard OR background I am used to having to state algorithms concisely, in a clear precise language, with clear definitions. I am sorry to see that people in this area seem to write without clearly defining terms and without clearly defining steps in the process.
This lack of clarity in writing has a number of impacts:
Perhaps the best hope for the future lies in a fusion of soft OR and hard OR. What soft OR offers in problem structuring methods are ways for participants in a problem to better understand it. What it lacks is any logical/objective way of deciding the most appropriate/best decisions to make (as we have seen above in soft OR agreeing on something is taken as self-evidently the best decision). What hard OR offers is precisely what soft OR lacks, logical objective ways to make appropriate/best decisions once a problem is clear. Time will tell whether hard and soft OR will come together, or whether, as often appears at the moment, they will remain bitter enemies.