The process of problem-formulation

The process of problem-formulation

Ken Bowen *

Royal Holloway, University of London, Egham Hill, Egham, Surrey TW20 0EX, UK

Abstract

The methodology described deals with the problem-formulation (PF) stage and is independent of the overall OR

process. It is set-theoretic in principle. In more recent practice, new techniques for interviewing clients have been used

and the inclusion of some of Checkland's ideas has improved the design of the underlying questionnaire. The central

focus is the use of diagrams to encapsulate the stated problem and to aid communication. Ó 2001 Elsevier Science B.V.

All rights reserved.

Keywords: Methodology; Problem-formulation; Systems; Communication; Interviewing; Con¯ict

1. Introduction

The methodology (or process) of problem-formulation (PF) described in this paper is, inthe main, a formalisation of the earlier practiceof the author in his initial interactions with cli-ents, in defence. A brief account of how thiscame about is given: this is not unimportant indealing with any methodology, because, as wellas having to have satisfactory theoretical under-pinning, it is bound to have stylistic qualitieswhich represent the experience and world-view ofits designer(s).

It has also been the case that, for the past 30years, the author has worked independently andnot been part of an organisation that would havetaken up, used and extended the work that he hasdone. The self-assessment of the value of the ex-

plicit methodology to consultancy work is, so far,only supported in minor ways by the work ofothers. Further, because case-studies have beendi�cult to write up, mainly for reasons of con®-dentiality, only a few readers will be aware of theideas summarised here.

The main aim of this account is to enable othersto judge whether the process is one which they maywish to adopt or adapt for their own purposes.

2. Precursors

The methodology emerged slowly over a periodof more than 20 years. In the 1950s, studies for theAdmiralty had seemed increasingly restricted,since Royal Navy activities were examined in iso-lation from the other Services. A move to centraldefence OR, in 1965, surmounted that hurdle, onlyto ®nd that others took its place.

European Journal of Operational Research 128 (2001) 258±265www.elsevier.com/locate/dsw

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0377-2217/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.

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The principal one was that the studies asked forwere about how to win wars that had broken out,not to examine how to prevent them. This led tothe author's central research, from 1967, on con-¯ict in the widest sense, how con¯ict arose fromperceived problems and how its escalation led tonew problems. It was accepted that con¯ict ofsome degree, benevolent con¯ict, was essential toprogress. In a paper, written in 1972 for a multi-disciplinary discussion on models in the socialsciences [2], it was seen as likely that the con¯ictmodelling ideas, system-based and presented dia-grammatically, were relevant to inquiries into thenature and environment of any problem-situation.

During the 1970s, the author was also muchinvolved with others interested in methodology.Acko�'s work, particularly that with Emery onpurposeful systems [1], was closely studied [3].Indirectly, this led to contact with the research ofEden, that was one strand of the coming `soft' OR[e.g. 15,16]. By the 1980s, the author was one of anumber of process enthusiasts working together,both informally and within the OR Society'sMethodology (later Process of OR) Study Group.A one-day conference in December, 1977, hadprovided the ®rst public debate on where this workmight be going [5].

The author's interest remained centred on thequestion ``What is the problem?'' White hadshown that a gap existed here and, at the otherend, in the implementation of decision [4,19].Some aspects of implementation, such as the ex-istence of an organisation to manage change, had,of course, to be regarded as part of the problem.While Eden's work was clearly relevant to all theseissues, it was decided to go ahead and make ex-plicit ideas which would o�er an alternative ap-proach, one more in keeping with the implicitapproach previously used with clients to whom adiagrammatic language of the type envisagedwould be readily acceptable.

The research was carried out formally [7] afterthe author's retirement from the Ministry of De-fence, and was used in consultancy work onresearch contracts at Royal Holloway, Universityof London. Although the author had doctoralstudents and research assistants under his super-vision [8], the methodology, apart from the special

interview technique used, has remained, in gen-eral, a personal way of exploring what the prob-lem is.

3. Towards validation

It was recognised, during the developmentstage, that, while a methodology could not beproved as a theory can, it would be useful if itcould be potentially `falsi®able', by identifyingaspects of a problem-situation that could not beusefully formulated. Accordingly, the bricks whichwere to build a conceptual model of that situationwould be of a limited number of types: a simpleprocess, like a simple theory, is more likely tobreak down under determined scrutiny. The no-tation that would be used to describe the modelwas, similarly, to have only a few basic elements,and this was achieved by building on ideas gen-erated in the earlier con¯ict modelling [2].

Experimental work [6] was based on an aca-demic problem of OR course design. By itself, thiswas not adequate for the purpose of validation.However, along with other issues examined alongsimilar lines, results were encouraging. The modelsdeveloped were able to contain what the problem-owners saw as essential aspects of their problemand proved to be a good medium for aidingcommunication [7].

Later uses of the process increased con®dencethat the simplicity of the elements used and thesmall number of types of element were su�cientfor the purpose. Some concerns of a di�erent na-ture are discussed in the penultimate section: theseshould not however, a�ect the validity of theprocess.

For simplicity, the notation and the conceptsthat it represents will be discussed ®rst, and willthen be used to examine the process, bearing inmind that perceiving the problem-situation insystemic or set terms is part of the process. AsinStrategic Options and Development Analysis(SODA) [15,16] where cognitive mapping is atechnique used in a particular way to aid the pro-cess, so with this PF process; the notation used is atechnique developed to match the process and toaid its progress.

K. Bowen / European Journal of Operational Research 128 (2001) 258±265 259

4. The notation

A problem is to be described as a number ofinter-related systems (sets). These will be of twotypes. A circle (or an oval or something similar)will represent a person, a purposeful system. Arectangle will describe any other system, and mayhave people within it. Some systems will be col-lections of ideas (concepts) assumed to have beenmade explicit to some extent and consequentlyhaving an existence in the real world. In somecases, such concepts are more suitably shownwithin the relevant circle (person). They could beshown as a cognitive map or a group of inter-re-lated ideas, a sub-system of a person.

All sub-systems have some interaction with the(parent) system of which they are a part. Suchinteractions are shown only if they have somespecial importance. Systems which, in set-theoreticterms are adjoint will also theoretically interact:importantly such systems may be in con¯ict. Againtheoretically, sub-systems are assumed to interactwith systems in the environment of the parentsystem only through that parent system (but seepenultimate section). If they sometimes act inde-pendently of that system, they are assumed to havea second persona, as with an individual playingseveral roles. They are thus treated as existing indi�erent environments (enclosing systems) at dif-ferent times, although a primary role in the prob-lem situation will be de®ned in most cases.Hatched lines (see Fig. 1) denote such a multi-rolestate.

No systems overlap except in that sub-systemsare completely contained. Systems ®rst discussedas overlapping are rede®ned by splitting them intoparts or treating some parts as multi-role systems.Importantly, every system and sub-system willhave a name. A system's name must be relevant toits sub-systems. If `environment' is used as part ofa name, it must be an enclosing system of all sys-tems of which it is the environment, i.e. systemsare sub-systems of their environment. Thus a sys-tem is part of its environment.

Interactions are of four types:· con¯ict, potential or actual (as mentioned

above);· purposeful action;

· communication; and· general but unspeci®ed linkages or in¯uences.Purpose must come from a person and may a�ectany type of system. Communication must be to aperson and may come from any type of system,e.g. a machine can communicate with a person,but a person can only programme a machine.Sometimes purpose will demand communicationand vice versa: what is shown depends on what theclient wishes to say.

The foregoing is summarised in Fig. 1 whichalso shows other notational devices which werefound to be needed on occasion. A break in in-teraction lines indicates a negative, e.g. no com-munication or no con¯ict. A zig-zag denotes delay(this has only been used once, but is potentiallydesirable). Finally, interactions which are intended

Fig. 1. The notation.

260 K. Bowen / European Journal of Operational Research 128 (2001) 258±265

to be purposeful or to communicate may not op-erate very successfully and some distortion takesplace, denoted by the rounding of the bases of thearrowheads.

This limited set of symbols can provide a veryrich picture of how people perceive their situation.Only those interactions which they mention, andwish to stress, are shown, but a host of other in-teractions are implicit in the diagrams. Conven-tionally, if the person in charge of a system isshown, the corresponding circle is in the top left-hand corner of the rectangle. Otherwise, the sys-tems and sub-systems are placed so that the picturepresented is easy to look at and to understand.Arrow lines are kept as short as possible and as faras is possible they do not cross each other.

Fig. 2, which formed part of a description ofthe M.Sc. course development study [6] tackled inthe experimental stage referred to earlier, is given

here as a simple example of the notation in use. Itshows some of the dissatisfactions of students withthe courses and projects so far developed. Reso-lution depended on the clarity and completeness ofcommunication to and from the course organiser,and a later failure of this led to crisis. The problemthen changed, temporarily, to that of the resolu-tion of the new con¯icts engendered between thesta� members concerned.

5. The process

The material that is to be coded has to be ob-tained. Fig. 3 shows the cyclic process that takesplace. P� is the consultant's (facilitator's) problemof accessing and presenting the information that isto formulate the problem of the client(s). Note that

Fig. 2. Monitoring and coordination of an M.Sc. programme P1; . . . ; C1; . . . are projects and courses.


this is a further simple use of the notation to de®nethe metaproblem.

The opening phase (not shown) is a series of,initially unstructured, interviews with those whoown the problem in part or in whole. Such a fa-miliarisation stage, including the reading of doc-uments, may take many forms: it has to lead to theconsultant (C)'s being able to start the process,which is based on formal interviews, and follow-updiscussions, with those who, to various degrees,own the problem.

C has purposefully produced a notation whichwill be communicated to each client (only one, A, isshown). A will, initially, be less than fully aware ofthe meaning of the notation. However, A will re-ceive C's ®rst attempt to state the problem dia-grammatically, and may also be a little unsure of allthat is said by it. Nevertheless, A will comment on it± mistakes, omissions, etc. ± and may also add towhat has been said before. A may do this by using

C's notation or otherwise. C, in so far as the com-munication from A is understood, will makechanges and re-submit the diagram. This develop-ment of P0, the problem statement, goes on untilA is satis®ed that ownership of the diagram canbe accepted. In this process, C may suggest thatchanges, other than those required by A, are worthconsidering, but what is eventually included is A'sprerogative. The process ends, but may need to bereturned to, when clients and consultant achieve anagreed mutual understanding of the issues they face.

The A±C con¯ict shown is hoped to be oftemporary duration. It is however essential torealise that there may be misgivings about theprocess on A's side and C has to `sell' it. This needstact, humility and other `perfect' qualities that fa-cilitators aspire to. It may be that, because C hasto play a more forceful role than would be neededin cognitive mapping, these qualities are even morenecessary.

Fig. 3. The problem of problem-formulation.


6. Interviewing

Today, the post-familiarisation phase startswith system-based interviewing (SBI). This usesan open-ended questionnaire which leaves the in-terviewee free to comment on all aspects of his orher problem-situation, but at the same time thereis a hidden structure, based on Checkland's For-mal Systems Model [14] that enables analysis,including comparisons between perceptions ofdi�erent interviewees, to take place. It wasdeveloped in the middle 80s by Moynihan [17] inwork for the Navy Department of the UK Min-istry of Defence.

In the late 1980s, it was used in a study ofSignals Passed at Danger (SPAD) for British Rail:train drivers were crossing the stop-line when sig-nals were at red, in many cases causing damage,including injuries to and deaths of people. Ex-changes, with managers at all levels, were aimed atexploring their separate concepts of safety, par-ticularly the SPAD issue, in the context of theiroverall tasks, and were con®dential.

It was encouraging that managers accepted theprocess seriously: one manager was quite worriedwhen he mislaid his `picture', which he apparentlyused regularly, and requested an urgent replace-ment. It was striking to observe how far outwardsthe systemic representations reached. While simi-lar at similar levels of responsibility, they con-tracted markedly as one went from topmanagement perceptions to those of middle andlower management. Unfortunately the hoped foropportunity to merge same-level diagrams (re-gional managers) did not occur.

In the early 1990s, the design of questionnaireswas improved by using other concepts fromCheckland's Soft Systems Methodology (SSM),primarily Root De®nitions [14]. This is describedin two papers on a study carried out for a privateschool [9,10]. In this study the PF methodologywas used but the notation was incorporated in aless detailed way, since there was not much timeavailable. Nevertheless, the picture provided of theintegrated views of 25 members of sta� resulted inan agenda of key issues based on the identi®cationof important interactions. The action taken wasvery positive [10].

The most recent account of the use of SBI is bySkinner [18]. He made an interesting modi®cationby allowing clients to see the main questions inadvance. SBI was also discussed in an address tothe 1998 Young OR Conference [12].

7. Problems and clients

Although the intent of the diagrammatic nota-tion was to provide something familiar to the cli-ents whom the author was experienced in serving,practice with a wide range of clients has indicatedthat few people have any di�culties with it. Ittakes only a few minutes to summarise the wholenotational scheme and, generally, this is reinforcedby stating meanings in plain English as the dia-grams are explored.

The nature of the problem and its size do notseem to a�ect the use of the notation in principle.The number and complexity of diagrams clearlyincrease as problem size and complexity increase:the number of detailed discussions of and changesto diagrams also increase before an acceptablestage is reached. Basically, however, a serviceabletool for easier communication is created after the®rst system-based interview. How this has to growis a joint decision of client and analyst and thispoint is referred to again towards the end of thenext section.

Whether there may be clients who react badlyto the approach used here or problems for which itis really unsuited, is not known. The importance ofa methodology is that it re¯ects the way in whichthe individual using it goes about his or her task.We cannot work in other people's ways and wecannot be successful (or as successful) with allclients. Probably no approach will capture all di-mensions of a problem, nor will it necessarily suitall clients and all problems. These matters areseparately addressed elsewhere [13].

8. Pros and Cons

The process has certainly helped the author,and some of his students and colleagues, in es-tablishing, with clients, a clear picture of their


problem-situation. Clients do not have to botherunduly about the niceties of the logic inherent inthe way systems relationships are developed, andrarely themselves modify the diagrams directly.However, they ®nd the diagrams easy to under-stand and use, and they ®nd it convenient to havea mass of relevant and related information on asingle A4 or A6 sheet of paper. Being able to makepoints by reference to the diagrams is useful inavoiding misunderstanding in communication.

In meeting clients' needs, there is still a prob-lem. Constructing the diagrams is a time-con-suming process. Even minor changes can require aconsiderable re-orientation of the many systems,sub-systems and interaction arrows that describethe individual's perception. No software exists thatcould ease the tasks both of experimenting withlayout and testing logic and completeness. Itwould be nice to think that there may also be rulesthat govern production of an aesthetically pleasingand tidy picture, but my experience has not un-covered anything of moment.

There is also a di�culty that is probably sharedby any descriptive method, namely the represen-tation of time. Depending on the particular case, anumber of ways of getting the sense of time pass-ing have been tried other than the obvious one ofusing a sequence of descriptions of the `same sys-tem' at sequential stages (a simple example wasgiven in a paper [11] discussing the management ofchange in a complex system).

A second way, illustrated in the original thesis[7], was to extend the environment outwards (di-agrammatically) to contain sequential additions toa problem-situation when the changes were ex-pected to be the increases in external in¯uences. Athird, peculiar to a hospital study, was to track apatient through the various hospital sub-systems.The patient was considered as a source of datafeeding the records of several departments, datawhich would become available to appropriatemedical sta� dealing with the patient. The patient'stour (hatched circles in many places) could beappropriately marked and its sequence could be ofconsiderable relevance.

Time passing is, of course, implicitly recognisedin the cyclical nature of some sets of interactions(e.g. communication in Fig. 3). There is also much

in the minds of clients that the diagrams producedneed only remind them of, such as the need tocontrol undesirable con¯ict. This points to a needfor further re¯ection on what would be a `completeand satisfactory' PF; perhaps the diagrams' mainpurpose should be to keep a client's mind focusedclearly on what, at the time, the problem-situationis perceived to be.

Finally, there is the question of `cutting corners'to make diagrams, and communication, simpler. Itis convenient to talk of communication with anorganisation rather than with speci®c individuals,and consequently communication arrows aresometimes similarly treated. Purpose, similarly,may be deemed to come from organisations. It iseasy to `break' the rules by allowing interactions tocross system boundaries (it is, for example, as if fora period of time a person was acting as an indi-vidual free of bureaucratic constraints). Yet it isalways necessary to consider whether the systemstructure allows such liberties. If for example thereis communication by letter, directly with, say, themanager of some concern, there may be delaysproduced by getting out of one system and intoanother: the letter may well be `sat on' by themanager's secretary, and this could be an extremecase for arrows indicating `no communication',`distortion' or delay. However, overall, `breaking'the rules for the convenience of achieving simplerdiagrams has been found acceptable, provided thatwhat is shown has been reached by a process thatdoes not bypass the discipline of inquiry that therules should impose.

9. Concluding remarks

The above does not in itself provide informa-tion su�cient to enable a reader to adopt themethodology. This would require considerable useof the references and, even then, a certain amountof direct discussion on practice would seem ad-visable. The aim has been to expose the thinkingbehind the methodology and describe the sort ofcreature it is.

It would have been useful potentially to in-clude a recent real PF diagram, but con®dential-ity makes this di�cult. Further the interpretation


of content requires a wealth of background ma-terial: consequently, such a diagram might looksuper®cially impressive, but convey very little tothe reader. Figs. 2 and 3, albeit very simple,indicate the form of presentation: other exampleswould be of the same nature with perhaps ahundred or more named sets, with a similarnumber of arrows emphasising important inter-actions. Linked diagrams extend the detail inmany cases.

It is never easy to describe a methodology onpaper in su�cient detail to enable it to be judged.It has to be seen in action. While experience maybe validation enough for the individual concerned,others will properly demand more. Currently, theauthor is discussing PF problems arising in studiesof antisocial behaviour in cities and of ethnic andgender inequalities in the workplace. These inqui-ries may lead to a wider practice of the process,importantly involving new users. Similarly, helpwill be given to any readers who may wish to testthe methodology or to modify it to suit their ownways of working. There may also be someone whowould ®nd the provision of suitable software to bean interesting challenge.

References

[1] R.L. Acko�, F.E. Emery, On Purposeful Systems, Tavi-

stock, London, 1972.

[2] K.C. Bowen, D.G. Smith, The development of models for

the study of con¯ict, in: L. Collins (Ed.), The Use of

Models in the Social Sciences, Tavistock, London, 1976,

pp. 149±172.

[3] K.C. Bowen, Purposeful systems and operational research,

Operational Research Quarterly 26 (1975) 125±131 (an

extended review of Ref. [1]).

[4] K.C. Bowen, Formalisation of the OR process, Opera-

tional Research Quarterly 28 (1977) 369±376 (an extended

review of Ref. [19]).

[5] K.C. Bowen (Ed.), The King is Dead: Long Live the King?,

in: Proceedings of a One-Day Conference held at the

University of Aston, OR Society, Birmingham, 1977.

[6] K.C. Bowen, An experiment in problem-formulation,

Journal of the Operational Research Society 34 (1983)

685±694.

[7] K.C. Bowen, A methodology for problem-formulation,

Ph.D. Thesis, University of London, 1983.

[8] K.C. Bowen, Research on decision-making: How to be a

DSS, in: A.G. Lockett, G. Islei (Eds.), Improving Decision

Making in Organisations, Springer, Berlin, 1989, pp. 510±

516.

[9] K. Bowen, System-based interviewing: Understanding

community problems and developing a strategy, 1991, in:

I. Tsivacou (Ed.), A Challenge for Systems Thinking: The

Aegean Seminar, University of the Aegean, Athens, 1993,

pp. 267±276.

[10] K. Bowen, System-based interviewing: Its role is co-

operative group decision, 1992, in: S. Ruuth, R. Lahdelma

(Eds.), New Management Technologies and Transition to

Market Economies, Research Report A34, Systems Anal-

ysis Laboratory, Helsinki University of Technology,

Espoo, Finland, 1994, pp. 14±28.

[11] K. Bowen, Understanding and structuring new problems,

in: S. Ruuth, R. Lahdelma (Eds.), 1992 in: S. Ruuth, R.

Lahdelma (Eds.), New Management Technologies and

Transition to Market Economies, Research Report A34,

Systems Analysis Laboratory, Helsinki University of

Technology, Espoo, Finland, 1994, pp. 2±13.

[12] K. Bowen, Answering the right question, Operations

Research Insight 11 (3) (1998).

[13] K. Bowen, Some thoughts on multimethodology, Systemic

Practice and Action Research 11 (2) (1998) 169±177.

[14] P. Checkland, Systems Thinking, Systems Practice, Wiley,

1981.

[15] C. Eden, S. Jones, D. Sims, Thinking in Organisations,

Macmillan, London, 1979.

[16] C. Eden, S. Jones, D. Sims, Messing About in Problems,

Pergamon Press, Oxford, 1983.

[17] P. Moynihan, K. Bowen, System-based interviewing: an

inquiry into the needs of those in command, in: G.K. Rand

(Ed.), Operational ResearchÕ87, North-Holland, Oxford,

1988, pp. 582±593.

[18] I. Skinner, Transport policy and reality ± can system-based

interviewing unravel the di�erences?, Operations Research

Insight 11 (1) (1988) 10±15.

[19] D.J. White, Decision Methodology, Wiley, London, 1975.


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The process of problem-formulation