Developments in undergraduate education for operational research in the U.K. since 1965 ground in some basic discipline, and that this is demonstrated by tke possession of a degree or professional qualification. Frequently this is a scientific or quantitative based subject. Engineering, Mathematics and Economics are popular examples. Moreover this is consistent with the inter-disciplinery origins (see [12]) and nature of Operational Research. Ackoff and Sasieni [1 ] consider OR to be "the application of scientific method by inter-disciplinary t e a m s . . . " , and that the use of inter-disciplinary teams is an essential characteristic of Operational Research. Beer [3] discussing the origins of OR, states that "OR became at once, and remains today, an inter-disciplinary activity". It is not surprising that with this background, formal educational courses in OR at universities and polytechnics initially developed primarily at postgraduate level. Most admissions tutors preferred applicants to have some industrial experience, and for some courses this was mandatory. However, recent developments in the U.K. have resulted in a change in the postgraduate population. These developments include higher levels of fees, increasing difficulty in obtaining financial support from traditional sources (for example, the research councils, industrial sponsorship), and the uncertainty that students embarking on a course feel about the availability of suitable employment on completion of the course. As a consequence, the postgraduate population now tends to have a higher proportion of overseas students; until very recently they seem to have found funding more easily. Fewer students have industrial experience before coming on a course, since those with a secure job, in the current economic climate, are less willing to leave this *.o go on a course. Also as a consqquence of the economic climate, employers are far less willing to sponsor employees or potential employees on courses. Students seem less certain of the value of a postgraduate qualification in the current job market. Some students finishing undergraduate courses, hold places on postgraduate courses as an 'insurance policy' against f'mding employment; if a suitable job is offered they will take this rather than go on the course. Quite recently, when Haley [7] discussed the issue
A l a n P. M U H L E M A N N Department of Management Sciences, University of Manchester, Manchester M60 I QD, United Kingdom
Received December 1979 Revised February 1980 Until quite recently most courses in Operational Research at Universitiesin the U.K. have been at postgraduate or post experience level. Entrance requirements have frequently been a degree or equivalent professional qualification, and for some of the mote well established and popular courses, industrial experience in addition. An often used argument is that the inter-disciplinary origins and nature of Operational Research require those entering the profession to have basic training in some discipline, most commonly reflected in the possession of a degree or professional qualification. Frequency this is a scientific or quantitative subject. Engineering, Mathematics, Economics are common cxamples. In recent years, however, there has been an increasing trend within Universities to mount undergraduate courses involving substantial portions of material which is taught under the title of Operational Research. This paper looks at this tren0 in more detail, and the courses themselves are analysed. Some of the reasons for these developments are discussed, their effects on the OR Profession and the Education Sector outlined, and future trends suggested.
1. Introduction Much has been written over the years on the general topic of Education for Operational Research, and articles on this topic always seem to guarantee a lively correspondence. Cook [5] presented a comprehensive analysis of Operational Research training from a practitioner's viewpoint, while an Editorial [9] on Education, which included some mention of the relationship between OR and the Universities, provoked much interest and comment. Much of the discussion ranges about the balance between short courses, long courses and practical training within the educational programme. Nearly all assume that new entrants to the Operational Research profession have a backThe author would like to thank Professor Dr. I. Ilhami Karayalcin for his assistance in making this paper mote suitab!e for publication from a viewpoint outside the U.K. © North-Holland Publishing Company European Journal of Operational Research 6 (1981) 252-257 252
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A.P. Muhlemann / Undergraduate education for operational research
trated. An attempt will be made to identify some of the reasons for this development, and to assess its impact on postgraduate studies, an area already under pressure.
of Operational Research and Education in the Journal of the Operational Research Society, he introduced aspects of formal education and its aim and purpose, together with a list of unanswered questions. He looked at four areas of formal education in OR: Research, Postgraduate, Undergraduate, Short courses. In discussing undergraduate degrees in more detail he states "Sections of Mathematics or Business degrees are called OR and consist of a handful of lectures on Linear Programming or Queuing Theory. An attempt is sometimes made to cover ten topics in eight lectures. The staff used are frequently employed in other capacities and merely teach this subject as part of a total load". Mercer [8] confirms that "University departments of mathematics, which are able to attract talented mathematicians, are increasingly including the techniques of operational research in their undergraduate courses, with the degree of rigour depending on the students' abilities". In the last ten years there has been a rapid growth in the extent of undergraduate teaching of Operational Research. The University Entrance Handbook published by the Universities Central Council on Admissions (UCCA) [10] for entry in 1979 indicates that 40% of universities are offering undergraduate courses involving substantial portions of Operational Research. In the following sections the development of this teaching of OR will be analysed, and the extent to which the statements made in the previous paragraph have been overtaken by events will be illus-
2. Undergraduate developments in OR The basic source of historical data on courses involving a substantial portion of Opera!ional Research was taken from the UCCA handbook [10] for students intending to commence study in a particular year. It was felt that this had a number of advantages over other sources of data. It provided a common base for each year. It was the starting point for the prospective student. Error in classifying courses was partially eliminated, with the possibility of underestimating the extent of development. This data was supplemented by the current prospectus for the universities concerned. Generally speaking only those courses involving a substantial portion of OR are included. A B.Sc. course in Mechanical Engineering, where a student can opt to study OR for two hours per week as one of his six courses taught in final year is not included in the data. Fig. 1 shows the growth in both the number of universities, and in the percentage of universities offering undergraduate courses involving substantial portions of OR, since 1965. As stated above, this is almost certainly an underestimate. The source is the
40
20-
KEY [~ number
ao
percentage c/)
LU t-C/3 ;>
2o
10"
Z
~o
- lg~5
I
i
i
119701
I ,
%
lC. 75
1979
YEAR
Fig. 1. The growth in the number of universitiesand in the percentage of universities offering courses involvingsubstantialportions of OR.
254
A.P. Muhlemann / Undergraduate education for operational research
KEY 40
~ number
I
-2
ratio
I
! "
20"
UJ
E i,
0
oz
r
1965
r
r
rr[ 1970
I
1975
1979
YEAR
Fig. 2. The growth in the number of courses and in the ratio of the number of courses to the number of universitiesofferingsuch courses.
OR classification in [ 10], and such courses as mathematics for management are not always included in this although clearly there is overlap between this and OR. Moreover these figures take no account of undergraduate degree level teaching taking place in Polytechnics and Colleges. Five Institutions are listed in [6] offering courses which could be considered to include substantial portions of OR. There has been a substantial increase, since 1970, in both the number of universities and the percentage of universities involved in teaching OR in their undergraduate programs. These current figures are confirmed by the Commonwealth Universities Yearbook [2], in which OR is one of the topics included in the analysis of courses. This shows that one third of all universities have OR forming a main part of a course leading to a first degree, another third have OR as a subject which may be studied as part of a course leading to a first degree, while only a third have no mentio.,~Lof OR teaching. Fig. 2 shows the growth in the actual ~ umber of courses, and the ratio of the n~Jmber of courses to the total number of universities offering a course in each year. Again the growth in the number of comses has been quite large since 1970, and since 1974, a substantial number of universities have offered more than one course. Of the universities currently offer. ing courses, 3~o have more than one on offer. Next an attempt will be made to measure the rela-
tive weight of OR in the various courses and to look at these courses in more detail. They will be classified as follows: (a) single honours courses in a group of related subjects including OR (for example, Mathematics and Operational Research); (b) combined honours courses in two subjects, one of which is OR (for example, Operational Research and Physics); (c) honours courses in a related subject with OR (for example, Computing with Operational Research); (d) honours courses where OR is specifically stated as a possible specialisation, generally at least one third of the final year, building on courses in previous years (for example, Business Administration with specialisation in Operational Research). This classification comes from the title given to a particular course, and although universities are usually very careful in giving a title to a course, the classification is rather fuzzy. The classification couid be thought of as reflecting a reducing weighting being given to the OR portion of the course. Table 1 shows the result of classifying the forty-two courses currently offered into these categories. The first two appear more popular and in broad terms it might be argued that these involve the most OR. Again there is some underestimation of the number of courses counted in the last category since no1 all universities specify their options within a particular course in suf-
A.P. Muhlemann / Undergraduate education for operational research
Table 1 Classification of current courses Type
Number
a b
12 19
c d
5 6
29 45 12 14
42
100
Totals
Percentage
ficient detail in [ 10]. When the actual courses are examined in some detail, some interesting facts emerge. The most popular subjects to combine with OR are, not unsurprisingly, Mathematics, Statistics and Computing. Of the 36 courses in the first three categories, 13 have mathematics in their title, 19 have statistics in their title, and 7 have computing in their title. By contrast there are joint courses combining studies of OR and Chemistry, and OR and Civil Engineering - more unexpected combinations. Many Business Studies courses have OR/Quantitative options in their later years, but it appears rather arbitrary as to
whether they choose to include this fact in [ 10]. This could be considered rather surprising since it is the initial source of information for the prospective undergraduate student. It is interesting to look at the content of some of the courses offered. The level of detail published by the individual universities varies considerably; 17 of the 20 universities have been included in this analysis. All include coverage of the more common OR models/techniques under various different titles (a comprehensive list is given in [8]). Using each university's handbook as a source of data, some of ~he other topics covered either compulsorily (c) or optionally (o) are analysed by their frequency on the courses in Table 2. The topics were deliberately chosen quite broadly to give a better overall picture of course content. Computing includes programming, data processing, systems analysis; accounting includes finance; micro, macro and managerial economscs are included within economics. Psychology, sociology, organisation behaviour are included within behavioural science, it was possible to break the topics down into those studied in the different years of the course but again
Table 2 Frequency of different topics included in courses Topic
Category of course b
Statistics/l~obability
Total c
:
d
0,4
,4 ,5
Computing Accounting
o°
Economics
Mathematics Management Principles Behavioural Science Production Management
c
1 1 0}
o
c
o
0 1}1
0) 0
0} 1 1
1)1
2}3
9
)9
255
31}4
~}6 8
1
0
10
0}1
1}1
2}12
Case Studies Project/Dissertation
5 4
15 17
2 3
4 5
24 29
Total courses in category
9
17
4
5
35
256
A.P. Muhlemann / Undergraduate education for operational research
it was felt that this did not contribute to the broad picture. The table shows the numbers of courses in each category involving either compulsory (c) or optional (G) study of a particular topic. There is no double counting if a topic is studied in more than one year of a course or if a topic is compulsory in one year with an option to continue in a subsequent year. Statistics, computing and mathematics form a popular base. Course categories (c) and (d) tend to have a broader spread of topics (including some not mentioned here, like Business Law). Behavioural Science does not seem too popular, reinforcing the idea that this aspect is perhaps best learnt through practical experience. It is interesting to note the use made of case study material to relate theoretical studies to practical applications, and that" over 80% of the courses involve a major project in the final year. In fact four courses were of the sandwich type - four years duration - the third being spent away from university, in industry.
3. Discussion There has been a significant development and growth in undergraduate courses involving substantial portions of OR in the last ten years. It is interesting to try to identify some of the reasons for this development. One of the reasons could be the expansion, since 1965, in the number of universities, which has increased from 30 to just over 50 in this period. Moreover a significant number are the 'technological universities' - originally Colleges of Advanced Technology gwen university status (charters to award their own degrees) in the 1960s. These new universities were (and still are) committed to courses which are more vocationally oriented. Moreover in recent years. there has been an increasing trend for universities in general to demonstrate the practical relevance of their courses, and clearly OR satisfies this criterion. Another reason is the growth in the commercial use of computers in recent years; allied to this there has been the increasing use being made of scientific management and the increased need for people trained in and sympathetic to its use. It is estimated [11 ] that there are 500 OR groups with 5000 people actively engaged in OR in the U.K., moreover there is also OR being applied outside the framework of OR' groups. Clearly these courses have been developed to meet a demand.
A number of joint courses have been developed, for example OR and Chemistry. There are some who would argue that this development has taken place in order to reverse the downward trend in the number of students studying chemistry, by giving them an alternative area in which to find a job on graduation, where there are likely to be more openings than in chemistry. However it could be argued that students in their final years at school, looking at university courses, will be attracted to these joint courses by the subject they are familiar with, while not fully understanding the nature of OR. This is because OR is not a subject which is normally introduced in schools; and because of the closed circle of the educational system (school-university-school), few teachers have much contact with industry, and few have encountered OR. Next we look at some of the effects of the development of OR undergraduate teaching. The OR profession in general is being affected by these developments. Mercer [8] feels that ideally employers would like to recruit students with a postgraduate degree to work in their operational research groups and that the output from undergraduate OR courses should not be seen as a source of OR professionals. These graduates are, rather, seen as potential line management, and errployers like employees to have an understanding of real world systems. Moreover these graduates have an awareness of the scope and limitations of OR, and are likely to be sympathetic to its use. However the many courses in Business Studies and related subjects are producing graduates for the same market. It is likely that some graduates from OR courses will move into OR. Moreover some employers will prefer these °graduates for OR work, completing their training by sending them on short courses as and when appropriate to the projects on which they work. These graduates could be cheaper to employ than those with a postgraduate degree in OR. There is a degree of overlap between universities offering undergraduate courses in OR and those offering postgraduate courses in OR. Twenty universities offering postgraduate courses in OR are listed in [4]. Eight of these are also offering courses at undergraduate level included in the earlier analysis. All of these institutions are faced with the problem of how best to allocate their increasingly scarce resources and to decide whether to undertake new developments in teaching OR at undergraduate level, or to consolidate teaching at one level only, possibly di,~ontinuing courses. These decisions are likely to be influenced by
A.P. Muhlemann / Undergraduate education for operational research
the pressures to fill the gap left whea the effect of the reduction in the birth rate reaches the universities. It seems likely that the growth in the number of undergraduate courses specialising in OR has stabilised. It is likely that the market for these graduates is being satisfied. An area where there is likely to be continued growth is the provision of appreciation and less in-depth courses for students in related topics like Engineering, Economics, Accounting. These undergraduate courses in OR are likely to have an effect on the viability of postgraduate courses, which are already under pressure in common with the whole of postgraduate education, discussed earlier. It is 'easier' to study OR at undergraduate level than at postgraduate level because of the funding situation. A student satisfying certain residential conditions, and satisfying a university's entrance requirements, can get his fees paid, and a meanstested maintenance grant from his Local Education Authority for an undergraduate course. As discussed earlier, funding for postgraduate courses is more difficult. It could be that in future there will be a reduction in the number of full-time postgraduate courses in OR, with a switch to a mixture of modular parttime or evening courses leading to postgraduate qualifications, and short (one to three week) postexperience courses on specific topics. This structure already exists at some institutions.
257
References [ 1 ] R.L. Ackoff and M.W. Sasieni, Fundamentals of Operations Research (Wiley, New York, 1968). [2] Association of Commonwealth Universities, Commonwealth Universities Yearbook, Vol. l (Macmillan, London, 1979). [3] S. Beer, Management Science (Aldus Books, London, 1967). [4] Committee of Vice Chancellors and Principals of Universities in the U.K., Schedule of Post Graduate Courses in U.K. Universities (London, 1978). [5] S.L. Cook, Education for operational research: a practioner's viewpoint, Operational Res. Quart. 16 (2) (1965) 145-175. [6] Council for National Academic Awards, Directory of First Degree Courses 1978-79 (Lo,',don, 1978). [7] K.B. Haley, Operational research and education, Operational Res. Quart. 27 (I il) (197.~) 193-198. [8] A. Mercer, Education in operational research - a personal viewpoint, European J. Operational Res. I (6) (1977) 352-360. [91 B.H.P. Rivett, Editorial,Operr tional Res. Quart. 18 (I) (I 967) 1-4. [10l Universities Central Council on Admissions, How to Apply for admission to a U),iversity (Cheltenham, (1965-1978). [11] University of Strathclyde, Pro~Dectus 1979/80 (T.&A. Constable, Edinburgh, 1979). [12] C.H. Waddington, OR in World War II (Elek Science, London, 1973).