OR/MS EDUCATION IN AUSTRALASIA H.G. ickle niversity anterbury · Research", reporting to the Academic Committee of Senate, and charged with the planning and co-ordination of courses

NZOR Volume 8 nwriber 2 July 1980

OR/MS EDUCATION IN AUSTRALASIA

H.G. D a e l l e n b a c h , D,C. M c N i c k l e

U n i v e r s i t y o f C a n t e r b u r y

SUMMARY

A survey of OR/MS teaching at tertiary institutions in Australia, New Zealand and the South Pacific, including detailed course and degree listings.

During the second half of 1979, a questionnaire was mailed to 90 heads of departments or schools of tertiary teaching institutions in Australia, New Zealand, Fiji and Papua New Guinea, The objectives of the survey were three­fold:(1) to compile an annotated list (as complete as possible)

of all undergraduate and graduate courses covering OR techniques or OR methodology currently offered;

(2) to compile a list of degrees in OR, or with significant OR emphasis;

(3) to obtain statements concerning the teaching of OR, about educational aims and philosophy, structure and emphasis, teaching approaches, and any substantive changes planned for the near future.

Non-respondents were approached up to two more times in view of securing their co-operation. Even so we ended up with a few nil returns from institutions which to our knowledge offer OR type courses. Where possible, data on their course offerings were obtained from relevant university catalogues. In view of the great diversity of OR teaching, some institutions, particularly in Australia, will have been missed. We sincerely apologise to them.

The results of the survey are organised into two parts: PART I summarises the findings for New Zealand and the South Pacific countries, while PART II deals with Australia.

PART I: OR/MS EDUCATION IN NEW ZEALAND AND THE SOUTH PACIFIC

All six New Zealand universities now offer courses with substantial OR content. At Auckland, Canterbury and Vic­toria, active structured OR programmes are available, usually in the form of a four-year honours degree. At Canterbury recognisable OR courses appear in the second year of the programme, and at Auckland and Victoria in year three. Auckland, Canterbury, Massey and Victoria also offer post­

1 22

graduate degrees or diplomas aimed at numerate graduates from other disciplines.

Few changes appear to be planned in the near future. Relatively low student numbers and hence little chance of extra staff appointments was mentioned in three replies. Student numbers in many courses, especially at the third year level, do appear low when compared with the numbers in mathe­matics and statistics courses at the same institutions. It would seem that OR courses are not yet widely seen to offer any advantage in training or employment prospects over a traditional mathematics degree.

M. Rosser, R. Brodie, L. Foulds, R. Johnson, D. Joyce,B. Smith and J. Turner helped with information on the New Zealand and South Pacific OR courses. The following summaries are extracted from their replies.

UNIVERSITY OF AUCKLAND

1979 saw the formation of a "Committee on Operations Research", reporting to the Academic Committee of Senate, and charged with the planning and co-ordination of courses in Operations Research throughout the University. It comprises representatives from the Departments of Management Studies, Mathematics, and Theoretical and Applied Mechanics.

At the undergraduate level there are two basic papers in OR available to students in Arts, Commerce, Engineering and Science. These are listed as Applied Mathematics papers26.391 and 26.395. The material in these is also available under the Engineering numbers of 54.258/9 (in 1981 to be combined as 54.251), and 54.458/9 for the degree of B.E. (Engineering Science) . Stress is laid on the importance of building OR within another discipline, which may be Engineer­ing, Management Studies or Mathematics. A B.Sc. or B.Com. with emphasis on OR would normally include 26.391 and 26.395.26.380 is also part of the suggested B.Sc. course. A B.Sc. (Hons.) course can also be taken. All students for B.E. (Engineering Science) take 54.258/9 in their third year.In the fourth year an OR student takes 54.458/9 as well as a project (54.410) and seven other papers.

It is possible to obtain a Masters degree in Commerce, Engineering or Science with substantial OR content. In addition, the M.Phil. degree is specifically designed for students who wish to follow a Masters programme in a Faculty other than that of their Bachelor degree. Graduate papers in OR are available in Economics, Management Studies and Engineering Science.

Numbers of Graduates: The following numbers represent those whose course at final year(s) would have included 25% to 50% OR (or very closely related) courses.

1 23

1977 1978 1979 1980B.E. 2 4 3 8B.Sc. 13 21 23 25M .Com.(M.Phil.) 2 1 - 2M.E.(M.Phil.) 4 2 1 2M.Sc. 1 - - -Ph.D. - - 2 2

Commerce13.203 Managerial Economics

Elementary introduction to OR. Enrolment: 75.

Engineering54.230 Systems Analysis

Introductory OR for non-specialists. Enrolment: 20.54.258 Operations Research IA (36 hours)

Linear programming, simplex and revised simplex, duality, post-optimality, decomposition.Enrolment: 12.

54.259 Operations Research IB (36 hours)Simulation techniques and applications, Monte-Carlo methods, statistical analysis. Enrolment: 12.

54.458 Operations Research IIC (36 hours)Queueing theory, inventory control, reliability, Markov decision processes, risk analysis. Case studies. Enrolment: 10 .

54.459 Operations Research IIP (36 hours)Integer programming, dynamic programming, network analysis, transportation and flow problems. Case studies. Enrolment: 10.

54.410 ProjectA report on the analysis of a problem (usually from a real-life source). Enrolment: 4.

Science26.380 Probability (72 hours)

Recurrent event theory, Markov chains, discrete branch­ing processes, Poisson processes, queueing.Enrolment: 30.

26.391 Optimization in Operations Research (72 hours)Linear programming, simplex and revised simplex, duality, post-optimality, decomposition, integer programming, dynamic programming, network analysis, transportation and flow problems. Text: Wagner. Enrolment: 25.

26.3 95 Mathematical Modelling for Operations Research (72 hrs) Simulation, Monte-Carlo methods, statistical analysis, queuing theory, inventory control, reliability, Markov decision processes, risk analysis. Text: Wagner. Enrolment: 25.

1 24

UNIVERSITY OF CANTERBURY

OR courses are available in the Economics Department for the B.A., B.Com. and B.Sc. degrees. Two graduate and one undergraduate programmes are also offered. The B.Sc.(Hons.) degree in OR is a four-year course containing all six under­graduate OPRE papers and a final year consisting of five OPRE 400 papers and an applied project. The last one (or two) years of this programme are also offered to qualified graduates as an M.Com. degree in OR. The educational objec­tive is to provide both a good coverage of all major OR techniques, including methodology and the systems approach, as well as their practical use. The latter is achieved through case studies at the third year level and a substantial project at the fourth year Honours and M.Com. levels, requiring some 400-500 hours for each student.

The M.Sc. in OR is a two-year course of six papers and a thesis, usually on an applied topic. The department also has two Ph.D. candidates at present. One course in Mechanical Engineering also covers OR modelling.

Enrolments of Students Majoring in OR/MS:1978 1979 1980

B.Sc., B.A., B.Com. (Stage III) 20 12 19B.Sc.(Hons.) (final) 2 3 2M .Com. 2 5 2M.Sc. (total) - 1 3Ph.D. (total) 1 1 2

OPRE 201 Decision Analysis (72 hours)Introduction to OR techniques, decision theory, inventory control, project scheduling, transportation problems, waiting lines. Text: Buffa & Dyer.Enrolment: 90 (plus 25 fourth year Forestry students).

OPRE 2 02 Linear Programming (72 hours)Linear programming, simplex method, sensitivity analysis and duality, transportation and network algorithms.Text: Daellenbach & George. Enrolment: 68.

OPRE 210 Quantitative Methods in Econometrics and OR (72 hrs) Numerical linear algebra, applied statistical inference, statistical computer packages, econometric models, fore­casting. Text: Wonnacott & Wonnacqtt. Enrolment:71 .

OPRE 301 Applied OR (72 hours)Methodology of OR, applications in inventory and production control, finance, distribution, marketing. Enrolment: 20.

OPRE 302 Mathematical Programming (48 hours)Advanced methods of linear programming, integer and non-linear programming. Texts: Hadley, Daellenbach & George. Enrolment: 19.

125

OPRE 303 Stochastic OR Models (48 hours)Applied stochastic processes, queueing, dynamic programming, Markovian decision processes, simulation. Text: Daellenbach & George. Enrolment: 20.

OPRE 451 Mathematical ProgrammingInteger programming, formulation and solutions of problems using TEMPO. Enrolment: 5.

OPRE 452 Stochastic ModelsQueueing theory, networks, multivariate statistical models, time series analysis. Enrolment: 6.

OPRE 453 OptimizationScheduling, networks, combinatorial optimization. Enrolment: 8.

OPRE 454 Large Scale ModelsDecomposition, multicriteria decision-making, applica­tion to energy, resource systems. Enrolment: 6.

Mechanical EngineeringENME 420 Engineering Organisations

Structural relationships, organisations and models. Text: Daellenbach & George. Enrolment: 85.

LINCOLN COLLEGE

Two undergraduate courses have significant OR/MS content:

ECMK Econometrics (Mathematical Programming section)(30 hours out of 104)Linear programming, sensitivity and parametric analysis, integer programming, input-output models. Text: Williams, "Model Building in Mathematical Programming".

FMGT 402 Farm Management IllbIncludes use of linear programming, decision theory, inventory analysis. Text: Nutthal , "Economic Analysis of Farming Systems".

OR is also available as a paper at the post-graduate level. Topics include the application of linear and dynamic programming to farming systems, integer and quadratic programming. Emphasis is placed on the construction and application of relevant models. Text: Hadley.

MASSEY UNIVERSITY

OR courses are available in Mathematics, Industrial Management and Computer Science. Structured OR programmes are a B.A. in OR and the graduate Diploma in Social Science. The B.A. course must include 60.305, 60.314 and 58.311 as well as six other prescribed papers. The Diploma course

1 26

requires four papers, of which at least two are OR papers, and a project. The aim of this programme is to retrain someone in industry with a degree containing at least 200- level mathematics in an area (OR) which will enable them to make a more effective contribution in their work. So far one person has graduated with a B.A. in OR. However, with the advent of 300-level extramural courses there may be a number of students who will obtain B.A.s in OR extramurally in the future.

60.305 OptimizationLinear, dynamic, integer and non-integer programming, network analysis. Enrolment: 18.

60.314 Applied Probability and ORInventory control, replacement, queueing, reliability, simulation. Enrolment: 4.

6 0.4 08 Advanced OptimizationAdvanced mathematical programming and network analysis. Enrolment: 2.

43.308 Operations Research (Industrial Management)Forecasting, linear and dynamic programming, queueing, simulation, inventory and replacement problems. Enrolment: 50.

58.311 Operations Research (Computer Science)A selection of topics from forecasting, mathematical programming, queueing, simulation. Enrolment: 26.

UNIVERSITY OF OTAGO

Operations Research at Otago is taught in the context and within a framework of other disciplines: Economics, Mathematics, Mineral Technology and Commerce. The following courses have substantial OR content. All are in the context of a discipline other than pure OR.

Economics Enrolment

ECON 2 53 (Part 1) Mathematical Economic Analysis 6ECON 3 07 Economic Programming and Planning 5ECON 353 (Parts 2 & 3) Theoretical Analysis 6

Mathematics

MATH 206 Applied Statistics and OR 19MATH 256 (Part 1) Applied Statistics and OR 1MATH 308 Advanced Applied Statistics and OR 2MATH 358 (Part 2) Advanced Applied Statistics and OR 7

Mineral Technology

MINT 416 Mineral Operations Management. Includes 11 introduction to OR techniques relevant to the mineral industry.

1 27

Commerce Enrolment

Quantitative and Computer Studies:102 Mathematical Techniques in Business 201 Further Statistical and OR Techniques

18821

Master of Business Administration:603 Quantitative Techniques 622 Operations Research

618

UNIVERSITY OF THE SOUTH PACIFIC

Some aspects of OR/MS are taught in Mathematics, Accounting and Economics courses.

ED 314 Numerical Analysis (84 hours)Includes linear programming and optimization. Enrolment: 15.

SE 271 Managerial AccountingLinear programming (2 weeks), sensitivity analysis (2 weeks), simulation (2 weeks).

VICTORIA UNIVERSITY OF WELLINGTON

Courses in Operations Research are offered by the Information Science Department at both the graduate and undergraduate level. The undergraduate offering is at the final year level and is taken primarily by B.Sc. students with backgrounds in mathematics and/or computer science. Enrolments by B.C.A. students with backgrounds in accoun­tancy, business administration and economics are however on the increase.

The development and training of potential OR profes­sionals is the major objective of the post-graduate courses. Two alternative programmes are available: a one-year Honours course in information science or a Diploma in Operations Research and Statistics. The Diploma is run in conjunction with the Mathematics Department and covers material in both statistics and OR. The Diploma offers more opportunities for developing statistical knowledge and applied OR, Conversely, in the Honours programme there is greater opportunity to study OR techniques at an advanced level.

Enrolments of Students Majoring in OR/MS:1978 1979 1980

B.Sc.B .Sc.(Hons.)Dip. OR & Statistics

732

936

1313

(text continued on page 146)

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TABLE 2 : DEGREE SUMMARY

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AUSTRALIAAdelaide U.: Appl.Math. X X

Aust.Grad.School of Mgt. oAust.Nat.U.: Econ.Stat. o oCanberra A.E.: Inf.Sci. X +Capricornia I.A E. :

Math. & Comp. Business

X

o oX

Caulfield I.T.: Math. X

Flinders U.: Math.Sci. oFootscray I.T.: Math. o X X

James Cook U .: Civ. & Sys.Eng. X X

Macquarie U.: Econ. & Fin .St. o

Melbourne U.: Math. X

Mitchell C.A.E. o oMonash U.: Economet./OR X + o oNewcastle U.: Mech.Eng. X X

New England U.: Econ.Stat. o o o oN.S.W. U.: Indust.Eng.

Math.o

o oX

N.S.W. I.T.: Appl.Math. X +Queensland U.: Math. X o X

Queensland I.T.Math. & Comp. X

Royal Melbourne I.T. :Math. & Comp. X +

S.Aust. I.T.: Math. X +Swinburne Col.Tech.:

Math . X

Sydney U.: Arch.Sci. Econ.Stat. o X

+X

W.Aust. U.: Econ. o oW .Aust. I.E.: Math. & Comp. o oWollongong U . : Math. X X X X

NEW ZEALANDAuckland U . : Com.

Eng. Math.

X

X

X

X

X

Canterbury U. : Econ. X X X + +Massey U. : Math. oVictoria U .: Inf.Sci. X X +

146

INFO 301 Operations Research Techniques (75 hours)Mathematical programming, critical path, decision theory,forecasting, inventory control and queueing. Text:Taha. Enrolment: 35.

INFO 348 Simulation and Heuristics (36 hours)Simulation and problem formulation, simulation languages, analysis of simulation runs, heuristics. Enrolment: 20.

INFO 349 Applied Operations Research (36 hours)Case studies in production planning, facilities location, investment analysis, queueing. Enrolment: 20.

INFO 4 01 OR MethodologyCase studies and seminar discussions dealing with applications of OR and problem solving. Enrolment:3-6 .

INFO 403 OR ApplicationsLectures and reading related to public sector, inventory, production, distribution and facilities planning problems. Enrolment: 3-6.

INFO 421 OR TechniquesAdvanced methods of mathematical programming, decision theory, forecasting and queueing theory. Enrolment:3-6 .

INFO 441 SimulationAdvanced material in discrete event and continuous time simulation. Use of simulation languages such as SIMON and GASP IV. Statistical analysis, including variance reduction and design of simulation experiments.Enrolment: 3-6.

INFO 449 Special TopicResearch into an area of OR application and/or technique.

The B.Sc.(Hons.) course for OR majors usually consists of four papers chosen from the five INFO 400 papers.

Students undertaking the Diploma in OR and Statistics would choose five papers from a range of papers including the above and courses in Statistics and Economics offered by the Mathematics and Economics Departments respectively.

UNIVERSITY OF WAIKATOThe Departments of Mathematics and Management Studies

each offer two courses in OR/MS.Management Studies

All B.M.S. students take 40.231. 40.331 is taken as an option by third or fourth year students. The department does not offer a major in the OR/MS field as yet, but plans

1 47

to introduce a Management Science major with an anticipated enrolment of 20 by 1982.40.231 Management Systems

Introduction to techniques such as allocation, inven­tory, queueing and simulation methods. Text:Shamblin & Stephens.

40.331 Management SystemsFurther study on techniques with emphasis on simulation and applications.

Mathematics23.301 is available to undergraduate level III students.

23.502 is intended for M.Sc. or M.Soc.Sc. students majoring in Mathematics or Computer Science.23.301 Probability and Operational Research

Probability theory through to semi-Markov processes, mathematics of OR topics. Text: Phillips, Ravindran & Solberg. Enrolment: 17.

23.502 Operational ResearchApproximately half mathematical programming and half stochastic OR models. Text: Taha. Enrolment: 4.

PART II: OR/MS EDUCATION IN AUSTRALIAOR COURSE LISTING

Table 1 contains the list of OR or OR related courses offered in Australia, using the conventions shown on page 1 28 This list indicates an amazing wealth of OR teaching at all levels, with the major concentration being in mathematics, then followed by economics/econometrics/economic statistics, business or management, and engineering. The odd-man-out, and without doubt almost unique in the world, is the impressive graduate diploma programme offered by the Architectural Science Department at the University of New South Wales. The predominance of mathematics is largely due to the growth of advanced optimization techniques, as a natural development in numerical analysis. The latter has traditionally been a strength of Australian universities.One could rightfully question whether this development should really be viewed as part of operations research or rather as an area of applied mathematics. The fact that many of these courses either use well-recognised OR texts or are even part of OR diploma courses indicates that they are more than simply applied mathematics. Hopefully, OR methodology and the OR philosophy are not completely side-stepped in these courses.

This predominance of mathematics is in sharp contrast to the OR scene in the United States and also in England to some extent, where the major strength in OR is concentrated either

148

in separate OR departments, which quite often are an out­growth of former industrial engineering departments, and in business schools. It would be highly interesting to explore the effect that the Australian situation has had on the development of OR in that country and, in particular, on its acceptance as a management tool in Australian business, industry and government.DEGREE SUMMARY

Table 2 summarises the information about degrees (P- 145), grouped into three classes: degrees named OR (+), degrees with an opportunity for substantial OR specialization (x), and degrees which allow some, but limited, OR emphasis (o).The cut-off points for the second category were chosen arbitrarily, along similar lines as the 1974/75 survey done by R.B. Mitchell.

There seems to be a definite reluctance of university institutions in Australia to label their degrees "OR". With the exception of Monash University, the name OR as part of the degree title is only used by colleges of advanced educa­tion or technical institutes. The graduate diplomas offered by these institutes (as well as Monash) follow largely the British model of so-called "conversion" courses offered by a number of British universities. They are aimed at graduates with undergraduate degrees in subjects other than OR. These courses clearly fill an important need. The findings in the article by Wright (this issue of NZOR) indicates that the greater diversity in the educational background of such graduates, in fact, seems to give them an edge over other graduates in terms of their future professional effective­ness. However, with the increasing number of undergraduate degrees with substantial OR specialization offered, there also seems to develop a need for more advanced programmes leading to masterates in OR. In contrast again to the United States and England, there seems to be some scope for further growth in this direction in Australia.

According to our findings, there are currently at most six masters degrees offered that can clearly be labelled OR, namely: James Cook University (Civil and Systems Engineer­ing) , Monash University (Econometrics and OR), University of Newcastle (Mechanical Engineering), University of New South Wales (Industrial Engineering), University of Queensland (Mathematics), and University of Wollongong (Mathematics). Surprisingly, none of the M.B.A. programmes available offers a clear OR type specialization - again contrary to the United States scene.SUMMARY OF COMMENTS ON OR TEACHING PHILOSOPHY

Unfortunately, few respondents took advantage of the opportunity to comment on the educational aims and the teaching philosophy underlying their degrees or OR course offerings.

1 49

As expected, where the teaching is mainly aimed at students in business and management, the emphasis is to impart some appreciations for quantitative methods, their strengths and weaknesses. The objective is not to equip the student with the necessary know-how for undertaking major OR type projects by themselves, but rather to give them an ability to recognise situations where quantitative approaches can assist in decision making, and help them to become good liaison people and ultimately (we hope) "sponsors" of OR projects. Course emphasis is therefore on an elementary survey of techniques by means of examples and practical applications, often coupled with case studies.

The teaching philosophy for undergraduate degrees with substantial OR emphasis is somewhat mixed. At one end of the scale is the following comment from the head of a mathe­matics department:

"We do not teach an undergraduate degree in OR because in my experience as an OR manager, people with degrees in philosophy, physics, engineering, psychology, and sometimes mathematics, make far better OR scientists than people with first degrees in OR. The unsurprising reason may be that the surface techniques of OR are easily learnt, but the deep structures of thought which it takes to do a fruitful project comes from an ability to juxtapose novel perspectives; and this is acquired by doing something divergent."

This echoes again the theme in Wrights paper mentioned earlier. In fact, one could generalise whether any under­graduate degree, no matter what field, really should be viewed as producing a professionally "finished" product, ready to be inserted in the proper slot in an organization.A number of well-known OR teachers all over the world indicate strong convictions that OR requires a good dose of maturity and world experience that is usually not present in undergraduates, in other words, OR is really a graduate subject.

At the other end of the scale, a typical statement of objectives, again from a mathematics department, is:

"The purpose of our programme is to produce graduates who can immediately be employed to advantage in OR situations and who will have the basis for further study. They will have a good understanding of the mathematical tools of OR, and flexible building capabilities. As well as this, it is hoped that they will be in a position to recognize the applicability of new results in areas such as combinatorics and mathematical programming to problems in OR."As far as the diploma course is concerned, several

statements emphasise the need for providing students either with first-hand experience - actual project work in the community - or pseudo experience based on case studies.Some respondents comment on the importance of providing close and proper supervision for such practical projects to

'0

be successful as a learning experience in OR, of ensuring that the teaching staff has good practical OR experience (Ackoff again!), or maintaining good relations with local business and industry, and of giving students full access to computational facilities.

AcknowledgementWe would like to express our thanks for the help offered by all partici­pants of this survey. We are especially grateful to Robert B. Mitchell and Roger Curnow of the Canberra College of Advanced Education for their help in organising the survey in Australia and in reviewing the prelimi­nary survey results. We take though complete responsibility for any mistakes remaining in this report, and there will undoubtedly be some.

REFERENCES

1 Mitchell, R.B., Australian Society for Operations Research Inc. - Survey of Tertiary O.R. Education, 1974/5, CAE, Canberra.

2 Wright, David, "An Examination of the Relationship between Change Agent Ability and OR/MS Success, NZOR, July 1980.

151

APPENDIX OF LISTED TEXT-BOOKSAckoff R.L.Ackoff & M.Sasieni, Fundamentals of OR, Wiley.Adby P.P.Adby & M.A.H. Dempster, Intro, to Optimisatn. Methods, Chapman, 74.A-D-H J.R.Anderson et al., Agricultural Decision Analysis, Iowa State U.P.Anderson D.R.Anderson et al., Essentials of MS, West, 78.Andrews J.G.Andrews & R.P.McClone, Math. Modelling, Autumn, 76.Arrow K.J.Arrow et al., Studies in the Math. Theory of Inv. & Prod.,

Stanford U.P.Baker K.R.Baker, Intro, to Sequencing & Scheduling, Wiley, 74.Barlow R.Barlow & F. Proschan, Stat. Theory of Reliability & Life Testing, Holt.Bensoussan A.Bensoussan et al., Mgt. Applications of Modern Control Theory, North-

Holland, 74.Bhat U.N.Bhat, Elements of Applied Stoch. Processes, Wiley, 65.Bierman H.Bierman et al., Quant. Analysis for Business Decisions, Irwin.Bondy Bondy & Murty, Graph Theory with Applications, Macmillan, 77.Buffa (1) E.S.Buffa, Readings in Prod. & Operations Mgt., Wiley, 6 6 .Buffa (2) E.S.Buffa, Modern Production Mgt., Wiley, 77.Claycombe W.W.Claycombe & W.G.Sullivan, Foundations of Math.Programming, Reston. Cohen Cohen et al., Simulation Modelling & Programming with SPURT/76,

Northwestern, 76.Cook Cook & Russell, Intro, to MS.Cox D.R.Cox & W.L.Smith, Queues, Methuen.Daellenbach H,G.Daellenbach & J.A.George, Intro, to OR Techniques, Allyn & Bacon, 78. Dantzig G.Dantzig, Linear Programming & Extensions, Princeton U.P.D & B H.G.Daellenbach & E.J.Bell, User's Guide to LP, Prentice-Hall, 70.De Groot M.H. de Groot, Optimal Statistical Decisions, McGraw-Hill, 70.De Neufville (1) R. de Neufville & D.H. Marks, Systems Planning & Design, P-H, 74.De Neufville (2) R. de Neufville & J.H.Stafford, Systems Analysis for Eng, & Mgrs.,

McGraw-Hill.R.Dorfman et al., Linear Programming & Ec. Analysis, McGraw-Hill, 58. R.D.Eck, QM - An Intro, to QM for Bus. Applications, Wadsworth.R.S.Garfinkel & G.L. Nemhauser, Integer Programming, Wiley, 72.

DorfmanEckGarfinkelGassGrossmanHastingsHastings

HillierHuHughes

5.1.Gass, Linear Programming, McGraw-Hill.5.1.Grossman & J.E.Turner, Math, for Biological Sciences, Macmillan,

(1) N.A.J. Hastings & J.M.C.Mello, Decision Networks, Wiley.(2) N.A.J. Hastings, Dynamic Programming with Mgt. Applications,

Butterworth, 73.F.Hillier & G.Lieberman, Operations Research, Holden-Day, 74.T.C.Hu, Integer Programming & Network Flows, Addison-Wesley, 6 8 .A.J.Hughes & D.E. Grawoig, Linear Programming: An Emphasis on Dec. Mak., Addison-Wesley.

74.

Oxford U.P.Techn. for Bus. Decisions, P-H, 76.

Jacobs Jacobs, Intro, to Control TheoryJohnson R.D.Johnson & B.P. Siskin, QuantJones G.T.Jones, Simulation in Business Decisions, Penguin, 72.Lasdon L.Lasdon, Optimization Theory for Large Systems, Macmillan, 70.Levin R.I. Levin & D.A.Kirkpatrick, Quant. Approaches to Mgt., McGraw-Hill.Lewis C.D.Lewis, Scientific Inventory Control, Butterworths, 70.Liu C.L.Liu, Intro, to Combinatorial Mathematics, McGraw-Hill, 6 8 .Lockyer K.Lockyer, Stock Control - A Practical Approach, Cassel, 72.Loomba Loomba, Management - A Quantitative Perspective, Macmillan, 78. Luenberger Luenberger, Intro, to Linear & Nonlinear Programming, Addison-Wesley.Makower M.S.Makower & E.Williamson, Operational Research, Hodder.Martin M.J.C.Martin & R.A.Denison, Case Exercises in OR, Wiley.Meredith D.D.Meredith et al., Design & Planning of Engrg. Systems, P-H, 73.

T

152

MetwallyMooreNaylor (1)

(2)

(3)Naylor Naylor Nemhauser Open U .

OrchardPaikPlaneRaiffaRiggsRivettRossSasieniSchwarz.ShamblinShubikSimmonsStantonStarrTahaTakayanaThieThierauf Tocher Trustum Van de Wadhwa

M.M.Metwally et al., OR: Theory & Appl. to Bus. & Econ., J.K.Pub., 80. P.G.Moore et al., Anatomy of Decision & Case Studies in Dec. Analysis. T.H. Naylor, Computer Simulation Experiments with Models of Ec.Systems, Wiley, 71.T.W. Naylor & E.T.Byrne, Linear Programming Methods & Cases, Wadsworth. T.H. Naylor et al. , Computer Simulation Techniques, Wiley.G.L.Nemhauser, Intro, to Dynamic Programming, Wiley, 6 6 .Open University, Linear Math. Units 18 & 28, Linear Programming,Theory of Games.W.Orchard-Hays, Adv. Linear Programming Computing Techn., McG-H., 6 8 .C.M.Paik, Quant. Methods for Managerial Decisions, McGraw-Hill, 73.D.R.Plane et al., Discrete Optimization, Prentice-Hall.H.Raiffa & R.Schlaifer, Applied Stat. Decision Theory, MIT Press, 61. J.L.Riggs, Production Systems, Wiley, 77.P.Rivett, Principles of Model Building, Wiley.S.M.Ross, Intro, to Probability Models, Academic Press, 72.M.Sasieni et al., OR - Methods & Problems, Wiley, 59.J .Schwarzenbach & K.F.Gill, Systems Modelling & Control.J.E.Shamblin et al., OR - A Fundamental Approach, McGraw-Hill.M.Shubik, Games for Society, Business & War, Elsevier, 74.Simmons, Linear Programming for OR, Holden-Day.H.G.Stanton, Austr. Case Studies in Bus., Stat. & OR, Cassel.M.Starr, Systems Management of Operations, Prentice-Hall, 71.H.A.Taha, OR - An Introduction, Macmillan, 71.A.Takayana, Math. Economics, Dryden, 74.P.R.Thie, An Intro. to LP & Game Theory, Wiley.R.J.Thierauf et al., Dec. Making Through OR, Wiley.Tocher, The Art of Simulation, E.U.P.

Routledge.North-Holland.

K.Trustum, Linear Programming,Panne C . Van de Panne, LP & Related Techniques,

L.C.Wadhwa & K.P.Stark, Lecture Notes - Intro, to Systems Management,James Cook University, 78.

Wagner H.M.Wagner, Principles of OR, Prentice-Hall.Wilson R.Wilson, Intro, to Graph Theory, Oliver & Boyd, 72.Zangwill W .I.Zangwill, NLP - A Unified Approach, Prentice-Hall, 69.Zimmermann H.J.Zimmermann et al., Quant. Models for Prod. Mgt■, Prentice-Hall, 74.