Teaching LP
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July - September 1996
Teaching LP - a case study approach offers a richer learning experience Cecilio Mar Molinero Academic Operational Researchers are inevitably expected to teach Mathematical Modelling, Linear Program-
ming (LP) and related subjects such as Optimisation.
Linear Programming is their bread and butter. We should not be surprised to discover that many students associate OR and LI'. But, as we all know, OR is more than LP, more than a collection of mathematical techniques. I will argue that a way of dispelling prejudice is to engage in OR teaching in such a way that we develop technical ability, stimulate creative problem solving attitudes and build teamnwork into the syllabus.
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I will start with a metaphor. Teaching OR is like teaching Art. Fine Art students need to know how to mix colours, how to hold a brush, how to carve a stone. But this by itself does not teach them how to
produce a work of art. How does one create an artist? Perhaps this cannot be done: some people are born artists and others are not. lt would be
unthinkable to structure a Fine Art course around a set of twenty lectures, ten classes and a textbook. Art students know that they have to do much work of their own in order to reach a satisfactory standard. Those students who can produce good work of the required standard will welcome the opportunity to show what they can create. Why should we not apply the same principles to mathematical subjects? lt is said that Blaise Pascal used to hold the view that it is absurd to try to teach how to think mathematically. But, are we giving students an opportuni-
ty to display their mathematical flair when they have it? Are we falling into the trap of teaching techniques without stimulating modelling creativity? How can we do both? In the case of a Fine Art
course we would take students to the museum to see works of art; we would ask them to produce a work on a particular topic and we would give them a free hand to choose their own technique and style; we might even ask them to work in groups. As I see it, the same principles should apply to a Mathematical Programming (MP) course.
How is a traditional MP course organised? A
normal pre-requisite is a Matrix Algebra introducCoptright @ /996 Operational Research Society.
tion. This is followed by a graphical approach to solving LP problems. Inevitably, this is continued
by the workings out of the Simplex algorithm with a discussion of sensitivity analysis and duality. This
forms the basics. Depending on time available, extensions such as Integer Programming, Goal Programming, Data Envelopment Analysis, Quad-
ratic Programming and Dynamic Programming complete the syllabus. It can be done at various
levels of mathematical sophistication. Such a course would typically include some more or less mechanistic standard exercises and some experience in the use of a small computer package to solve small arti-
ficial problems. The course would be assessed by means of a traditional written examination in which some students would do be
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