OR/MS Today - August 1997 - Issues in Education

OR/MS Today, August 1997

Students Sink Their Teeth Into
Fun LP Problems

By Nicola Petty

It was my first year teaching a first-year course in operations research. I needed to come up with a linear programming assignment. It was a class of 600, most of whom were doing the course as a pre-requisite for later business courses. The class included mainly 18-year-olds with some mature students. The level of motivation was varied, and there was even some antagonism to the quantitative nature of the latter part of the course.

The point of teaching linear programming was to introduce the students to an optimizing method. It was also to develop their skills in using Excel, and to help them gain an appreciation of "real-life" possibilities for OR/MS. What was I to do?

A colleague showed me the "Big Mac Attack" article in OR/MS Today [Robert A. Bosch, Vol. 20, No. 4]. It was the answer. The assignment was very successful, in ways that have already been discussed in the original article.

This was all wonderful, and a good start to life with an entry-level OR course, but 12 months later I had to invent another assignment, a similarly exciting, open-ended problem.

Here are the ideas I came up with for the next two years. Both have been extremely successful in getting the students involved in the problem.

The Hiking Diet Problem (1995)
The instructions to the students are as follows:

"You are going hiking for three days. You want to work out what food to take. The food must be within certain specifications in terms of nutrition and cost. You want to minimize the weight of the food."

An accompanying table gave a selection of 17 food items with their associated energy, carbohydrate, protein, fat, fiber and salt values. The daily requirements for one person were also given, and a cost constraint of $30 for three days.

Again the students found the problem relevant and involving. The original solution was unpalatable. It consisted of margarine, skim milk and dehydrated potato patties. The minimum weight was 1.58kg, and the cost was $26.90.

Although this was clearly not a suitable solution, it provided a lower bound for the weight. There were several interesting effects which helped to encourage the students to think about the problem further. As the problem became more tightly constrained, the price often decreased, as the light items were more expensive. The students also discovered that bounds set too tightly could lead to unfeasibility.

One student commented to her tutor, "I hated this subject and thought it had no use at all until I did this assignment. I go hiking a lot, and now I see that linear programming can be useful." Another group of students decided on their own solution and set off hiking to try it out.

The Combie Shop Problem (1996)
Instructions to the students read:

"You are going to a Folk Festival in the country for a week. You are going to load up your VW Combie van with items to sell and try to make as much profit as possible. The van can carry you and your friend and your gear, plus 500kg of items to sell. There is space for about 1.5m by 1m by 1.5m of goods to sell. Between the two of you, you manage to scrape together $4,000 of capital with which to buy the goods."

A table was available on the network with the relevant data for this assignment. It included the volume, cost price, selling price and weight of 20 possible items. With a smaller class it could be beneficial to have them collect the data.

The initial solution includes very large numbers of condoms and soap. The students found this amusing, but realized that it might be less than practical. Again, there was interesting discussion of the relevant hard and soft aspects of the problem.

The Value of This Kind of Assignment

These exercises allow students to answer to their own level. Very capable students did extremely interesting analyses, while the less able students were still able to experience success by finding an answer.
The students are interested. Young men and women straight from high school have somewhat limited life experience, and many business applications are irrelevant at their level of understanding. However, eating at McDonald's, hiking and selling out of a van are nearer to what interests them.
The actual problems are simple. This means the effort is spent working with linear programming and sensitivity analysis, rather than in trying to understand the actual problem behind it. (Other assignments or exercises aim at that.)
The problems are real, if eating for a month at a fast food outlet could be classified as real. The numbers are not simplified or the choices cut down. There are soft constraints. Students' ideas of a reasonable diet are subjective &endash; a reality in the world of operations research. The grading is straightforward. Marks were awarded for a correct formulation and answer to the original problem, style of spreadsheet design and the analysis of the later solutions. It was not difficult to set up a marking scheme for the tutors to mark in a consistent fashion.

Conclusions
Exercises such as these go a long way in catching the imagination of the students. They give a taste of the practicality of OR/MS. The students like them.

Nicola Petty is a lecturer in Management Science at the University of Canterbury, Christchurch, New Zealand.

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