The Department of Operations Research at the University of North Carolina realizes the vital need on campus for students to be able to recognize the importance of the computer as a tool in solving complex social and economic problems, and to develop the skills necessary to model and solve these problems using available software. The department has been a leader in making computational tools an integral part of its teaching curriculum. To reach the widest - and specifically, a more non-technical - audience, however, it is important to be able to introduce students to the most widely-used software models in a computing environment that involves a minimum of technical hassle and knowledge of computer details. This was the main outcome of the project A Curriculum in Modeling and Solving Problems Using Computers performed under one of the 1996-97 Chancellor's Awards for Instructional Technology .

The result of this project is IDEAS, the Operations Research Instructional Database for Educational and Academic Software. IDEAS is actually a computing platform that enables an instructor to develop software tools in a computationally intensive environment, while at the same time letting the students use these tools in a technologically friendly setting. Written in the powerful MATLAB language for technical computing, its purpose is to present computational models to students in a way that shows them how the model components interact, lets them work through solution techniques, and helps them find and test solutions for these problems using powerful MATLAB operations. The entire platform is windows-driven, so that the student merely has to click buttons and fill in the blanks in order to formulate and solve problems using the appropriate model.

IDEAS can be easily loaded as a MATLAB application and run in any computer laboratory, classroom computer, or personal computer that has MATLAB installed. (It is currently operational in the Mathematical Sciences Laboratory in Phillips Hall, and is being used in the master classroom in Smith Building.) It can be set up to start simply by clicking on the appropriate icon for IDEAS. The user is immediately presented with easy-to-understand choices for the courses, models, and specific examples relevant to the course material of interest.
 

To illustrate the power of the IDEAS software, we give an example of a set of windows that might be used for demonstrating the concept of a linear programming model. This model comes up in a wide variety of applications involving the efficient use of scarce resources. Because it is a complex mathematical model it can be difficult for the student to understand both how it models a real-life situation and how a solution can be found. The IDEAS software package can be used to aid the teaching of both these issues in a number of different ways. We will present an example of a simple linear program that models the most profitable production of chairs and tables using limited amounts of pine, mahogany, and labor. By invoking the linear programming model and providing the number of variables and resources, the student is provided a template with which to input the linear program itself.
 
 

The user simply has to fill in the boxes of this template, giving names to the problem, variables, and constraints, and then filling in the numbers representing the amount of each resource used by each variable, the amount of resources available, and the profit associated with each item produced. The user also has choices concerning types of variables, constraints, objective, and linear program, each choice being given by "choice menus" available at the appropriate location.

After inputting this model by hand, or reading it from a previously saved file or sample file provided by the instructor, the student can then work with the model in one of several contexts:
 
 

1. Have the computer solve the problem: the student can instruct the computer to solve the model. The computer can at the same time produce easily readable output and other analyses, such as resource pricing information sensitivity of the solution to input.

 

 
 



Figure 3: LP solution templates




2. Compete with the computer: the student can try to find a solution to the problem by trial-and-error, selecting the amounts of chairs and tables, while the computer keeps track of the amounts of pine, mahogany, and labor used for each choice. The student can then compare his or her best solution with the (optimal) solution found by the computer.

 

 
 



Figure 4: Competing with the computer




3. See a graphical representation: the computer can draw a complete 2-dimensional picture of the set of chairs and tables which satisfy the resource constraints, together with an indicator of the location of the more profitable solutions. The student can then move the associated solution point around the picture to see its relationship to both the constraint set structure and the profit indicator.

 

 
 



Figure 5: Graphical representation




4. Step through solution computations: the student can solve the problem algebraically. Here the software does all of the tedious auxiliary computations, so that the student can concentrate on the basic ideas underlying an algebraic solution to the problem, and can do further algebraic analysis with the help of the computer.

Each of the above windows can be obtained with simple point-and-click mouse access, so that the student can concentrate on the essential modeling, algebraic, and geometric features of the problem. Separate windows can be linked as well, so that, for example, the results of the algebraic computations can be simultaneously shown on the graphical picture.

The IDEAS platform has been a valuable teaching tool for several undergraduate courses taught by the Operations Research Department.  Next semester it will be the featured software for our freshman level course, Models in Decision Making, which will be taught partly in a computer laboratory setting. We currently have analogous computational tools and examples for

• transportation & assignment models
• PERT analysis
• game theory
• network models, such as shortest path, spanning trees, and Chinese postman
• probability models & distributions
• Markov chains
• queuing models
• elementary simulation

The value of the IDEAS platform is also brought out in its ability to use externally produced software packages, particularly those developed using MATLAB. We have been working with Professors J.P. Jarvis and D.R. Shier from Clemson University to incorporate their MATLAB package for creating and manipulating network models. This package has added a significant component to the software currently available in the database, and a preliminary version has been incorporated into the IDEAS set of routines.  

The Department of Operations Research is excited about the potential of the IDEAS database to provide a powerful interactive teaching tool for the presentation of computational models and software. The value of this platform is clearly not restricted to operations research courses, but could be used with curricula in mathematics, statistics, business, and any area that makes significant use of computational models and software. In bringing this software to the user in a non-technical and easy-to-use format, the IDEAS database can help to make students more aware of the role of the computer in solving difficult decision and analysis problems, and give them the most effective access to the appropriate computational tools.