Mathematical definition of a goal programming model

Question

I am evaluating Wolfram Mathematica 8 for a university course project.

I'm having difficulty defining a goal programming model. Firstly, because I am very poor in math :) Secondly, because I found in the official documentation (look for "Multipurpose optimization: programming goals",).

I am trying to define a small model for resource allocation during the maintenance phase of a software project. This model definition is unofficial :

Don't worry about function . This is an activation function that returns 1 if the number of hours exceeds a threshold value. A threshold is the average number of hours it takes to fix a bug.

Please do not comment on the usefulness of this model: this is not the purpose of the course. In addition, the number of hours here is random, for testing.

I ask for help expressing this informal model in the Mathematica goal programming model. That is, I am having problems with syntax and built-in functions.

Comment here if you need more information, I will provide them.

For moderators: linear goals and tag modeling can be useful here, but I don’t have a reputation for creating them.

Answer 1

This is how I solved it. Probably :) My professor will tell.

Of course, this is not elegant, keep in mind that I have been using Mathematica for a couple of weeks, and I have never done such a development before.

It uses a conventional target programming model, such as the model proposed by Ignizio, JP (1978) .

At the moment, there is only one “stage” of minimization.

I provide screenshots if some of you are interested in the source code, just write a comment with some contact details.

1 : Overview of goal programming: a multi-criteria analysis tool. James P. Ignizio Journal of the Society for Operational Research, vol. 29, No. 11 (November 1978), pp. 1109-1119 http://www.jstor.org/stable/10.2307/3009359