JRP Submission ID#96
Submitted on May 11, 2007

TITLE: Formalizing the Problem Definition Stage in Operations Research

ABSTRACT: This paper looks at the problem definition stage, choosing
what information from a problem to represent, in several research
domains. The problem definition stage seems to have been overlooked in
Operations Research (OR). A step towards formalizing the problem
definition stage as part of the problem solving process is made by
creating evaluation criteria for the timetabling problem at the
faculty of applied science and engineering at the University of Toronto.

Keywords: Operations Research; problem definition; optimization;
university course timetabling

EXCERPTS:

Each combination of assumptions creates a specific problem definition.
These definitions, although they describe the same problem are not
mathematically equivalent. Each problem definition will create a
different model and will result in a different solution to the
problem. This solution must be checked to ensure that it works in the
real world. One can imagine that there are sets of assumptions that
will create a solution that is unusable as well as sets of assumptions
that do not simplify the problem enough to make any difference. Often,
models have objective functions. However, those optimization criteria
do not necessarily measure how well the solution works in the real
world. . . .

The problem definition can be illustrated using the example of integer
programming (IP). IPs can be difficult to solve since there is no
generic, computationally effective algorithm for solving them. A
classic assumption to simplify an IP is to relax the integrality
constraint and formulate it as a linear program (LP). . . .

In this section, we look at the problem definition stage in software
engineering, enterprise modeling, and OR. . . .


Interested reviewers may please respond.

DP
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