| Instructor: | Professor David Rader |
| Time: | Periods 3 MTRF |
| Prerequisite: | MA 221, or permission of instructor (ie., some matrix algebra knowledge) |
| Credits: | 4 |
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(1) How do companies decide how much of a product to make and where
to ship it?
(2) How do theme parks manage ride capacities and visitor flows?
(3) How should we cut sheets of papers from large rolls in order
to minimize waste?
(4) How can we schedule conference basketball games when there are
many constraining situations?
(5) How do engineers layout a machine shop's floor area in order
to minimize the material handling cost (i.e., minimize the product of between-machine
flows and the distance between their locations)?
This course deals with formulating these and other problems as mathematical optimization models. We will then derive algorithms for solving such problems. In the process, we will describe how algorithms for optimization problems are typically created, from deciding what optimization criteria need to be met, how to represent potential optimal solutions, and how to improve upon current solutions until we are at the optimal one. To do all of this, we will "create" the necessary theory to show our algorithms are correct.
The mathematical models we will be studying include linear programs, integer programs, and some network models such as maximum flow models and minimum cost network flow models. In addition, we will look at how these and other models are currently being used to solve many real-world problems.
This is an applied math course for computer scientists, engineers ( especially
those with managerial aspirations) and, of course, mathematicians.
It assumes elementary background in linear algebra, especially vector/matrix
notation and arithmetic, as well as in mutivariable differential calculus.
"The importance of quantitative analysis in decision making ensures that training in operations research will continue to be valuable in obtaining employment. Employment opportunities will occur in the transportation, manufacturing, finance, and services sectors, where the use of quantitative analysis can achieve dramatic improvements in operating efficiency and profitability. "