Integer Linear Programming

H. A. Eiselt and Carl-Louis Sandblom
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H. A. Eiselt: University of New Brunswick
Carl-Louis Sandblom: Dalhousie University

Chapter 5 in Operations Research, 2022, pp 161-213 from Springer

Abstract: Abstract Not too long after more and more applications of linear programming were developed it became apparent that in some of these applications, the variables would not be able to attain just any (nonnegative) value but should be integers. As a simple example, if a variable has been defined to denote the number of cans of beans manufactured in the planning period, then surely it would make no sense to make, say, 1,305,557.3 cans: the last 0.3 cans would have to be rounded up or down. While this may be an acceptable practice when dealing with this application (after all, it makes very little difference whether or not we make 0.3 cans more or less), in other applications this may make a huge difference. For instance, assigning airplanes to routes or trucks to deliveries may very well make the difference between gain and loss. Furthermore, simply rounding up or down a noninteger (usually referred to as a continuous solution) will not necessarily result in an optimal integer solution. We will demonstrate this fact below.

Date: 2022
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DOI: 10.1007/978-3-030-97162-5_5

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