Synopsis
Explore how changing the right-hand side reshapes integer programming, using a practical branch-and-bound approach.
This paper develops a parametric view of the right-hand-side case and shows how to drive a direction through the feasible region while tracking optimal solutions.
In a clear, step-by-step way, the work adapts a simple LP-based branch-and-bound framework to handle parametric right-hand sides. It introduces how to compute and use lower and upper bound functions that depend on the parameter, and it explains how to identify incumbents and update bounds as the parameter varies. The result is a method that can reveal how optimal solutions change as inputs shift, with careful tests to prune unlikely branches.- Learn how the algorithm extends a prototype branch-and-bound method to parametric integer programming.
- See how bounds are redefined as functions and how dual solutions provide powerful, data-driven tests.
- Understand the practical steps: solving subproblems, generating bound functions, using heuristics, and splitting candidate problems.
- Review an example and computational results that illustrate how the method behaves on real problems.
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Parametric Integer Programming: The Right-Hand-Side Case (Classic Reprint)
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