Abstract
The methodology suggested in this book is based on three mathematical tools — optimal control, combinatorics and mathematical programming — which are traditionally related to separate areas of research and application. The methodology involves, first, investigating a continuous-time problem with the aid of the maximum principle and then reducing it to a discrete combinatorial or mathematical programming problem solvable in polynomial time. The following sections present selected combinatorics, the maximum principle and a constructive approach for integrating both mathematical tools.
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Kogan, K., Khmelnitsky, E. (2000). Mathematical Background. In: Scheduling: Control-Based Theory and Polynomial-Time Algorithms. Applied Optimization, vol 43. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4675-7_2
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DOI: https://doi.org/10.1007/978-1-4615-4675-7_2
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