Abstract
This is the first of a pair of chapters that deal with optimization problems on “directed networks.” This chapter is focused on path-length problems, the next on network-flow problems. Path-length problems are ubiquitous. A variety of path-length problems will be posted in this chapter. They will be solved by linear programming and, where appropriate, by other methods.
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Notes
- 1.
Richard Bellman’s books include the classic, Dynamic Programming, Princeton University Press, 1957, reprinted by Dover Publications, 2003.
- 2.
Richard Bellman, Eye of the Hurricane: an Autobiography, World Scientific Publishing Co, Singapore, 1984.
- 3.
See, for instance, E. V. Denardo and B. L. Fox, “Shortest-route methods: 1. Reaching, pruning and buckets,” Operations Research, 27, pp. 161-186, 1979.
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Denardo, E.V. (2011). Path Length Problems and Dynamic Programming. In: Linear Programming and Generalizations. International Series in Operations Research & Management Science, vol 149. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-6491-5_8
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DOI: https://doi.org/10.1007/978-1-4419-6491-5_8
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