Abstract
A staircase linear program is a linear program in which the variables can be partitioned into a set of time periods, with constraints relating only variables in adjacent periods. This paper describes a specialized technique for solving staircase LP’s, called a “nested decomposition” algorithm. This technique applies the Dantzig-Wolfe decomposition principle to the dual of the LP in a recursive manner. The resulting algorithm solves a sequence of small LP’s, one corresponding to each period. Each period communicates with the period that follows it by determining its right-hand side and with the period that precedes it by adding constraints. Some computational experience is presented.
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Dedicated to Professor George B. Dantzig on the occasion of his seventieth birthday.
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© 1985 The Mathematical Programming Society, Inc.
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Wittrock, R.J. (1985). Dual nested decomposition of staircase linear programs. In: Cottle, R.W. (eds) Mathematical Programming Essays in Honor of George B. Dantzig Part I. Mathematical Programming Studies, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121043
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DOI: https://doi.org/10.1007/BFb0121043
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