Dual nested decomposition of staircase linear programs

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.