Theorem and a D Algorithm for Large Scale Stochastic Integer Programming � Set Convexi cation (original) (raw)

This paper considers the two stage stochastic integer programming problems with an emphasis on problems in which integer variables appear in the second stage Drawing heavily on the theory of disjunctive programming we characterize convexi cations of the second stage problem and develop a decomposition based algorithm for the solution of such problems In particular we verify that problems with xed recourse are characterized by scenario dependent second stage convexi cations that have a great deal in common We refer to this characterization as the C Common Cut Coe cients Theorem Based on the C Theorem we develop an algorithmic methodology that we refer to as Disjunctive Decomposition D We show that when the second stage consists of MILP problems we can obtain accurate second stage objective function estimates after nitely many steps We also set the stage for comparisons between problems in which the rst stage includes only variables and those that allow both continuous and integer var...