A New Decomposition Method for Birandom Programming and Its Application

Birandom programming (BRP) is an important class of uncertain programming models, and its interesting applications can be found in the literature. In this paper, we further develop this issue and present a new solution method for two-stage BRP problems, which is a kind of expected value models. Based on the concept of birandom variables, we first build two-stage BRP problems, and then discuss some properties for discrete birandom variables with fixed recourse. After that, by exploiting the properties and special structure of two-stage BRP problems with discrete distribution, we develop a modified multicut L-shaped algorithm to solve it. At last, we utilize the developed algorithm to solve an multi-product multi-period (MPMP) production planning problem with birandom demands.