An L-shaped method with strengthened lift-and-project cuts

Lift-and-project (L &P) cuts are well-known general 0–1 programming cuts which are typically deployed in branch-and-cut methods to solve MILP problems. In this article, we discuss ways to use these cuts within the framework of Benders’ decomposition algorithms for solving two-stage mixed-binary stochastic problems with binary first-stage variables and continuous recourse. In particular, we show how L &P cuts derived for the master problem can be strengthened with the second-stage information. An adapted L-shaped algorithm and its computational efficiency analysis is presented. We show that the strengthened L &P cuts can significantly reduce the number of iterations and the solution time.