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

Pavlo Glushko (), Csaba I. Fábián () and Achim Koberstein ()
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Pavlo Glushko: European University Viadrina
Csaba I. Fábián: John von Neumann University
Achim Koberstein: European University Viadrina

Computational Management Science, 2022, vol. 19, issue 4, No 1, 539-565

Abstract: Abstract 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.

Keywords: Stochastic programming; L-shaped method; Lift-and-project cuts; Benders’ decomposition (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10287-022-00426-y

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