A Hierarchical Lagrangean Relaxation Procedure for Solving Midterm Planning Problems

Abstract

An efficient decomposition procedure for solving midterm planning problems is developed based on Lagrangean relaxation. The basic idea of the proposed solution technique is the successive partitioning of the original problem into smaller, more computationally tractable subproblems by hierarchical relaxation of key complicating constraints. The systematic identification of these complicating constraints is accomplished by utilizing linear programming relaxation dual-multiplier information. This hierarchical Lagrangean relaxation procedure, along with an upper bound generating heuristic, is incorporated within a subgradient optimization framework. This solution strategy is found to be much more effective, in terms of both quality of solution and computational requirements, than commercial mixed-integer linear programming solvers in bracketing the optimal value, especially for larger problems.

Temporal and spatial Lagrangean decompositions in multi-site, multi-period production planning problems with sequence-dependent changeovers

“…This paper presents temporal and spatial Lagrangean decompositions that allow the independent solution of time periods, production sites, and markets. The importance of choosing between alternative Lagrangean relaxations of the same planning model is discussed by Gupta and Maranas (1999). Jackson and Grossmann (2003) use temporal decomposition for solving a multi-site, multi-period planning problem.…”

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