A Decomposition Heuristic for the Maximal Covering Location Problem

This paper proposes a cluster partitioning technique to calculate improved upper bounds to the optimal solution of maximal covering location problems. Given a covering distance, a graph is built considering as vertices the potential facility locations, and with an edge connecting each pair of facilities that attend a same client. Coupling constraints, corresponding to some edges of this graph, are identified and relaxed in the Lagrangean way, resulting in disconnected subgraphs representing smaller subproblems that are computationally easier to solve by exact methods. The proposed technique is compared to the classical approach, using real data and instances from the available literature

A Decomposition Heuristic for the Maximal Covering Location Problem

This paper proposes a cluster partitioning technique to calculate improved upper bounds to the optimal solution of maximal covering location problems. Given a covering distance, a graph is built considering as vertices the potential facility locations, and with an edge connecting each pair of facilities that attend a same client. Coupling constraints, corresponding to some edges of this graph, are identified and relaxed in the Lagrangean way, resulting in disconnected subgraphs representing smaller subproblems that are computationally easier to solve by exact methods. The proposed technique is compared to the classical approach, using real data and instances from the available literature

Optimizing the woodpulp stowage using Lagrangean relaxation with clusters

The cargo stowage process in ships consists in arranging items into holds. This paper approaches the problem of finding the maximum number of stowed units of woodpulp into holds of dedicated maritime international ships. This problem, essentially three-dimensional can be reduced for the two-dimensional case due to constraints provided by the transport, and becomes similar to the manufacturer’s pallet loading problem. We present in this paper a formulation to the woodpulp stowage solved by a lagrangean relaxation with clusters (LagClus) that considers the conflict graph generated by overlaps of woodpulp units. Computational tests are performed and compared with the real results obtained in Brazilian ports. The results obtained by LagClus were better than the real results, and consequently, it can provide savings if we look at the shipping logistics costs