Extensions to a Lagrangean relaxation approach for the capacitated warehouse location problem (with N.Christofides), European Journal of Operational Research, vol.12, 1983, pp19-28
In this paper we present a lower bound for the capacitated warehouse location problem based upon the lagrangean relaxation of a mixed-integer formulation of the problem, where we use subgradient optimisation in an attempt to maximise this lower bound. Problem reduction tests based upon this lower bound and the original problem are given. Incorporating this bound and the reduction tests into a tree search procedure enables us to solve problems involving up to 50 warehouses and 150 customers.
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J E Beasley