We investigate solution approaches for large instances of the capacitated facility location problem (CFLP). we present details of a Lagrangean Decomposition algorithm for solving such problems. We introduce a new tightening constraint and dual estimates that lead to improved lower bounds. In our computer environment, we describe a number of Greedy heuristics that provide good upper bound solutions. We describe how these results can be exploited by warm starting our upper bound procedure in the Lagrangean Decomposition approach. We present our results that indicate the benefits of being able to incorporate these warm starts. We show for small instances of the CFLP, it is effective to have tight linking constraints. We report results that illustrate the trade off between these constraints, solution time, and solution quality. We describe an effective routine, whereby at each pass in the algorithm, these constraints can be sequentially added. We present a new heuristic called the ¿unit cost technique¿, to improve the upper bound. Also we show through solving very large instances of the CFLP that our algorithm scales up well in terms of computational time and solution quality.