A decomposition approach for a very large scale optimal diversity management problem

This paper focuses on the solution of the optimal diversity management problem formulated as a p-Median problem. The problem is solved for very large scale real instances arising in the car industry and defined on a graph with several tens of thousands of nodes and with several millions of arcs. The particularity is that the graph can consist of several non connected components. This property is used to decompose the problem into a series of p-Median subproblems of a smaller dimension. We use a greedy heuristic and a Lagrangian heuristic for each subproblem. The solution of the whole problem is obtained by solving a suitable assignment problem using a Branch-and-Bound algorithm.