Primal and dual bounds for the vertex p-median problem with balance constraints

In this paper the vertex p -median problem with balance constraints is studied (i.e. it is required to group a set of objects into groups, balanced with respect to some measures of activity). A Lagrangean relaxation scheme is proposed to obtain lower bounds and a primal heuristic is proposed to obtain upper bounds for the problem. A heuristic procedure is used to obtain feasible solutions for the problem. This heuristic procedure first provides feasible allocations given a set of medians, then improves the solutions using a median exchange procedure. Two set of instances are used to test all methods. Computational results show that the proposed methods provide good lower and upper bounds in reasonable computing times.