The multicommodity maximal covering network design problem

We introduce the multicommodity maximal covering network design problem (MCNDP) in the context of determining critical routes for earthquake management. We seek low cost routes that cover the maximum population while satisfying budget constraints introduced by the need to retrofit bridges on the critical routes. The MCNDP seeks the subnetwork that minimizes the total routing cost and maximizes the total demand covered for a pre-determined set of origin-destination (O-D) pairs subject to budget constraints. An integer programming formulation of the MCNDP is presented. It is applied to an earthquake management problem in southwestern Indiana. Insights on the model are illustrated by evaluating the tradeoffs between the two objectives over a range of budget values.