Facility Location: A Robust Optimization Approach
Article first published online: 15 NOV 2010
© 2010 Production and Operations Management Society
Production and Operations Management
Volume 20, Issue 5, pages 772–785, September/October 2011
How to Cite
Baron, O., Milner, J. and Naseraldin, H. (2011), Facility Location: A Robust Optimization Approach. Production and Operations Management, 20: 772–785. doi: 10.1111/j.1937-5956.2010.01194.x
- Issue published online: 13 SEP 2011
- Article first published online: 15 NOV 2010
- History: Received: November 2008; Accepted: June 2010 by Panos Kouvelis, after 1 revision.
- facility location;
- robust optimization;
- robust counterpart
In this research, we apply robust optimization (RO) to the problem of locating facilities in a network facing uncertain demand over multiple periods. We consider a multi-period fixed-charge network location problem for which we find (1) the number of facilities, their location and capacities, (2) the production in each period, and (3) allocation of demand to facilities. Using the RO approach we formulate the problem to include alternate levels of uncertainty over the periods. We consider two models of demand uncertainty: demand within a bounded and symmetric multi-dimensional box, and demand within a multi-dimensional ellipsoid. We evaluate the potential benefits of applying the RO approach in our setting using an extensive numerical study. We show that the alternate models of uncertainty lead to very different solution network topologies, with the model with box uncertainty set opening fewer, larger facilities. Through sample path testing, we show that both the box and ellipsoidal uncertainty cases can provide small but significant improvements over the solution to the problem when demand is deterministic and set at its nominal value. For changes in several environmental parameters, we explore the effects on the solution performance.