A reliable budget-constrained facility location / network design problem with unreliable facilities

The combined facility location and network design problem is an important practical problem for locating public and private facilities. Moreover, incorporating aspects of reliability into the modeling of facility location problems is an effective way to hedge against disruptions in the system. In this paper, we consider a combined facility location/network design problem that considers system reliability. This problem has a number of applications, many of which fall into the category of service systems, such as regional planning and locating schools, health care service centers and airline networks. Our model also includes an investment budget constraint. We propose a mixed integer programming formulation to model this problem, as well as an efficient heuristic based on the problem’s LP relaxation. Numerical results demonstrate that the proposed heuristic significantly outperforms CPLEX in terms of solution speed, while still maintaining excellent solution quality. Our results also suggest a favorable tradeoff between the “nominal cost” (including fixed facility location costs and link construction costs, as well as transportation costs) and system reliability; that is, substantial improvements in reliability are often possible with only slight increases in the total cost of investment and transportation.