A Reliable Budget-Constrained FL/ND 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.

[1]  Mohamad Saeed Jabalameli,et al.  Modeling the budget-constrained dynamic uncapacitated facility location-network design problem and solving it via two efficient heuristics: A case study of health care , 2013, Math. Comput. Model..

[2]  Oded Berman,et al.  Location and reliability problems on a line: Impact of objectives and correlated failures on optimal location patterns , 2013 .

[3]  Jesse R. O'Hanley,et al.  Designing robust coverage networks to hedge against worst-case facility losses , 2008, Eur. J. Oper. Res..

[4]  Mark S. Daskin,et al.  Capacitated facility location/network design problems , 2001, Eur. J. Oper. Res..

[5]  Charles S. ReVelle,et al.  The Location of Emergency Service Facilities , 1971, Oper. Res..

[6]  Zvi Drezner,et al.  NETWORK DESIGN: SELECTION AND DESIGN OF LINKS AND FACILITY LOCATION , 2003 .

[7]  M. John Hodgson,et al.  A network location-allocation model trading off flow capturing andp-median objectives , 1992, Ann. Oper. Res..

[8]  Lian Qi,et al.  The Effect of Supply Disruptions on Supply Chain Design Decisions , 2010, Transp. Sci..

[9]  Mohammad Saeed Jabalameli,et al.  A hybrid model for multi-objective capacitated facility location network design problem , 2011 .

[10]  Lawrence V. Snyder,et al.  Reliability Models for Facility Location: The Expected Failure Cost Case , 2005, Transp. Sci..

[11]  Armin Jabbarzadeh,et al.  Designing a Supply Chain Network under the Risk of Disruptions , 2012 .

[12]  António Pais Antunes,et al.  Integrated modeling of urban hierarchy and transportation network planning , 2010 .

[13]  Maria Paola Scaparra,et al.  Hedging against disruptions with ripple effects in location analysis , 2012 .

[14]  Alfred A. Kuehn,et al.  A Heuristic Program for Locating Warehouses , 1963 .

[15]  Zuo-Jun Max Shen,et al.  The Reliable Facility Location Problem: Formulations, Heuristics, and Approximation Algorithms , 2011, INFORMS J. Comput..

[16]  David Simchi-Levi,et al.  A Heuristic Algorithm for the Traveling Salesman Location Problem on Networks , 1988, Oper. Res..

[17]  Iván A. Contreras,et al.  General network design: A unified view of combined location and network design problems , 2012, Eur. J. Oper. Res..

[18]  Satish V. Ukkusuri,et al.  A Voronoi-Based Heuristic Algorithm for Locating Distribution Centers in Disasters , 2012 .

[19]  Amanda J. Schmitt,et al.  OR/MS models for supply chain disruptions: a review , 2014 .

[20]  Mark S. Daskin,et al.  AN INTEGRATED MODEL OF FACILITY LOCATION AND TRANSPORTATION NETWORK DESIGN , 2001 .

[21]  Mercedes Landete,et al.  Design and analysis of hybrid metaheuristics for the Reliability p-Median Problem , 2012, Eur. J. Oper. Res..

[22]  Andrew Lim,et al.  Reliable logistics networks design with facility disruptions , 2011 .

[23]  Benjamin F. Hobbs,et al.  Nash-Cournot Equilibria in Power Markets on a Linearized DC Network with Arbitrage: Formulations and Properties , 2003 .

[24]  Alper Murat,et al.  A swarm intelligence based sample average approximation algorithm for the capacitated reliable facility location problem , 2013 .

[25]  Avijit Ghosh,et al.  Spatial analysis and location-allocation models , 1987 .

[26]  Charles ReVelle,et al.  Concepts and applications of backup coverage , 1986 .

[27]  Oded Berman,et al.  On n-facility median problem with facilities subject to failure facing uniform demand , 2011, Discret. Appl. Math..

[28]  Armin Jabbarzadeh,et al.  Facility Location-Network Design Problem: Reliability and Investment Budget Constraint , 2014 .

[29]  Oded Berman,et al.  Facility Reliability Issues in Network p-Median Problems: Strategic Centralization and Co-Location Effects , 2007, Oper. Res..

[30]  Ragheb Rahmaniani,et al.  A combined facility location and network design problem with multi-type of capacitated links , 2013 .

[31]  Alan T. Murray,et al.  Strategic Network Restoration , 2010 .

[32]  Cara Cocking Solutions to facility location-network design problems , 2008 .

[33]  Pushkin Kachroo,et al.  Dynamic Modeling of Performance Indices for Planning of Sustainable Transportation Systems , 2016 .

[34]  Richard L. Church,et al.  The maximal covering location problem , 1974 .

[35]  Ting L. Lei Identifying Critical Facilities in Hub‐and‐Spoke Networks: A Hub Interdiction Median Problem , 2013 .

[36]  Brian Tomlin,et al.  On the Value of Mitigation and Contingency Strategies for Managing Supply Chain Disruption Risks , 2006, Manag. Sci..

[37]  Qingquan Li,et al.  Finding Reliable Shortest Paths in Road Networks Under Uncertainty , 2013 .

[38]  Gerhard Reinelt,et al.  Minimizing the maximum travel time in a combined model of facility location and network design , 2012 .

[39]  S. L. Hakimi,et al.  Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph , 1964 .

[40]  M. Daskin,et al.  Integration of Multiple, Excess, Backup, and Expected Covering Models , 1988 .

[41]  Mohammad Saeed Jabalameli,et al.  Improving the Efficiency of Medical Services Systems: A New Integrated Mathematical Modeling Approach , 2013 .

[42]  K. B. Hendricks,et al.  An Empirical Analysis of the Effect of Supply Chain Disruptions on Long‐Run Stock Price Performance and Equity Risk of the Firm , 2005 .

[43]  O. Kariv,et al.  An Algorithmic Approach to Network Location Problems. II: The p-Medians , 1979 .

[44]  Zvi Drezner,et al.  Heuristic Solution Methods for Two Location Problems with Unreliable Facilities , 1987 .

[45]  Stefan Nickel,et al.  Multi-product Capacitated Single-Allocation Hub Location Problems: Formulations and Inequalities , 2014 .

[46]  Changhyun Kwon,et al.  Robust Facility Location Problem for Hazardous Waste Transportation , 2014 .

[47]  Hyun Kim,et al.  Reliable P-Hub Location Problems in Telecommunication Networks , 2009 .