A Hierarchical Multi-Period Approach to Integrated Facility Location and Network Design Problem

Document Type : Research Paper

Authors

1 Associate Professor, Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran

2 M.Sc., Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran

3 Ph.D. Candidate, Department of Industrial Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran

Abstract

This study addresses an integrated problem of hierarchical facility location and network design, which involves multiple decisions about the opening of facilities and network links at various levels. We introduce a novel multi-period model that integrates these problems, taking into account budgetary constraints and addressing the specific challenge of optimizing hierarchical upgrades for urban centers and transportation network links within each time period. The aim is to determine the optimal upgrade levels for urban centers and transportation network links in each time period, subject to a predefined budget. The proposed model is formulated as a mixed-integer linear programming problem. To solve the developed model, we employ a heuristic algorithm that combines simulated annealing with different neighborhood structures and fix-and-optimize strategies. The efficiency of the proposed algorithm is demonstrated through various instances, showing superior performance compared to the CPLEX solver, especially for larger problem instances. Furthermore, we illustrate the practical utility of this model in real-world decision-making processes, underscoring its efficacy. By addressing these factors, the proposed model provides valuable insights for organizational managers and planners.

Keywords

Main Subjects

References

[1] R. D. Galv, L. Gonzalo, A. Espejo, and B. Boffey, “Discrete Optimization A hierarchical model for the location of perinatal facilities in the municipality of Rio de Janeiro,” European Journal of Operational Research, vol. 138, pp. 495–517, 2002.
[2] R. D. Galva, L. Gonzalo, A. Espejo, B. Boffey, and D. Yates, “Load balancing and capacity constraints in a hierarchical location model,” European Journal of Operational Research, vol. 172, pp. 631–646, 2006.
[3] V. Yasenovskiy and J. Hodgson, “Hierarchical location-allocation with spatial choice interaction modeling,” Annals of the Association of American Geographers, vol. 97, no. 3, pp. 496–511, 2007.
[4] Y. Song and C. Teng, “Optimal decision model and improved genetic algorithm for disposition of hierarchical facilities under hybrid service availability,” Computers and Industrial Engineering, vol. 130, no. February, pp. 420–429, 2019.
[5] H. Jang and J. Lee, “A hierarchical location model for determining capacities of neonatal intensive care units in Korea,” Socio-Economic Planning Sciences, 2019.
[6] N. Zarrinpoor, M. S. Fallahnezhad, and M. S. Pishvaee, “The design of a reliable and robust hierarchical health service network using an accelerated Benders decomposition algorithm,” European Journal of Operational Research, vol. 265, no. 3, pp. 1013–1032, 2018.
[7] J. Kratica, D. Dugošija, and A. Savić, “A new mixed integer linear programming model for the multi level uncapacitated facility location problem,” Applied Mathematical Modelling, vol. 38, no. 7–8, pp. 2118–2129, 2014.
[8] S. J. Ratick, J. P. Osleeb, and D. Hozumi, “Application and extension of the Moore and ReVelle Hierarchical Maximal Covering Model,” Socio-Economic Planning Sciences, vol. 43, no. 2, pp. 92–101, 2009.
[9] S. Melkote and M. S. Daskin, “An Integrated Model of Facility Location and Transportation Network Design,” TRansportation Research Part A, no. 35, pp. 515–538, 2001.
[10]         S. Melkote, “Integrated Models of Facility Location and Network Design,” Northwestren University, 1996.
[11]         S. Melkote and M. S. Daskin, “Capacitated facility location / network design problem,” European Journal of Operational Research, pp. 481–495, 2001.
[12]         C. Cocking and G. Reinelt, “Heuristics for Budget Facility Location–Network Design Problems with Minisum Objective,” in Operations Research Proceedings 2008, 2008, pp. 563–568.
[13]         Z. Drezner and G. O. Wesolowsky, “Network design : selection and design of links and facility location,” TRansportation Research Part A, vol. 37, pp. 241–256, 2003.
[14]         J. F. Bigotte, D. Krass, A. P. Antunes, and O. Berman, “Integrated modeling of urban hierarchy and transportation network planning,” Transportation Research Part A, vol. 44, no. 7, pp. 506–522, 2010.
[15]         I. Contreras and E. Fernández, “General network design: A unified view of combined location and network design problems,” European Journal of Operational Research, vol. 219, no. 3, pp. 680–697, 2012.
[16]         G. Reinelt, I. Contreras, and E. Ferna, “Minimizing the maximum travel time in a combined model of facility location and network design,” Omega, vol. 40, pp. 847–860, 2012.
[17]         A. Ghaderi and M. S. Jabalameli, “Modeling the budget-constrained dynamic uncapacitated facility location-network design problem and solving it via two efficient heuristics: A case study of health care,” Mathematical and Computer Modelling, vol. 57, no. 3–4, pp. 382–400, 2013.
[18]         R. Rahmaniani and A. Ghaderi, “A combined facility location and network design problem with multi-type of capacitated links,” Applied Mathematical Modelling, vol. 37, no. 9, pp. 6400–6414, 2013.
[19]         R. Rahmaniani and M. A. Shafia, “A study on maximum covering transportation network design with facility location under uncertainty,” Journal of Industrial and Production Engineering, 2013.
[20]         D. Shishebori, M. S. Jabalameli, and A. Jabbarzadeh, “Facility Location-Network Design Problem : Reliability and Investment Budget Constraint,” no. 2008, pp. 1–10, 2009.
[21]         D. Shishebori and A. Yousefi Babadi, “Robust and reliable medical services network design under uncertain environment and system disruptions,” Transportation Research Part E: Logistics and Transportation Review, vol. 77, pp. 268–288, 2015.
[22]         R. Rahmaniani and A. Ghaderi, “An algorithm with different exploration mechanisms: Experimental results to capacitated facility location/network design problem,” Expert Systems with Applications, vol. 42, no. 7, pp. 3790–3800, 2015.
[23]         R. H. Pearce and M. Forbes, “Disaggregated Benders decomposition and branch-and-cut for solving the budget-constrained dynamic uncapacitated facility location and network design problem,” European Journal of Operational Research, vol. 270, no. 1, pp. 78–88, 2018.
[24]         A. A. Sadatasl, M. H. Fazel Zarandi, and A. Sadeghi, “A combined facility location and network design model with multi-type of capacitated links and backup facility and non-deterministic demand by fuzzy logic,” Annual Conference of the North American Fuzzy Information Processing Society - NAFIPS, vol. 0, 2016.
[25]         A. A. Sadat Asl, M. H. Fazel Zarandi, S. Sotudian, and A. Amini, “A fuzzy capacitated facility location-network design model: A hybrid firefly and invasive weed optimization (FIWO) solution,” Iranian Journal of Fuzzy Systems, vol. 17, no. 2, pp. 79–95, 2020.
[26]         M. A. Brahami, M. Dahane, M. Souier, and M. Sahnoun, “Sustainable capacitated facility location/network design problem: a Non-dominated Sorting Genetic Algorithm based multiobjective approach,” Annals of Operations Research, vol. 311, no. 2, pp. 821–852, 2020.
[27]         P. Pourrezaie-khaligh, A. Bozorgi-amiri, and A. Yousefi-babadi, “Fix-and-optimize approach for a healthcare facility location / network design problem considering equity and accessibility : A case study,” Applied Mathematical Modelling, vol. 102, pp. 243–267, 2022.
[28]         S. C. Narula and U. I. Ogbu, “An Hierarchal Location-Allocation Problem,” Omega, vol. 7, no. 2, pp. 137–143, 1979.
[29]         G. Sahin and H. Süral, “A review of hierarchical facility location models,” Computers & Operations Research, vol. 34, pp. 2310–2331, 2007.
[30]         A. Antunes, O. Berman, J. F. Bigotte, and D. Krass, “A location model for urban hierarchy planning with population dynamics,” Environment and Planning, vol. 41, pp. 996–1017, 2009.
[31]         V. Ghezavati, F. Soltanzadeh, and A. Hafezalkotob, “Optimization of reliability for a hierarchical facility location problem under disaster relief situations by a chance-constrained programming and robust optimization,” Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, vol. 229, no. 6, pp. 542–555, 2015.
[32]         M. M. Rastaghi, F. Barzinpour, and M. S. Pishvaee, “A Multi-objective Hierarchical Location-allocation Model for the Healthcare Network Design Considering a Referral System,” International Journal of Engineering, vol. 31, no. 2, pp. 365–373, 2018.
[33]         A. Balakrishnan, T. L. Magnanti, and P. Mirchandani, “Modeling and Heuristic Worst-case Performance Analysis of the Two-level Network Design Problem,” Management Science, vol. 40, no. 7, pp. 846–867, 1994.
Advances in Industrial Engineering
Volume 59, Issue 1
June 2025
Pages 23-41

Files

Share

How to cite

Statistics