Multi-Objective Multi-Period Facility Covering Location and Capacity Planning With Multiple Root Facilities Under Uncertainty
Abstract
This strategic planning framework is built upon a Multi-Objective Optimization core, balancing cost efficiency, service coverage, equity, and environmental impact. This core is intrinsically linked to Multi-Period Planning, which handles phased investment, capacity expansion, and network adaptation over time. To address real-world variability, Uncertainty Management techniques such as modeling stochastic demand, scenario-based planning, and service level constraints are integrated directly into the multi-period model. Finally, the physical and logical layout is governed by key Network Design Considerations, including the use of shortest path forests, multiple root facilities, modular capacity units, and resilience measures to ensure robust operation.
References
R.L.Church, “Alfred weber (1868–1958): The father of industrial location theory and supplychain design,” in Great Minds in Regional Science, Vol. 2. Springer, 2023, pp. 89–107.
S. L. Hakimi, “Optimum locations of switching centers and the absolute centers and medians of a graph,” Operations Research, vol. 12, no. 3, pp. 450–459, 1964. doi: 10.1287/opre.12.3.450
C. Revelle, D. Marks, and J. C. Liebman, “The maximum availability location problem,” Transportation Science, vol. 4, no. 2, pp. 137–152, 1970. doi: 10.1287/trsc.23.3.192
R. Church and C. ReVelle, “The maximal covering location problem,” Papers of the Regional Science Association, vol. 32, pp. 101–118, 1974. doi: 10.1137/0604028
J. C. Smith and Y. Song, “Discrete facility location problems with uncertainty,” European Journal of Operational Research, vol. 297, no. 3, pp. 803–816, 2022. doi: 10.1016/j.energy.2016.03.056
A. Jones, “The rural health care crisis,” Journal of Health Economics, vol. 68, p. 102234, 2019. doi: 10.1016/j.jhealeco.2019.102234
M. Schilde, K. F. Doerner, and R. F. Hartl, “Metaheuristics for the dynamic stochastic diala-ride problem with expected return transports,” Computers & Operations Research, vol. 38, no. 12, pp. 1719–1730, 2011. doi: 10.1016/j.cor.2011.02.006
V. Arabzadeh, M. I. Alizadeh, and M. P. Moghaddam, “A multi-objective optimization framework for risk-controlled integration of renewable energy sources into electricity markets,” Energy, vol. 196, p. 117080, 2020. doi: 10.1016/j.energy.2016.03.056
F. V. Louveaux, “Stochastic integer programming,” Handbooks in Operations Research and Management Science, vol. 36, pp. 183–197, 1986. doi: 10.1016/S0927-0507(03)10004-7
L. V. Snyder, “Facility location under uncertainty: a review,” IIE Transactions, vol. 38, no. 7, pp. 537–554, 2006. doi: 10.1080/07408170500216480
D. Bertsimas and A. Thiele, “Robust optimization with applications to inventory theory,” Operations Research, vol. 59, no. 1, pp. 13–24, 2011. doi: 10.1137/080734510
G. Mavrotas, “Effective implementation of the ε-constraint method in multi-objective mathematical programming problems,” Applied Mathematics and Computation, vol. 213, no. 2, pp. 455–465, 2009. doi: 10.1016/j.amc.2009.03.037
K. Deb, “Multi-objective optimization,” in Search Methodologies. Springer, 2014, pp. 403449.
Y. Kazama, R. Kiyohara, and J. Yajima, “Global optimization of facility location problems,” European Journal of Operational Research, vol. 288, no. 3, pp. 775–786, 2021. doi: 10.1016/j.ejor.2020.06.026
B. Esfandiyari, M. S. Jabalameli, and A. Jabbarzadeh, “Resilient facility location against disruption risks,” Transportation Research Part E: Logistics and Transportation Review, vol. 121, pp. 178–196, 2019. doi: 10.1016/j.tre.2018.11.006
Y. Wang, Q. Shi, and Q. Hu, “Dynamic multi-objective optimization for multi-period emergency logistics network,” Journal of Intelligent & Fuzzy Systems, vol. 37, no. 6, pp. 84718481, 2019.
M. M. Rahman and J.-C. Thill, “Facility location optimization for covid-19 vaccine distribution,” Applied Geography, vol. 135, p. 102538, 2021. doi: 10.1108/BIJ-02-2022-0089
R. Poudineh, “Electricity distribution networks post-liberalisation: Essays on economic regulation, investment, efficiency, and business model,” Ph.D. dissertation, Durham University, 2014.
J. A. Van Mieghem, “Capacity management, investment, and hedging: Review and recent developments,” Manufacturing & Service Operations Management, vol. 5, no. 4, pp. 269302, 2003.
Z. Wang and Y. Zhang, “Distributionally robust facility location under demand uncertainty,” Transportation Research Part E: Logistics and Transportation Review, vol. 169, p. 102985, 2023. doi: 10.1016/j.tre.2022.102985
A. M. Caunhye, X. Nie, and S. Pokharel, “Optimization models in emergency logistics: A literature review,” Socio-Economic Planning Sciences, vol. 46, no. 1, pp. 4–13, 2012. doi: 10.1016/j.seps.2011.04.004
A. Gupta and P. Kumar, “Equity in facility location problems: A survey,” Omega, vol. 110, p. 102619, 2022. doi: 10.1016/j.omega.2022.102619
M. M. H. Chowdhury, S. K. Paul, E. A. Khan, and A. S. Mahmud, “A decision support model for barriers and optimal strategy design in sustainable humanitarian supply chain management,” Global Journal of Flexible Systems Management, vol. 25, no. 3, pp. 467–486, 2024.
K. Miettinen, J. Hakanen, and D. Podkopaev, “Survey of methods to visualize alternatives in multiple criteria decision making problems,” OR Spectrum, vol. 34, no. 1, pp. 3–37, 2012. doi: 10.1007/s00291-011-0245-4
A. Azaron, H. Katagiri, K. Kato, and M. Sakawa, “Due date assignment in stochastic scheduling,” European Journal of Operational Research, vol. 209, no. 1, pp. 35–46, 2011. doi: 10.1016/j.ejor.2010.08.010
M. S. Daskin, Network and Discrete Location: Models, Algorithms, and Applications. John Wiley & Sons, 2011.
J. R. Birge and F. Louveaux, Introduction to Stochastic Programming. Springer Science & Business Media, 2011.
R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory, Algorithms, and Applications. Prentice Hall, 1993.
S. Melkote and M. S. Daskin, “An integrated model of facility location and transportation network design,” Transportation Research Part A: Policy and Practice, vol. 35, no. 6, pp. 515–538, 2001. doi: 10.1016/S0965-8564(00)00005-7
M. Ehrgott, Multicriteria Optimization, 2005.
S. Pineda and J. M. Morales, “Chronological multi-period capacity expansion planning,” European Journal of Operational Research, vol. 271, no. 3, pp. 1064–1077, 2018. doi: 10.1016/j.ejor.2018.06.008
D. Bertsimas, D. B. Brown, and C. Caramanis, “Theory and applications of robust optimization,” SIAM Review, vol. 53, no. 3, pp. 464–501, 2011. doi: 10.1137/080734510
M. A. Boschetti and V. Maniezzo, “A matheuristic for multi-objective optimization problems,” European Journal of Operational Research, vol. 276, no. 2, pp. 405–419, 2019. doi: 10.1016/j.ejor.2019.01.031
M.A.RahmanandR.A.Parvin, “Bangladesh’s digital evolution: Drivers, impacts, and future opportunities,” 2024.
A. Nikas and H. Doukas, “Augmented ε-constraint method for multi-objective optimization,” European Journal of Operational Research, vol. 280, no. 2, pp. 404–416, 2020. doi: 10.1016/j.ejor.2019.07.049
A. Raith and M. Schmidt, “Multi-objective facility location under uncertainty,” Computers & Operations Research, vol. 78, pp. 351–366, 2017. doi: 10.1016/j.cor.2016.09.016
P. M. Griffin and C. R. Scherrer, “Multi-period network design under demand uncertainty,” Transportation Research Part E: Logistics and Transportation Review, vol. 98, pp. 1–18, 2017. doi: 10.1016/j.tre.2016.11.003
S. L. Hakimi, “Optimum locations of switching centers and the absolute centers and medians of a graph,” Operations Research, vol. 12, no. 3, pp. 450–459, 1964. doi: 10.1287/opre.12.3.450
C. Revelle, D. Marks, and J. C. Liebman, “The maximum availability location problem,” Transportation Science, vol. 4, no. 2, pp. 137–152, 1970. doi: 10.1287/trsc.23.3.192
R. Church and C. ReVelle, “The maximal covering location problem,” Papers of the Regional Science Association, vol. 32, pp. 101–118, 1974. doi: 10.1137/0604028
J. C. Smith and Y. Song, “Discrete facility location problems with uncertainty,” European Journal of Operational Research, vol. 297, no. 3, pp. 803–816, 2022. doi: 10.1016/j.energy.2016.03.056
A. Jones, “The rural health care crisis,” Journal of Health Economics, vol. 68, p. 102234, 2019. doi: 10.1016/j.jhealeco.2019.102234
M. Schilde, K. F. Doerner, and R. F. Hartl, “Metaheuristics for the dynamic stochastic diala-ride problem with expected return transports,” Computers & Operations Research, vol. 38, no. 12, pp. 1719–1730, 2011. doi: 10.1016/j.cor.2011.02.006
V. Arabzadeh, M. I. Alizadeh, and M. P. Moghaddam, “A multi-objective optimization framework for risk-controlled integration of renewable energy sources into electricity markets,” Energy, vol. 196, p. 117080, 2020. doi: 10.1016/j.energy.2016.03.056
F. V. Louveaux, “Stochastic integer programming,” Handbooks in Operations Research and Management Science, vol. 36, pp. 183–197, 1986. doi: 10.1016/S0927-0507(03)10004-7
L. V. Snyder, “Facility location under uncertainty: a review,” IIE Transactions, vol. 38, no. 7, pp. 537–554, 2006. doi: 10.1080/07408170500216480
D. Bertsimas and A. Thiele, “Robust optimization with applications to inventory theory,” Operations Research, vol. 59, no. 1, pp. 13–24, 2011. doi: 10.1137/080734510
G. Mavrotas, “Effective implementation of the ε-constraint method in multi-objective mathematical programming problems,” Applied Mathematics and Computation, vol. 213, no. 2, pp. 455–465, 2009. doi: 10.1016/j.amc.2009.03.037
K. Deb, “Multi-objective optimization,” in Search Methodologies. Springer, 2014, pp. 403449.
Y. Kazama, R. Kiyohara, and J. Yajima, “Global optimization of facility location problems,” European Journal of Operational Research, vol. 288, no. 3, pp. 775–786, 2021. doi: 10.1016/j.ejor.2020.06.026
B. Esfandiyari, M. S. Jabalameli, and A. Jabbarzadeh, “Resilient facility location against disruption risks,” Transportation Research Part E: Logistics and Transportation Review, vol. 121, pp. 178–196, 2019. doi: 10.1016/j.tre.2018.11.006
Y. Wang, Q. Shi, and Q. Hu, “Dynamic multi-objective optimization for multi-period emergency logistics network,” Journal of Intelligent & Fuzzy Systems, vol. 37, no. 6, pp. 84718481, 2019.
M. M. Rahman and J.-C. Thill, “Facility location optimization for covid-19 vaccine distribution,” Applied Geography, vol. 135, p. 102538, 2021. doi: 10.1108/BIJ-02-2022-0089
R. Poudineh, “Electricity distribution networks post-liberalisation: Essays on economic regulation, investment, efficiency, and business model,” Ph.D. dissertation, Durham University, 2014.
J. A. Van Mieghem, “Capacity management, investment, and hedging: Review and recent developments,” Manufacturing & Service Operations Management, vol. 5, no. 4, pp. 269302, 2003.
Z. Wang and Y. Zhang, “Distributionally robust facility location under demand uncertainty,” Transportation Research Part E: Logistics and Transportation Review, vol. 169, p. 102985, 2023. doi: 10.1016/j.tre.2022.102985
A. M. Caunhye, X. Nie, and S. Pokharel, “Optimization models in emergency logistics: A literature review,” Socio-Economic Planning Sciences, vol. 46, no. 1, pp. 4–13, 2012. doi: 10.1016/j.seps.2011.04.004
A. Gupta and P. Kumar, “Equity in facility location problems: A survey,” Omega, vol. 110, p. 102619, 2022. doi: 10.1016/j.omega.2022.102619
M. M. H. Chowdhury, S. K. Paul, E. A. Khan, and A. S. Mahmud, “A decision support model for barriers and optimal strategy design in sustainable humanitarian supply chain management,” Global Journal of Flexible Systems Management, vol. 25, no. 3, pp. 467–486, 2024.
K. Miettinen, J. Hakanen, and D. Podkopaev, “Survey of methods to visualize alternatives in multiple criteria decision making problems,” OR Spectrum, vol. 34, no. 1, pp. 3–37, 2012. doi: 10.1007/s00291-011-0245-4
A. Azaron, H. Katagiri, K. Kato, and M. Sakawa, “Due date assignment in stochastic scheduling,” European Journal of Operational Research, vol. 209, no. 1, pp. 35–46, 2011. doi: 10.1016/j.ejor.2010.08.010
M. S. Daskin, Network and Discrete Location: Models, Algorithms, and Applications. John Wiley & Sons, 2011.
J. R. Birge and F. Louveaux, Introduction to Stochastic Programming. Springer Science & Business Media, 2011.
R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory, Algorithms, and Applications. Prentice Hall, 1993.
S. Melkote and M. S. Daskin, “An integrated model of facility location and transportation network design,” Transportation Research Part A: Policy and Practice, vol. 35, no. 6, pp. 515–538, 2001. doi: 10.1016/S0965-8564(00)00005-7
M. Ehrgott, Multicriteria Optimization, 2005.
S. Pineda and J. M. Morales, “Chronological multi-period capacity expansion planning,” European Journal of Operational Research, vol. 271, no. 3, pp. 1064–1077, 2018. doi: 10.1016/j.ejor.2018.06.008
D. Bertsimas, D. B. Brown, and C. Caramanis, “Theory and applications of robust optimization,” SIAM Review, vol. 53, no. 3, pp. 464–501, 2011. doi: 10.1137/080734510
M. A. Boschetti and V. Maniezzo, “A matheuristic for multi-objective optimization problems,” European Journal of Operational Research, vol. 276, no. 2, pp. 405–419, 2019. doi: 10.1016/j.ejor.2019.01.031
M.A.RahmanandR.A.Parvin, “Bangladesh’s digital evolution: Drivers, impacts, and future opportunities,” 2024.
A. Nikas and H. Doukas, “Augmented ε-constraint method for multi-objective optimization,” European Journal of Operational Research, vol. 280, no. 2, pp. 404–416, 2020. doi: 10.1016/j.ejor.2019.07.049
A. Raith and M. Schmidt, “Multi-objective facility location under uncertainty,” Computers & Operations Research, vol. 78, pp. 351–366, 2017. doi: 10.1016/j.cor.2016.09.016
P. M. Griffin and C. R. Scherrer, “Multi-period network design under demand uncertainty,” Transportation Research Part E: Logistics and Transportation Review, vol. 98, pp. 1–18, 2017. doi: 10.1016/j.tre.2016.11.003
Published
2025-12-17
How to Cite
HAILEMARIAM, Girma; THILLAIGOVINDAN, Natesan; ALEMAYHU, Getenet.
Multi-Objective Multi-Period Facility Covering Location and Capacity Planning With Multiple Root Facilities Under Uncertainty.
Yugoslav Journal of Operations Research, [S.l.], dec. 2025.
ISSN 2334-6043.
Available at: <https://yujor.fon.bg.ac.rs/index.php/yujor/article/view/1376>. Date accessed: 20 dec. 2025.
doi: https://doi.org/10.2298/YJOR250715043H.
Issue
Section
Research Articles
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
