A multi-objective robust optimization model to design a network for Emergency Medical Services under uncertainty conditions: A case study

Document Type: Research Paper


School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran


The present research introduces a multi-objective robust optimization model to design emergency medical services network for uncertain costs and demands. The proposed model determines the location and the optimum capacity of relief medical service centers. In addition, the model determines the number and the type of ambulances that should be placed in each of the centers and allocated to demand zones. The multi-objective model attempts to maximize the coverage of demand zones, the availability of ambulances and minimizing the total costs simultaneously. A robust model is applied to our real word case study in an urban district.


Main Subjects

Alexandris, G., & Giannikos, I. (2010). A new model for maximal coverage exploiting GIS capabilities. European Journal of Operational Research, 202(2), 328-338.


Araz, C., Selim, H., & Ozkarahan, I. (2007). A fuzzy multi-objective covering-based vehicle location model for emergency services. Computers & Operations Research, 34(3), 705-726.


Asiedu, Y., & Rempel, M. (2011). A multiobjective coverage‐based model for Civilian search and rescue. Naval Research Logistics (NRL)58(3), 167-179.


Bardossy, M. G., & Raghavan, S. (2013). Robust optimization for the connected facility location problem. Electronic Notes in Discrete Mathematics, 44, 149-154.


Batanović, V., Petrović, D., & Petrović, R. (2009). Fuzzy logic based algorithms for maximum covering location problems. Information Sciences, 179(1-2), 120-129.


Ben-Tal, A., & Nemirovski, A. (2000). Robust solutions of linear programming problems contaminated with uncertain data. Mathematical programming, 88(3), 411-424.


Berman, O., & Wang, J. (2011). The minmax regret gradual covering location problem on a network with incomplete information of demand weights. European Journal of Operational Research, 208(3), 233-238.


Berman, O., Drezner, Z., & Wesolowsky, G. O. (2009). The maximal covering problem with some negative weights. Geographical analysis, 41(1), 30-42.

Berman, O., & Krass, D. (2002). The generalized maximal covering location problem. Computers & Operations Research, 29(6), 563-581.


Bertsimas, D., & Sim, M. (2004). The price of robustness. Operations research, 52(1), 35-53.


Blanquero, R., Carrizosa, E., & Hendrix, E. M. (2011). Locating a competitive facility in the plane with a robustness criterion. European Journal of Operational Research, 215(1), 21-24.


Church, R., & ReVelle, C. (1974, December). The maximal covering location problem. In Papers of the Regional Science Association (Vol. 32, No. 1, pp. 101-118). Springer-Verlag.


Curtin, K. M., Hayslett-McCall, K., & Qiu, F. (2010). Determining optimal police patrol areas with maximal covering and backup covering location models. Networks and Spatial Economics, 10(1), 125-145.


de Assis Corrêa, F., Lorena, L. A. N., & Ribeiro, G. M. (2009). A decomposition approach for the probabilistic maximal covering location-allocation problem. Computers & Operations Research, 36(10), 2729-2739.


Geroliminis, N., Karlaftis, M. G., & Skabardonis, A. (2009). A spatial queuing model for the emergency vehicle districting and location problem. Transportation research part B: methodological, 43(7), 798-811.


Gülpınar, N., Pachamanova, D., & Çanakoğlu, E. (2013). Robust strategies for facility location under uncertainty. European Journal of Operational Research, 225(1), 21-35.


Ibri, S., Nourelfath, M., & Drias, H. (2012). A multi-agent approach for integrated emergency vehicle dispatching and covering problem. Engineering Applications of Artificial Intelligence, 25(3), 554-565.


Indriasari, V., Mahmud, A. R., Ahmad, N., & Shariff, A. R. M. (2010). Maximal service area problem for optimal siting of emergency facilities. International Journal of Geographical Information Science, 24(2), 213-230.


Kanoun, I., Chabchoub, H., & Aouni, B. (2010). Goal programming model for fire and emergency service facilities site selection. INFOR: Information Systems and Operational Research, 48(3), 143-153.


Mavrotas, G. (2009). Effective implementation of the ε-constraint method in multi-objective mathematical programming problems. Applied mathematics and computation, 213(2), 455-465.


Moore, G. C., & ReVelle, C. (1982). The hierarchical service location problem. Management science, 28(7), 775-780.


Murawski, L., & Church, R. L. (2009). Improving accessibility to rural health services: The maximal covering network improvement problem. Socio-Economic Planning Sciences, 43(2), 102-110.


Navazi, F., Tavakkoli-Moghaddam, R., & Sazvar, Z. (2018). A Multi-Period Location-Allocation-Inventory Problem for Ambulance and Helicopter Ambulance Stations: Robust Possibilistic Approach. IFAC-PapersOnLine, 51(11), 322-327.


Nikulin, Y. (2006). Robustness in combinatorial optimization and scheduling theory: An extended annotated bibliography (No. 606). Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel.


Noyan, N. (2010). Alternate risk measures for emergency medical service system design. Annals of Operations Research, 181(1), 559-589.


O’Hanley, J. R., & Church, R. L. (2011). Designing robust coverage networks to hedge against worst-case facility losses. European Journal of Operational Research, 209(1), 23-36.


Ratick, S. J., Osleeb, J. P., & Hozumi, D. (2009). Application and extension of the Moore and ReVelle hierarchical maximal covering model. Socio-Economic Planning Sciences, 43(2), 92-101.


Soyster, A. L. (1973). Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations research, 21(5), 1154-1157.


Shavandi, H., & Mahlooji, H. (2006). A fuzzy queuing location model with a genetic algorithm for congested systems. Applied mathematics and computation, 181(1), 440-456.


Sorensen, P., & Church, R. (2010). Integrating expected coverage and local reliability for emergency medical services location problems. Socio-Economic Planning Sciences, 44(1), 8-18.


Snyder, L. V. (2006). Facility location under uncertainty: a review. IIE transactions, 38(7), 547-564.


Yin, P., & Mu, L. (2012). Modular capacitated maximal covering location problem for the optimal siting of emergency vehicles. Applied Geography, 34, 247-254.


Zhang, J., Liu, H., Yu, G., Ruan, J., & Chan, F. T. (2019). A three-stage and multi-objective stochastic programming model to improve the sustainable rescue ability by considering secondary disasters in emergency logistics. Computers & Industrial Engineering.


Zhang, Z. H., & Jiang, H. (2014). A robust counterpart approach to the bi-objective emergency medical service design problem. Applied Mathematical Modelling, 38(3), 1033-1040.


Zokaee, S., Jabbarzadeh, A., Fahimnia, B., & Sadjadi, S. J. (2017). Robust supply chain network design: an optimization model with real world application. Annals of Operations Research, 257(1-2), 15-44.