Development of Variable Radius Covering Model for Locating Relief Facilities under Demand Uncertainty

Document Type : Research Paper

Authors

1 Industrial Engineering Department, Islamic Azad University, Tehran North Branch, tehran, Iran

2 Industrial Engineering Department, Engineering Faculty, Islamic Azad University, Tehran North Branch, Tehran, Iran

Abstract

Crisis Management includes planning and readiness to respond to the inevitable and unpredictable natural disasters. One of the aspects of crisis planning and management is the establishment of relief centers in suitable locations for responding promptly to potential victims after the disasters. In this paper, the problem locating relief centers in relief logistics is investigated in the framework of the problem of locating with the variable coverage radius model. It is assumed that the time to reach all points of the demands is not greater than a predetermined value.Since the population in need of relief (demand) is a function of the severity of the disaster and certainly is not determined before the occurrence, the proposed model is considered uncertain. In this paper, a robust two-objective mathematical planning model (minimizing logistics costs and maximizing the covered population) is developed with uncertain demand to determine the number, location, coverage, and capacity of different relief centers with different service levels. To evaluate the validity of the proposed model, one of the districts of Tehran was studied as a case study to determine the number and location of the relief centers, along with their capacity and type of service.
The results in the case study show we need to construct five relief centers with appropriate distribution in the region which capable of to cover 90 percent of all potential demand points.

Keywords


1. توکلی مقدم، رضا؛ صمیمی، یاسر، اسماعیلی، حمید؛ عظی مزاد، نیما ) 1384 (.بررسی و مقایس هی عملکرد روش های ابتکاری برای حل مدل مکان یابی
Maximal Covering . چهارمین کنفرانس بین المللی مهندسی صنایع.
2. Rvelle, C., Marks, D. and Leibman, J.C. (1970). Ananalysis of private and public sector location models,
Management Science, 16(11): pp. 692-707.
3. Apta, A. (2009). Humanitarian logistics: A new fieldof research and action. Foundations and Trends in
Technology, Information and Operation Management,3(1): pp .1-100.
4. Jia, H., Ordonez, F. and Dessouky M. (2007). A modelingframework for facility location of medical servicesfor large-scale emergencies. IIE Transactions,39(1): pp. 41-55.
5. Toregas, C., Swain, R., ReVelle, C. and Bergman,L. (1971). The location of emergency
service facilities. Operations Research, 19(6):pp. 1363-1373.
6. Church, R. and Velle, C.R. (1974). The Maximal CoveringLocation Problem. Papers in Regional Science,
32(1): pp.101-118.
7. Berman, O., Drezner, Z., Krass, D., Wesolowsky, G.O.(2009), The variable radius covering problem. EuropeanJournal of Ooerational Research, 196(2): p.516-525.
8. Hakimi, S.l. (1965). Optimum distribution of switchingcenters in a communication network and some
related graph theoretic problems. Operation Research,13: pp. 447-462.
9. Berman, O. and Krass D. (2002). The generalized maximalcovering location problem. Operations Research,29(6): pp. 563-581.
10. Berman, O. and Krass, D., and Drezner, Z. (2003). Thegradual covering decay location problem on a network.European Journal of Operational Research,151(3): pp.474-480
11. Drezner, T. and Wesolowsky G.O. (2004). The gradualcovering problem. Naval Research Logistics (NRL),51(6): pp.841-855
12. Drezner, T. and Goldstein, Z. (2010). A stochastic gradualcover location problem. Naval Research Logistics(NRL), 57(4): pp. 367-372.
13. Berman, O. and Krass, D. and Wang, J. (2011). Theprobabilistic gradual covering location problem on a
network with discrete random demand weights. OperationResearch, 38(11): pp. 1493-1500.
14. Berman, O., Drezner Z. and Krass D. (2011). Generalizedcoverage: New developments in covering locationmodels. Operation Research, 37(10): pp. 1675-
1687.
15. Jabalameli, M.S., Tabrizi, B.B., and Javadi, M.M.(2010). Capacitated Facility Location Problem with
Variable Coverage Coverage Radius in DistributionSystem. International Journal of Industrial Engineering,
21(4): pp. 231-237.
16. Jabalameli, M.S., Tabrizi, B.B., and Javadi, M.M.(2011). A Simulated Annealing method to solve a
generalized maximal covering location problem. InternationalJournal of Industrial Engineering. 2(2): pp.
439-448.
17. Fazel Zarandi, M.H., Davari, S. and Haddad Siasakht,S.A. (2011). The large scale maximal covering locationproblem. Scientia Iranica, 18(6): pp.1564-1570
18. Bashiri, M. and Fotuhi, F. (2009). A cost-based setcoveringlocation allocation problem with unknown
covering radius. IEEM 2009, IEEE InternatonalConference on In Industrial Engineering and Engineering
Management.
19. Meng, S. and Shia B.C. (2012). Set covering locationmodels with stochastic critical distances. Operational Research Society, Oline.
20. Viswanath K. and Peeta S. (2003). Multicommoditymaximal covering network design problem for planningcritical route for earthquake response, TransportationResearch Record: Journal of the TransportationResearch Board, 1857(01): pp. 1-10.
21. Dekle, J., Lavieri, M.S., Martin, E., Emir-Farinas, H. and Francis, R. (2005). A Florida
country locates disaster recovery centers,Interfaces, 35(2): pp. 133-139.
22. Hale, T. and Moberg C.R. (2005). Improving supplychain disaster preparedness: A decision process for
secure site location, International Journal of PhysicalDistribution & Logestics Managemnet, 35(3): pp. 195-
207.
23. Bleik, B. and Beamon B.M (2008), Facility location inhumanitarian relief. International Journal of Logistics,11(2): pp. 101-121.
24. Beraldi, P. and Bruni M.E. (2009). A probabilisticmodel allpied to emergency service vehicle location.
European Journal of Operational Research, 196(1): pp.323-331.
25. Pan, A. (2010). The applications of maximal coveringmodel in Typhoon Emergency shelter Location
problem, IEEE International Conference on in IndustrialEngineering and Engineering Management.
26. Nolz, P.C., Samet, F. and Doerner K.F. (2011), Riskapproaches for delivering disaster relief supplies. OR
spectrum, 33(3): pp. 543-569.
27. Murali, P., Ordonez, F. and Dessouky M.M. (2012).Facility location under demand uncertainty: Response
to a large-scale bio-terror attack, Socio-EconomicPlanning Sciences, 46(1): pp.78-87.
28. Li, X., Zhao, Z., Zhu, X. and Wyatt, T. (2011), Coveringmodels and optimization techniques for emergencyresponse facility location and planning: a review.Mathematical Methods of Operations Research,
74(3): pp. 281-310.
29. Toro-diaz, H., Mayorga, M. E., Chanta, S., McLay,L.A., (2013). Joint location and dispatching decisions
for Emergency Medical Services. Computers& Industrial Engineering 64 : pp. 917–928.
30. Barzinpour, F. and Esmaeili, V., (2013). A multiobjectiverelief chain location distribution model
for urban disaster management. International Journalof Advanced Manufacturing Technology , DOI
10.1007/s00170-013-5379-x
31. Esmaeili, V., Barzinpour, F., (2014). Integrated decisionmaking model for urban disaster management:
A multi-objective genetic algorithm approach. InternationalJournal of Industrial Engineering Computations
, 5(11): pp.55-70.
32. Grannan, B.C., Bastian, N.D., and McLay L.A.(2015). A maximum expected covering problem
for locating and dispatching two classes of militarymedical evacuation air assets. Optimization Letters 
9(8): pp. 1511-1531.
33. Ye, H. and Kim, H. (2016). Locating healthcare facilitiesusing a network-based covering location problem.GeoJourna, 81(6): pp. 875-890.
34. Mulvey, J.M., Vanderbei, R.J. and Zenios S.A. (1995).Robust optimization of large-scale systems. OperationResearch, 43(2): pp. 264-281.
35. Leung, S., Tsang, S., Ng, W.L. and Wu, Y (2007). Arobust optimization model for multi-site production
planning problem in an uncertain environment,European Journal of Operational Research, 181: pp.
224–238.
 ۳۶ یحی یزاده اندواری، یلدا؛ الفت، لعیا؛ امیری، مقصود ) 1395 (. رویکردبهینه سازی استوار در انتخاب تأمین کننده و تخصیص سفارش، مطالعات
مدیریت صنعتی، سال چهاردهم، شماره 40 ، ص. 52 - 25 .
37. Yu, C.S and Li, H.L. (2000). A robust optimizationmodel for stochastic logsistic problems, Internatioanl
Journal of Production Economics, 64: pp. 385-397.
 ۳۸ صفاری، امیر؛ ساسان پور، فرزانه؛ موس یوند، جعفر ) 1390 (. ارزیابی آسیبپذیری مناطق شهری در برابر خطر سیل با استفاده از سیستم اطلاعات
جغرافیایی و منطق فازی مطالعه موردی: منطقه 3 تهران، نشریه یتحقیقات کاربردی علوم جغرافیایی، جلد 17 ، شماره 20 ص. 150 - 129 .
 ۳۹ قهرودی تالی، منیژه؛ ثروتی، محمدرضا؛ صرافی، مظفر؛ پورموسوی،موسی؛ درفشی، خه بات. ) 1391 (. ارزیابی آسیب پذیری ناشی از سیلاب در
شهر تهران، فصلنامه ی علمی امداد و نجات، دوره 4، شماره ی 3، 79 - 92 .