Movatterモバイル変換

[0]ホーム
URL:

Skip to main content
Springer Nature Link
Log in

A Benders decomposition for the location-allocation and scheduling model in a healthcare system regarding robust optimization

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

The hospital location and service allocation is one of the most important aspects of healthcare systems. Due to lack of studies on covering location-allocation and scheduling problems with respect to the uncertain budget, this paper develops a bi-objective hybrid model to locate hospitals and allocate machines and services scheduled. The costs of establishing facilities are assumed to be uncertain, while a robust counterpart model is employed to overcome the uncertainty. Covering the demand of each service is limited as well. Moreover, hospitals have a limited space to the specialized equipment like CT scan and MRI machines, while there is a cost constraint on hospitals and the specialized equipment. The aim of this paper is to find a near-optimal solution including the number of hospitals and the specialized equipment, the location of hospitals, the assignment of demand of each service and the specialized equipment to hospitals, the determination of allowable number of each service of hospitals, the determination of demand that should be transferred from one hospital to another (patient transfer), and schedule services. As the proposed model, minimizing the total costs and the completion time of demand simultaneously, is an NP-hard problem, it is impossible to solve its large-scale version with exact methods in a reasonable time. Thus, a hybrid algorithm including simulated annealing optimization and the Benders decomposition is employed to solve it. The CPLEX optimizer verifies the presented algorithm to solve the proposed model. The sensitivity analysis is performed to validate the proposed robust model against of uncertain situations while the Monte Carlo simulation is used to analyze the quality and the robustness of solutions under uncertain situations. The results show that the uncertainty used in the proposed model properly formulates real-world situations compared to the deterministic case. Finally, the contributions and the future research are presented.

This is a preview of subscription content,log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Rais A, Viana A (2010) Operations research in healthcare: a survey. Int Trans Oper Res 18:1–31

    Article MathSciNet  Google Scholar 

  2. Rahman S-U, Smith DK (2000) Use of location-allocation models in health service development planning in developing nations. Eur J Oper Res 123:437–452

    Article MATH  Google Scholar 

  3. Dearing PM (1985) Location problems. Oper Res Lett 4:95–98

    Article MathSciNet MATH  Google Scholar 

  4. Finke G, Burkard RE, Rendl F (1987) Quadratic assignment problems. In: Silvano Martello GLMM, Celso R (eds) North-holland mathematics studies. Elsevier, North-Holland, pp 61–82

  5. Loiola EM, de Abreu NMM, Boaventura-Netto PO, Hahn P, Querido T (2007) A survey for the quadratic assignment problem. Eur J Oper Res 176:657–690

    Article MathSciNet MATH  Google Scholar 

  6. Owen SH, Daskin MS (1998) Strategic facility location: a review. Eur J Oper Res 111:423–447

    Article MATH  Google Scholar 

  7. ReVelle CS, Eiselt HA (2005) Location analysis: a synthesis and survey. Eur J Oper Res 165:1–19

    Article MathSciNet MATH  Google Scholar 

  8. Drira A, Pierreval H, Hajri-Gabouj S (2007) Facility layout problems: a survey. Ann Rev Control 31:255–267

    Article  Google Scholar 

  9. Farahani RZ, SteadieSeifi M, Asgari N (2010) Multiple criteria facility location problems: a survey. Appl Math Model 34:1689–1709

    Article MathSciNet MATH  Google Scholar 

  10. Farahani RZ, Asgari N, Heidari N, Hosseininia M, Goh M (2012) Covering problems in facility location: a review. Comput Ind Eng 62:368–407

    Article  Google Scholar 

  11. Boloori Arabani A, Farahani RZ (2012) Facility location dynamics: an overview of classifications and applications. Comput Ind Eng 62:408–420

    Article  Google Scholar 

  12. Baum R, Bertsimas D, Kallus N (2014) Scheduling, revenue management, and fairness in an academic-hospital radiology division. Acad Radiol 21:1322–1330

    Article  Google Scholar 

  13. Wakamiya S, Yamauchi K (2009) What are the standard functions of electronic clinical pathways? Int J Med Inform 78:543–550

    Article  Google Scholar 

  14. Huang Z, Dong W, Ji L, Gan C, Lu X, Duan H (2014) Discovery of clinical pathway patterns from event logs using probabilistic topic models. J Biomed Inform 47:39–57

    Article  Google Scholar 

  15. Salman FS, Gül S (2014) Deployment of field hospitals in mass casualty incidents. Comput Ind Eng 74:37–51

    Article  Google Scholar 

  16. Mestre AM, Oliveira MD, Barbosa-Póvoa AP (2015) Location–allocation approaches for hospital network planning under uncertainty. Eur J Oper Res 240:791–806

    Article MATH  Google Scholar 

  17. Li Y, Kong N, Chen M, Zheng QP (2016) Optimal physician assignment and patient demand allocation in an outpatient care network. Comput Oper Res 72:107–117

    Article MathSciNet MATH  Google Scholar 

  18. Gunpinar S, Centeno G (2016) An integer programming approach to the bloodmobile routing problem. Transp Res Part E Logist Transp Rev 86:94–115

    Article  Google Scholar 

  19. Mohammadi M, Tavakkoli-Moghaddam R, Siadat A, Dantan J-Y (2016) Design of a reliable logistics network with hub disruption under uncertainty. Appl Math Model 40(9–10):5621–5642

    Article MathSciNet  Google Scholar 

  20. Izadiniaa N, Eshghia K (2016) A robust mathematical model and ACO solution for multi-floor discrete layout problem with uncertain locations and demands. Comput Ind Eng 96:237–248

    Article  Google Scholar 

  21. Gülpınar N, Pachamanova D, Çanakoğlu E (2013) Robust strategies for facility location under uncertainty. Eur J Oper Res 225:21–35

    Article MathSciNet MATH  Google Scholar 

  22. Paul JA, MacDonald L (2016) Location and capacity allocations decisions to mitigate the impacts of unexpected disasters. Eur J Oper Res 251:252–263

    Article MathSciNet MATH  Google Scholar 

  23. Soleimani H, Kannan G (2015) A hybrid particle swarm optimization and genetic algorithm for closed-loop supply chain network design in large-scale networks. Appl Math Model 39:3990–4012

    Article MathSciNet  Google Scholar 

  24. Ardjmand E, Weckman G, Park N, Taherkhani P, Singh M (2015) Applying genetic algorithm to a new location and routing model of hazardous materials. Int J Prod Res 53:916–928

    Article  Google Scholar 

  25. Memari A, Rahim ARA, Ahmad RB (2015) An integrated production-distribution planning in green supply chain: a multi-objective evolutionary approach. Procedia CIRP 26:700–705

    Article  Google Scholar 

  26. Sadeghi J (2015) A multi-item integrated inventory model with different replenishment frequencies of retailers in a two-echelon supply chain management: a tuned-parameters hybrid meta-heuristic. OPSEARCH 52:631–649

    Article MathSciNet MATH  Google Scholar 

  27. Shahvari O, Salmasi N, Logendran R, Abbasi B (2012) An efficient tabu search algorithm for flexible flow shop sequence-dependent group scheduling problems. Int J Prod Res 50:4237–4254

    Article  Google Scholar 

  28. Shahvari O, Logendran R (2016) Hybrid flow shop batching and scheduling with a bi-criteria objective. Int J Prod Econ 179:239–258

    Article  Google Scholar 

  29. Shahvari O, Logendran R (2017) An enhanced tabu search algorithm to minimize a bi-criteria objective in batching and scheduling problems on unrelated-parallel machines with desired lower bounds on batch sizes. Comput Oper Res 77:154–176

    Article MathSciNet  Google Scholar 

  30. Sadeghi J, Mousavi SM, Niaki STA, Sadeghi S (2013) Optimizing a multi-vendor multi-retailer vendor managed inventory problem: two tuned meta-heuristic algorithms. Knowl Based Syst 50:159–170

    Article  Google Scholar 

  31. Mousavi SM, Sadeghi J, Niaki STA, Alikar N, Bahreininejad A, Metselaar HSC (2014) Two parameter-tuned meta-heuristics for a discounted inventory control problem in a fuzzy environment. Inf Sci 276:42–62

    Article MathSciNet  Google Scholar 

  32. Memari A, Abdul Rahim AR, Hassan A, Ahmad R (2016) A tuned NSGA-II to optimize the total cost and service level for a just-in-time distribution network. Neural Comput Appl 1–15. doi:10.1007/s00521-016-2249-0

  33. Mousavi SM, Hajipour V, Niaki STA, Alikar N (2013) Optimizing multi-item multi-period inventory control system with discounted cash flow and inflation: two calibrated meta-heuristic algorithms. Appl Math Model 37:2241–2256

    Article MathSciNet MATH  Google Scholar 

  34. Abdel-Basset M, Hessin A-N, Abdel-Fatah L (2016) A comprehensive study of cuckoo-inspired algorithms. Neural Comput Appl 1–17. doi:10.1007/s00521-016-2464-8

  35. Memari A, Abdul Rahim AR, Absi N, Ahmad R, Hassan A (2016) Carbon-capped distribution planning: a JIT perspective. Comput Ind Eng 97:111–127

    Article  Google Scholar 

  36. Haji-abbas M, Hosseininezhad SJ (2016) A robust approach to multi period covering location-allocation problem in pharmaceutical supply chain. J Ind Syst Eng 9:5

    Google Scholar 

  37. Fischetti M, Ljubić I, Sinnl M (2016) Benders decomposition without separability: a computational study for capacitated facility location problems. Eur J Oper Res 253:557–569

    Article MathSciNet MATH  Google Scholar 

  38. Habibzadeh Boukani F, Farhang Moghaddam B, Pishvaee MS (2016) Robust optimization approach to capacitated single and multiple allocation hub location problems. Comput Appl Math 35:45–60

    Article MathSciNet MATH  Google Scholar 

  39. Meraklı M, Yaman H (2016) Robust intermodal hub location under polyhedral demand uncertainty. Transp Res Part B Methodol 86:66–85

    Article  Google Scholar 

  40. Arabzad SM, Ghorbani M, Hashemkhani Zolfani S (2015) A multi-objective robust optimization model for a facility location-allocation problem in a supply chain under uncertainty. Eng Econ 26:227–238

    Google Scholar 

  41. Yang M, Wang X, Xu N (2015) A robust voting machine allocation model to reduce extreme waiting. Omega 57(Part B):230–237

    Article  Google Scholar 

  42. Álvarez-Miranda E, Fernández E, Ljubić I (2015) The recoverable robust facility location problem. Transp Res Part B Methodol 79:93–120

    Article  Google Scholar 

  43. Zahiri B, Tavakkoli-Moghaddam R, Pishvaee MS (2014) A robust possibilistic programming approach to multi-period location–allocation of organ transplant centers under uncertainty. Comput Ind Eng 74:139–148

    Article  Google Scholar 

  44. Rahmati SHA, Ahmadi A, Sharifi M, Chambari A (2014) A multi-objective model for facility location–allocation problem with immobile servers within queuing framework. Comput Ind Eng 74:1–10

    Article  Google Scholar 

  45. De Rosa V, Hartmann E, Gebhard M, Wollenweber J (2014) Robust capacitated facility location model for acquisitions under uncertainty. Comput Ind Eng 72:206–216

    Article  Google Scholar 

  46. Rezaei-malek M, Tavakkoli-Moghaddam R, Salehi N (2014) Robust location-allocation and distribution of medical commodities with time windows in a humanitarian relief logistics network. In: CIE 2014, 44th international conference on computers and industrial engineering and IMSS 2014. Adile Sultan Palace, Istanbul, Turkey, pp 134–147

  47. Yan Y, Meng Q, Wang S, Guo X (2012) Robust optimization model of schedule design for a fixed bus route. Transp Res Part C Emerg Technol 25:113–121

    Article  Google Scholar 

  48. Fazel-Zarandi MM, Beck JC (2009) Solving a location-allocation problem with logic-based Benders’ decomposition. In: Gent IP (ed) Principles and practice of constraint programming—CP 2009: 15th international conference, CP 2009 Lisbon, Portugal, September 20–24, 2009 proceedings. Springer, Berlin, Heidelberg, pp 344–351

  49. Sadeghi J, Niaki STA, Malekian M, Sadeghi S (2016) Optimising multi-item economic production quantity model with trapezoidal fuzzy demand and backordering: two tuned meta-heuristics. Eur J Ind Eng 10:170–195

    Article  Google Scholar 

  50. Shariff SSR, Moin NH, Omar M (2012) Location allocation modeling for healthcare facility planning in Malaysia. Comput Ind Eng 62:1000–1010

    Article  Google Scholar 

  51. Syam SS, Côté MJ (2010) A location–allocation model for service providers with application to not-for-profit health care organizations. Omega 38:157–166

    Article  Google Scholar 

  52. Kim D-G, Kim Y-D (2010) A branch and bound algorithm for determining locations of long-term care facilities. Eur J Oper Res 206:168–177

    Article MathSciNet MATH  Google Scholar 

  53. Feizollahi M-J, Modarres-Yazdi M (2012) Robust quadratic assignment problem with uncertain locations. Iran J Oper Res 3:46–65

    Google Scholar 

  54. Ben-Tal A, Ghaoui LE, Nemirovski A (2009) Robust optimization. Princeton University Press, Princeton

    Book MATH  Google Scholar 

  55. Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52:35–53

    Article MathSciNet MATH  Google Scholar 

  56. Yang X-S (2010) Engineering optimization an introduction with metaheuristic applications. Wiley, New Jersey

    Book  Google Scholar 

  57. Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numer Math 4:238–252

    Article MathSciNet MATH  Google Scholar 

  58. Sadeghi J, Sadeghi S, Niaki STA (2014) A hybrid vendor managed inventory and redundancy allocation optimization problem in supply chain management: an NSGA-II with tuned parameters. Comput Oper Res 41:53–64

    Article MathSciNet MATH  Google Scholar 

  59. Sadeghi J, Sadeghi S, Niaki STA (2014) Optimizing a hybrid vendor-managed inventory and transportation problem with fuzzy demand: an improved particle swarm optimization algorithm. Inf Sci 272:126–144

    Article MathSciNet  Google Scholar 

  60. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21:1087–1092

    Article  Google Scholar 

  61. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680

    Article MathSciNet MATH  Google Scholar 

  62. Černý V (1985) Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm. J Optim Theory Appl 45:41–51

    Article MathSciNet MATH  Google Scholar 

Download references

Acknowledgments

The authors are thankful for constructive comments of the anonymous reviewers. Taking care of the comments certainly improved the presentation.

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Sharif University of Technology, Tehran, 14588-89694, Iran

    Fatemeh Karamyar & Mohammad Modarres Yazdi

  2. School of Mechanical, Industrial and Manufacturing Engineering, Oregon State University, Corvallis, OR, 97331, USA

    Javad Sadeghi

Authors
  1. Fatemeh Karamyar

    You can also search for this author inPubMed Google Scholar

  2. Javad Sadeghi

    You can also search for this author inPubMed Google Scholar

  3. Mohammad Modarres Yazdi

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence toJavad Sadeghi.

Rights and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Karamyar, F., Sadeghi, J. & Yazdi, M.M. A Benders decomposition for the location-allocation and scheduling model in a healthcare system regarding robust optimization.Neural Comput & Applic29, 873–886 (2018). https://doi.org/10.1007/s00521-016-2606-z

Download citation

Keywords

Access this article

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Advertisement

[8]ページ先頭
©2009-2025 Movatter.jp