Optimal scheduling of logistical support for medical resource with demand information updating. (English) Zbl 1394.90288
Summary: This paper presents a discrete time-space network model for a dynamic resource allocation problem following an epidemic outbreak in a region. It couples a forecasting mechanism for dynamic demand of medical resource based on an epidemic diffusion model and a multistage programming model for optimal allocation and transport of such resource. At each stage, the linear programming solves for a cost minimizing resource allocation solution subject to a time-varying demand that is forecasted by a recursion model. The rationale that the medical resource allocated in early periods will take effect in subduing the spread of epidemic and thus impact the demand in later periods has been incorporated in such recursion model. A custom genetic algorithm is adopted to solve the proposed model, and a numerical example is presented for sensitivity analysis of the parameters. We compare the proposed medical resource allocation mode with two traditional operation modes in practice and find that our model is superior to any of them in less waste of resource and less logistic cost. The results may provide some practical guidelines for a decision-maker who is in charge of medical resource allocation in an epidemics control effort.
MSC:
| 90B35 | Deterministic scheduling theory in operations research |
| 90B06 | Transportation, logistics and supply chain management |
References:
| [1] | Hu, J.; Zeng, A. Z.; Zhao, L., A comparative study of public-health emergency management, Industrial Management and Data Systems, 109, 7, 976-992, (2009) · doi:10.1108/02635570910982319 |
| [2] | Zhang, J.; Ma, Z., Global dynamics of an SEIR epidemic model with saturating contact rate, Mathematical Biosciences, 185, 1, 15-32, (2003) · Zbl 1021.92040 · doi:10.1016/S0025-5564(03)00087-7 |
| [3] | Mishra, B. K.; Saini, D. K., SEIRS epidemic model with delay for transmission of malicious objects in computer network, Applied Mathematics and Computation, 188, 2, 1476-1482, (2007) · Zbl 1118.68014 · doi:10.1016/j.amc.2006.11.012 |
| [4] | Sun, C.; Hsieh, Y., Global analysis of an SEIR model with varying population size and vaccination, Applied Mathematical Modelling, 34, 10, 2685-2697, (2010) · Zbl 1201.34076 · doi:10.1016/j.apm.2009.12.005 |
| [5] | Zhang, J.; Li, J.; Ma, Z., Global dynamics of an SEIR epidemic model with immigration of different compartments, Acta Mathematica Scientia B: English Edition, 26, 3, 551-567, (2006) · Zbl 1096.92039 · doi:10.1016/S0252-9602(06)60081-7 |
| [6] | Saramäki, J.; Kaski, K., Modelling development of epidemics with dynamic small-world networks, Journal of Theoretical Biology, 234, 3, 413-421, (2005) · Zbl 1445.92280 · doi:10.1016/j.jtbi.2004.12.003 |
| [7] | Xu, X.; Peng, H. O.; Wang, X. M.; Wang, Y. H., Epidemic spreading with time delay in complex networks, Physica A: Statistical Mechanics and its Applications, 367, 525-530, (2006) · doi:10.1016/j.physa.2005.11.035 |
| [8] | Han, X. P., Disease spreading with epidemic alert on small-world networks, Physics Letters A, 365, 1-2, 1-5, (2007) · Zbl 1203.05143 · doi:10.1016/j.physleta.2006.12.054 |
| [9] | Jung, E.; Iwami, S.; Takeuchi, Y.; Jo, T., Optimal control strategy for prevention of avian influenza pandemic, Journal of Theoretical Biology, 260, 2, 220-229, (2009) · Zbl 1402.92278 · doi:10.1016/j.jtbi.2009.05.031 |
| [10] | Wang, J. X.; Xu, W. S.; Zhang, R. Q.; Wu, N., Epidemic prevention and infection control of a field dressing station in Wenchuan earthquake areas, International Journal of Infectious Diseases, 13, 1, 100, (2009) |
| [11] | Halloran, M. E.; Ferguson, N. M.; Eubank, S.; Longini, I. M.; Cummings, D. A. T.; Lewis, B.; Xu, S.; Fraser, C.; Vullikanti, A.; Germann, T. C.; Wagener, D.; Beckman, R.; Kadau, K.; Barrett, C.; Macken, C. A.; Burke, D. S.; Cooley, P., Modeling targeted layered containment of an influenza pandemic in the United States, Proceedings of the National Academy of Sciences of the United States of America, 105, 12, 4639-4644, (2008) · doi:10.1073/pnas.0706849105 |
| [12] | Kim, K. I.; Lin, Z.-G.; Zhang, L., Avian-human influenza epidemic model with diffusion, Nonlinear Analysis: Real World Applications, 11, 1, 313-322, (2010) · Zbl 1230.35047 · doi:10.1016/j.nonrwa.2008.11.015 |
| [13] | Liu, J.; Zhang, T., Epidemic spreading of an SEIRS model in scale-free networks, Communications in Nonlinear Science and Numerical Simulation, 16, 8, 3375-3384, (2011) · Zbl 1217.92067 · doi:10.1016/j.cnsns.2010.11.019 |
| [14] | Samsuzzoha, M.; Singh, M.; Lucy, D., Numerical study of an influenza epidemic model with diffusion, Applied Mathematics and Computation, 217, 7, 3461-3479, (2010) · Zbl 1202.92056 · doi:10.1016/j.amc.2010.09.017 |
| [15] | Samsuzzoha, M.; Singh, M.; Lucy, D., A numerical study on an influenza epidemic model with vaccination and diffusion, Applied Mathematics and Computation, 219, 1, 122-141, (2012) · Zbl 1291.92103 · doi:10.1016/j.amc.2012.04.089 |
| [16] | Yin, S.; Wang, G.; Karimi, H. R., Data-driven design of robust fault detection system for wind turbines, Mechatronics, 24, 4, 298-306, (2014) |
| [17] | Yin, S.; Li, X.; Gao, H.; Kaynak, O., Data-based techniques focused on modern industry: an overview, IEEE Transactions on Industrial Electronics, (2014) · doi:10.1109/TIE.2014.2308133 |
| [18] | Yin, S.; Wang, G., Robust PLS approach for KPI related prediction and diagnosis against outliers and missing data, International Journal of Systems Science, 45, 7, 1375-1382, (2014) · Zbl 1290.93212 |
| [19] | Zaric, G. S.; Brandeau, M. L., Resource allocation for epidemic control over short time horizons, Mathematical Biosciences, 171, 1, 33-58, (2001) · Zbl 0978.92027 · doi:10.1016/S0025-5564(01)00050-5 |
| [20] | Zaric, G. S.; Brandeau, M. L., Dynamic resource allocation for epidemic control in multiple populations, Journal of Mathematics Applied in Medicine and Biology, 19, 4, 235-255, (2002) · Zbl 1042.92032 · doi:10.1093/imammb/19.4.235 |
| [21] | Brandeau, M. L.; Zaric, G. S.; Richter, A., Resource allocation for control of infectious diseases in multiple independent populations: beyond cost-effectiveness analysis, Journal of Health Economics, 22, 4, 575-598, (2003) · doi:10.1016/S0167-6296(03)00043-2 |
| [22] | Zaric, G. S.; Bravata, D. M.; Cleophas Holty, J.; McDonald, K. M.; Owens, D. K.; Brandeau, M. L., Modeling the logistics of response to anthrax bioterrorism, Medical Decision Making, 28, 3, 332-350, (2008) · doi:10.1177/0272989X07312721 |
| [23] | Duintjer Tebbens, R. J.; Pallansch, M. A.; Alexander, J. P.; Thompson, K. M., Optimal vaccine stockpile design for an eradicated disease: application to polio, Vaccine, 28, 26, 4312-4327, (2010) · doi:10.1016/j.vaccine.2010.04.001 |
| [24] | Liu, M.; Zhao, L., Optimization of the emergency materials distribution network with time windows in anti-bioterrorism system, International Journal of Innovative Computing, Information and Control, 5, 11A, 3615-3624, (2009) |
| [25] | Wang, H. Y.; Wang, X. P.; Zeng, A. Z., Optimal material distribution decisions based on epidemic diffusion rule and stochastic latent period for emergency rescue, International Journal of Mathematics in Operational Research, 1, 1-2, 76-96, (2009) · Zbl 1176.90060 · doi:10.1504/IJMOR.2009.022876 |
| [26] | Qiang, P.; Nagurney, A., A bi-criteria indicator to assess supply chain network performance for critical needs under capacity and demand disruptions, Transportation Research A, 46, 5, 801-812, (2012) · doi:10.1016/j.tra.2012.02.006 |
| [27] | Rachaniotis, N. P.; Dasaklis, T. K.; Pappis, C. P., A deterministic resource scheduling model in epidemic control: a case study, European Journal of Operational Research, 216, 1, 225-231, (2012) · doi:10.1016/j.ejor.2011.07.009 |
| [28] | Barbarosolu, G.; Özdamar, L.; Çevik, A., An interactive approach for hierarchical analysis of helicopter logistics in disaster relief operations, European Journal of Operational Research, 140, 1, 118-133, (2002) · Zbl 1008.90514 · doi:10.1016/S0377-2217(01)00222-3 |
| [29] | Yan, S. Y.; Shih, Y. L., Optimal scheduling of emergency roadway repair and subsequent relief distribution, Computers & Operations Research, 36, 6, 2049-2065, (2009) · Zbl 1179.90167 · doi:10.1016/j.cor.2008.07.002 |
| [30] | Liu, M.; Zhao, L. D., Analysis for epidemic diffusion and emergency demand in an anti-bioterrorism system, International Journal of Mathematical Modelling and Numerical Optimisation, 2, 1, 51-68, (2011) · Zbl 1205.92067 · doi:10.1504/IJMMNO.2011.037199 |
| [31] | Liu, M.; Zhao, L.; Sebastian, H., Mixed-collaborative distribution mode for emergency resources in an anti-bioterrorism system, International Journal of Mathematics in Operational Research, 3, 2, 148-169, (2011) · Zbl 1209.90245 · doi:10.1504/IJMOR.2011.038908 |
| [32] | Tham, K. Y., An emergency department response to severe acute respiratory syndrome: a prototype response to bioterrorism, Annals of Emergency Medicine, 43, 1, 6-14, (2004) · doi:10.1016/j.annemergmed.2003.08.005 |
| [33] | Sheu, J. B., An emergency logistics distribution approach for quick response to urgent relief demand in disasters, Transportation Research E: Logistics and Transportation Review, 43, 6, 687-709, (2007) · doi:10.1016/j.tre.2006.04.004 |
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