基于SEIR传染病模型的应急救援物流调度优化
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摘要
传染病威胁着人类健康,传染病患者若得不到及时救治,会造成传染区域灾情泛滥.因此,在传染病流行之后,最迫切的是要掌握灾区对药物的需求量,进而针对传染病患者的需求进行应急救援物流调度优化.文中针对传染病应急救援具有时效性的特点,利用易感者、潜伏者、感染者及痊愈者(susceptible-exposed-infected-recovered,SEIR)数学模型描述整个应急救援阶段受感染群体的需求;构建基于传染病流行规律的应急救援物流调度多阶段混合整数规划模型,对救援车辆路径选择和药物资源调配进行优化;提出有效的Benders分解算法对模型进行求解;通过算例计算,证明了算法和模型的有效性,为应急救援决策者提供了科学决策依据,具有重要的理论意义和应用价值.
Infectious diseases are a major threat to human security. Infectious diseases can cause serious damage to the victims. Therefore, it is the most urgent thing to grasp the demand for drugs and optimize logistics dispatch of emergency rescue in disaster areas. In this paper, firstly, we use the susceptible-exposed-infected-recovered(SEIR) model to simulate the diffusion mechanism of infectious diseases and determine the number of infected groups in humanitarian relief phase. Secondly, a multistage mixed integer programming model for the humanitarian logistics and transport resource based on epidemic pattern of infectious disease is proposed. The model optimizes the route selection of rescue vehicles and the allocation of drug resources. Thirdly, the linear programming problem is solved by Benders decomposition algorithm. Finally, we use a case to prove the validity of the model and algorithm. The paper provides scientific decision-making basis for emergency rescue decision-makers, and has important theoretical significance and application value.
Infectious diseases are a major threat to human security. Infectious diseases can cause serious damage to the victims. Therefore, it is the most urgent thing to grasp the demand for drugs and optimize logistics dispatch of emergency rescue in disaster areas. In this paper, firstly, we use the susceptible-exposed-infected-recovered(SEIR) model to simulate the diffusion mechanism of infectious diseases and determine the number of infected groups in humanitarian relief phase. Secondly, a multistage mixed integer programming model for the humanitarian logistics and transport resource based on epidemic pattern of infectious disease is proposed. The model optimizes the route selection of rescue vehicles and the allocation of drug resources. Thirdly, the linear programming problem is solved by Benders decomposition algorithm. Finally, we use a case to prove the validity of the model and algorithm. The paper provides scientific decision-making basis for emergency rescue decision-makers, and has important theoretical significance and application value.
引文
[ 1 ] LIU M, LIANG J. Dynamic optimization model for allocating medical resources in epidemic controlling[J]. Journal of Industrial Engineering & Management, 2013, 6(1): 73-88.
[ 2 ] XIAO Y,LIU M. Optimal scheduling of logistical support for medical resource with demand information updating[J]. Mathematical Problems in Engineering, 2015(6): 1-12.
[ 3 ] 张刚庆, 洪文松, 张国伟,等. 基于SIR流行病模型的应急反应优化分析[J]. 中国急救复苏与灾害医学杂志, 2014,9(1): 59-61.
[ 4 ] BOLZONI L, BONACINI E, SORESINA C, et al. Time-optimal control strategies in SIR epidemic models[J]. Mathematical Biosciences, 2017(292): 86-96. DOI:10.1016/j.mbs.2017.07.011.
[ 5 ] LIU M, ZHANG Z, ZHANG D. A dynamic allocation model for medical resources in the control of influenza diffusion[J]. Journal of Systems Science and Systems Engineering, 2015, 24(3):276-292.
[ 6 ] ZHOU Y, LIU J, ZHANG Y, et al. A multi-objective evolutionary algorithm for multi-period dynamic emergency resource scheduling problems[J]. Transportation Research Part E: Logistics & Transportation Review, 2017,99: 77-95.
[ 7 ] OTHMAN S B, ZGAYA H, DOTOLI M, et al. An agent-based decision support system for resources′ scheduling in emergency supply chains[J]. Control Engineering Practice, 2017,59: 27-43.
[ 8 ] HUANG K, JIANG Y, YUAN Y, et al. Modeling multiple humanitarian objectives in emergency response to large-scale disasters[J]. Transportation Research Part E: Logistics & Transportation Review,2015,75: 1-17.
[ 9 ] 黄天春. 人道主义物流中灾害救援网络研究[J]. 物流工程与管理, 2013, 35(4): 99-100.DOI:10.3969/j.issn.1674-4993.2013.04.040.HUANG Tianchun. Research on the disaster relief network in humanitarian logistics[J]. Logistics Engineering and Management,2013, 35(4): 99-100. DOI:10.3969/j.issn.1674-4993.2013.04.040.(in Chinese)
[10] WANG H, WANG X, ZENG A Z. Optimal material distribution decisions based on epidemic diffusion rule and stochastic latent period for emergency rescue[J]. International Journal of Mathematics in Operational Research, 2009, 1(1/2): 76-96.
[11] BENDERS J F. Partitioning procedures for solving mixed-variables programming problems[J]. Numerische Mathematik,1962,4(1): 238-252.
[ 2 ] XIAO Y,LIU M. Optimal scheduling of logistical support for medical resource with demand information updating[J]. Mathematical Problems in Engineering, 2015(6): 1-12.
[ 3 ] 张刚庆, 洪文松, 张国伟,等. 基于SIR流行病模型的应急反应优化分析[J]. 中国急救复苏与灾害医学杂志, 2014,9(1): 59-61.
[ 4 ] BOLZONI L, BONACINI E, SORESINA C, et al. Time-optimal control strategies in SIR epidemic models[J]. Mathematical Biosciences, 2017(292): 86-96. DOI:10.1016/j.mbs.2017.07.011.
[ 5 ] LIU M, ZHANG Z, ZHANG D. A dynamic allocation model for medical resources in the control of influenza diffusion[J]. Journal of Systems Science and Systems Engineering, 2015, 24(3):276-292.
[ 6 ] ZHOU Y, LIU J, ZHANG Y, et al. A multi-objective evolutionary algorithm for multi-period dynamic emergency resource scheduling problems[J]. Transportation Research Part E: Logistics & Transportation Review, 2017,99: 77-95.
[ 7 ] OTHMAN S B, ZGAYA H, DOTOLI M, et al. An agent-based decision support system for resources′ scheduling in emergency supply chains[J]. Control Engineering Practice, 2017,59: 27-43.
[ 8 ] HUANG K, JIANG Y, YUAN Y, et al. Modeling multiple humanitarian objectives in emergency response to large-scale disasters[J]. Transportation Research Part E: Logistics & Transportation Review,2015,75: 1-17.
[ 9 ] 黄天春. 人道主义物流中灾害救援网络研究[J]. 物流工程与管理, 2013, 35(4): 99-100.DOI:10.3969/j.issn.1674-4993.2013.04.040.HUANG Tianchun. Research on the disaster relief network in humanitarian logistics[J]. Logistics Engineering and Management,2013, 35(4): 99-100. DOI:10.3969/j.issn.1674-4993.2013.04.040.(in Chinese)
[10] WANG H, WANG X, ZENG A Z. Optimal material distribution decisions based on epidemic diffusion rule and stochastic latent period for emergency rescue[J]. International Journal of Mathematics in Operational Research, 2009, 1(1/2): 76-96.
[11] BENDERS J F. Partitioning procedures for solving mixed-variables programming problems[J]. Numerische Mathematik,1962,4(1): 238-252.