为了优化应急物资配送系统,提高配送的时效性和经济性,以总时间最短和总成本最小为目标,建立了不确定双目标机会约束优化模型,在这个模型中综合考虑了需求点的限制期要求以及需求点物资需求量的不确定性、两节点运输时间的不确定性、若干车辆容量的有限性和若干候选救援中心容量的有限性,并且假设救援车辆完成自身的任务后停靠在就近已经启用的救援中心;运用遗传算法求解该模型,并且利用惩罚函数的思想以及加权法对目标进行了处理,最后给出数值例子验证该模型和算法的有效性.
For improving the efficiency of delivery time and reducing cost for emergency materials distribution after natural disasters, this paper aims to construct a uncertain bi-objective chance-constrained programing model for optimizing total travel time and total cost, where the time restriction of demand center, the candidate rescue centers capacity and the vehicles capacity are limited, and the demand of materials and the travel time between two nodes are uncertain. For saving cost, vehicles are considered to stand at the nearby opened rescue center when it finishes its delivery tasks. In this paper, the programming model is solved by a genetic algorithm and the objective is handled by the idea of penalty function and weighting method. Finally, an numerical example is designed to show that this model and the algorithm are useful and available.
[1] ÖZDAMAR L, ERTEM M A. Models, solutions and enabling technologies in humanitarian logistics[J]. Eur J Oper Res, 2015, 244(1): 55-65. DOI:10.1016/j.ejor.2014.11.030.
[2] 楼振凯.应急物流系统LRP的双层规划模型及算法[J].中国管理科学, 2017, 25(11): 151-157. DOI:10.16381/j.cnki.issn1003-207x.2017.11.016.
[3] VAHDANI B, VEYSMORADI D, SHEKARI N, et al. Multi-objective, multi-period location-routing model to distribute relief after earthquake by considering emergency roadway repair[J]. Neural Comput Appl, 2018, 30(3): 835-854. DOI:10.1007/s00521-016-2696-7.
[4] 袁涛,蔡佳,郑磊,等.考虑道路损毁情况的应急物流LRP研究[J].铁道运输与经济, 2021, 43(9): 30-37. DOI:10.16668/j.cnki.issn.1003-1421.2021.09.06.
[5] CAUNHYE A M, ZHANG Y D, LI M Z, et al. A location-routing model for prepositioning and distributing emergency supplies[J]. Transp Res E Logist Transp Rev, 2016, 90: 161-176. DOI:10.1016/j.tre.2015.10.011.
[6] 代颖,马祖军.应急物流系统中的随机定位—路径问题[J].系统管理学报, 2012, 21(2): 212-217, 223. DOI:10.3969/j.issn.1005-2542.2012.02.009.
[7] VAHDANI B, VEYSMORADI D, NOORI F, et al. Two-stage multi-objective location-routing-inventory model for humanitarian logistics network design under uncertainty[J]. Int J Disast Risk Reduct, 2018, 27: 290-306. DOI:10.1016/j.ijdrr.2017.10.015.
[8] MORENO A, ALEM D, FERREIRA D, et al. An effective two-stage stochastic multi-trip location-transportation model with social concerns in relief supply chains[J]. Eur J Oper Res, 2018, 269(3): 1050-1071. DOI:10.1016/j.ejor. 2018.02.022.
[9] ZHANG B, PENG J, LI S G. Covering location problem of emergency service facilities in an uncertain environment[J]. Appl Math Model, 2017, 51: 429-447. DOI:10.1016/j.apm.2017.06.043.
[10] ZHANG B, LI H, LI S G, et al. Sustainable multi-depot emergency facilities location-routing problem with uncertain information[J]. Appl Math Comput, 2018, 333: 506-520. DOI:10.1016/j.amc.2018.03.071.
[11] LIU B D. Uncertainty theory[M]. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. DOI:10.1007/978-3-662-44354-5. (
