Distributed preset reserve for multiple points with stochastic demands
Article Text (Baidu Translation)
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摘要: 考虑重点方向或区域中, 各重要隘口、通道、敏感地带等突发事件之间的关联性(连锁反应的可能性) 和需求的随机性, 在多个预置储备仓库构成储备网络和多个需求点组成需求网络的条件下, 研究了用储备网络保障需求网络的预置储备规模和储备分布优化问题, 分析了需求网络在各点突发事件和需求随机下总需求的分布特征; 在保证预置储备规模有效性、经济性与储备分布合理性的基础上, 建立了给定安全保障概率下的储备规模模型和过程响应准则下的分布式储备模型(统称储备模型); 根据模型特征将分布式储备模型分解为双层模型, 对随机需求采用样本化处理, 并在此基础上建立了针对性的遗传-模拟退火算法求解双层模型; 基于变异系数的概念, 提出了针对突发事件和需求随机的储备方案稳健性指标, 对储备模型及其算法进行了稳健性分析, 并通过案例应用验证了储备模型及其算法的有效性。研究结果表明: 相较于就近分区准则, 储备规模模型及其算法能在确保安全保障概率的前提下将储备规模降低约1/3;相较于极大极小化准则, 过程响应准则下的分布式储备方案可使首批物资响应时间减少11%, 使90%物资的响应时间减少21%;在面临需求网络中突发事件和需求的随机性波动时, 储备方案的波动幅度不超过需求波动的80%, 体现了较好的稳健性。Abstract: Considering the correlations of emergencies (possibility of chain reaction) among the important pass, passageway, and sensitive zone, and the randomness of demands in the key directions or areas, the optimization problems of preset reserve scale and reserve distribution about the reserve network supporting the demand network were studied. The reserve network consisted of multiple preset reserve warehouses, and the service demand network consisted of multiple stochastic demand points. The distribution characteristics of the total demand in the demand network were analyzed under the conditions that the emergency at each point and the demand quantity were random. Ensuring the effectiveness and economy of the preset reserve scale and the rationality of the reserve distribution, the reserve scale model under the given securityprobability and the distributed reserve model under the process response criterion (collectively called reserve model) were established. According to the characteristics of the model, the distributed reserve model was decomposed into a bi-level model. The sample processing method was used to resolve the random demand problem. On this basis, agenetic-simulated annealing algorithm was constructed to solve this model. Based on the concept of variation coefficient, a robustness index for reserve scheme with random emergency and random demand was proposed to analyze the robustness of the reserve model and its algorithm. The validities of the reserve model and its algorithm were verified by a case application. Research result shows that in comparison with the nearby partition principle, the reserve scale model and its algorithm can reduce the reserve scale by approximately 1/3 under the premise of ensuring the security probability. In comparison with the maximin criterion, the distributed reserve scheme under the process response criterion can reduce the response time of the first batch of materials by 11%, and the response time of 90% of materials reduces by 21%. When facing the stochastic fluctuation of emergency and demand in the demand network, the amplitude of fluctuation for the distributed reserve scheme is no more than 80% of the demand fluctuation, which suggests better robustness.
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图 2 极大极小化准则下最大响应时间分布
Figure 2. Distribution of maximum response time under maximin criterion
表 3 某重点区域总需求与突发事件的概率分布
Table 3. Probability distributions of total demand and emergency in a key area
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表 4 就近分区策略下储备仓库的保障对象与储备规模
Table 4. Support objects and reserve scales of reserve warehouses under nearby partition principle
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