Multi-Scenario Optimisation Model for Reusable Logistics Resource Allocation
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摘要: 针对极端不确定情况下同时调度多种类型、多种型号可复用物流资源调度优化问题，用情景规划方法研究了可复用物流资源调度多情景规划模型. 首先分析了可复用物流资源的特征和基于共用系统的可复用物流资源调度流程；其次考虑了资源可替代和不可替代两种情况，构建了可复用物流资源调度多情景规划模型，并将客户对资源的需求量、待回收资源的数量等因素分成了确定和极端不确定两部分；最后通过算例分析验证了模型的有效性，并基于研究成果提供了构建中欧班列可复用物流资源共用系统的方案. 研究结果表明：应用可复用物流资源调度多情景规划模型可获得较为满意的需求满足率和回收满足率；算例考虑的两种情况下，多情景规划模型比确定模型期望总成本可分别降低1.7%和5.7%.Abstract: In order to solve the reusable logistics resource（RLR）allocation problem where some uncertain parameters cannot be estimated using historical data, and the types and dimensions of RLR are varied, a multi-scenario optimisation model for RLR allocation was studied using the method of scenario planning. First, the features of RLR and the RLR allocation processes over a pooling system were analysed. Then, a multi-scenario optimisation model for RLR allocation was presented considering that some kinds of resources were capable of being replaced with other kinds while some other kinds of resources were not. The number of demand, recycle, and some other parameters were divided into two parts（certain and uncertain）in the model. Finally, the validity of the model was proved using a case study and the plan for the China-Europe express railway RLR system was proposed based on the results. The results showed that the proposed multi-scenario could make good demand fulfilment and recycling fulfilment. It was also proved that the total expected cost by using multi-scenario model could be reduced by 1.7% and 5.7%, as opposed to the deterministic models considered in both cases.
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Key words:
- logistics /
- reusable resources /
- uncertainty /
- scenario planning /
- China-Europe express railway
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表 1 单位运输成本
Table 1. Unitary transportation cost
调度
中心或客
户i1 i2 j1 j2 o1 o2 i1 3/2/5/1 4/3/5/1 5/4/7/2 6/5/7/2 i2 ∞/∞/∞/∞ 2/1/3/2 4/2/5/3 5/3/7/5 j1 3/2/5/1 ∞/∞/∞/∞ 7/5/8/6 8/6/8/6 j2 4/3/5/1 2/1/3/2 2/1/4/3 ∞/∞/∞/∞ o1 5/4/7/2 4/2/5/3 7/5/8/6 2/1/4/3 o2 6/5/7/2 5/3/7/5 8/6/8/6 ∞/∞/∞/∞ 注：表中有4个数的，分别代表 ${p_1}{\ell _1}$、 ${p_1}{\ell _2}$、 ${p_2}{\ell _1}$、 ${p_2}{\ell _2}$的运输成本. 
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表 2 运输能力
Table 2. Transportation capacity
调度中心或客户 i1 i2 j1 j2 o1 o2 i1 1 000 1 000 400 500 i2 0 700 300 500 j1 1 000 0 400 700 j2 1 000 700 300/300/0 0 o1 400 300 400 300/300/0 o2 500 500 700 0 注： 表中3个数的分别代表s1、s2、s3情景下的运输 能力，其余数字由于在s1～s3情景下的运输能 力相同，故只写一个数.
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表 3 供给和需求
Table 3. Supply and demand
调度中心或
客户${p_1}{\ell _1}$ ${p_1}{\ell _2}$ ${p_2}{\ell _1}$ ${p_2}{\ell _2}$ NKT i1 95/100/105 100 50 100 i2 200 150 100 100 j1 200 50 100/200/300 50 j2 400 80 100 50 o1 100/200/300 120 0/100/200 100 100/200/300 o2 200/400/600 200 0/200/400 100 100/200/300 注： 表中3个数的分别代表s1、s2、s3情景下的供给 或需求，其余数字由于在s1～ s3情景下的供给 或需求相同，故只写一个数.
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表 4 最优方案
Table 4. Optimal scheme
调度中心或客户 i1 i2 j1 j2 o1（NKT） o2（NKT） 租赁 i1 151/30/0/100 0/70/132/100 0/0/0/100 0/0/0/190 57/0/82/440 i2 0/90/100/0 369/85/0/0 0/0/0/100 0/0/0/0 169/25/0/0 j1 369/85/0/0 0/0/0/0 147/0/0/0 33/45/50/0 0/0/0/0 0/0/0/10 j2 33/45/50/0 33/45/50/0 0/0/0/0 0/0/0/0 0/0/0/0 0/0/0/0 注：表中4个数的分别代表 ${p_1}{\ell _1}$、 ${p_1}{\ell _2}$、 ${p_2}{\ell _1}$、 ${p_2}{\ell _2}$.
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表 5 结果分析
Table 5. Results
情景 需求率 回收满足率 ${p_1}{\ell _1}$ ${p_1}{\ell _2}$ ${p_2}{\ell _1}$ ${p_2}{\ell _2}$ NKT ${p_1}{\ell _1}$ ${p_1}{\ell _2}$ ${p_2}{\ell _1}$ ${p_2}{\ell _2}$ s1 100.0 100 100 100 100.0 100 100 87.5 100 s2 93.3 100 94 100 100.0 100 100 58.3 100 s3 66.7 100 47 100 66.7 100 100 48.7 100
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表 6 多情景规划和确定模型的总成本比较
Table 6. Compare the results of multi-scenario model and deterministic model
情景 $ {w_{s_1}} = 0.2$， ${w_{s_2}} = 0.4$，
${w_{s_3}} = 0.4$$ {w_{s_1}} = 0.4$， ${w_{s_2}} = 0.4$，
${w_{s_3}} = 0.2$确定模型 多情景规
划模型确定模型 多情景规
划模型s1 27 730 31 269 27 730 21 114 s2 25 835 24 240 25 835 27 383 s3 44 840 43 245 44 840 46 388 期望总
成本33 816.00 33 247.80 30 394.00 28 676.40
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