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摘要: 总结了Larson的SIRSA (Strategic Inventory and Routing Saving Algorithm) 启发式解法, 针对其补充周期短的缺陷, 提出了以库存补充周期和补充阶段为变量的PPSA (Period andPhase Saving Algorithm) 启发式解法。计算结果表明, 当车辆每作业一次能补充的客户数较多, 且客户间最大的可能补充时间间隔差别较大时, PPSA算法对车辆的需求明显少于SIRSA算法。Abstract: In order to amend the shortcomings of replenishment period short of Larson's SIRSA heuristic algorithm, the paper set up PPSA heuristic algorithm, in which the inventory replenishment period and inventory replenishment phase are variables. The computational results show that when the vehicle is large enough to replenish several customers in a single trip and there is significant variation in the maximum inter-replenishment intervals of the customers, the vehicle demand of SIRSA algorithm is larger than that of PPSA algorithm.
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表 1 基本参数
Table 1. Basic parameters
位置 客户的存储能力/单位 有效平均库存消耗μi/ (单位·d) Tmaxi/d x/km y/km 准备时间/h 装卸速率/ (单位·h) 0 ∞ 1 ∞ 0 0 0.75 7 000 1 1 800 2 000 0.900 -181.2 -66.1 0.167 3 500 2 1 690 380 4.447 -180.5 60.4 0.167 3 500 3 2 085 680 3.066 -187.9 -11.9 0.167 3 500 4 2 030 1 650 1.230 -143.5 152.7 0.167 3 500 5 1 515 3 570 0.424 -199.3 -14.6 0.167 3 500 6 1 560 2 820 0.553 -36.2 25.3 0.167 3 500 7 1 065 630 1.690 -174.1 16.4 0.167 3 500 8 1 880 1 285 1.463 -120.6 162.3 0.167 3 500 9 745 580 1.284 -149.5 -39.7 0.167 3 500 
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表 2 SIRSA的解
Table 2. Solution of SIRSA algorithm
客户集 路线 客户顺序 距离/km 旅行时间/h 库存补充时间间隔/d 平均车辆需求/veh 1 1 0-1-5-0 447.2 7.7 0.424 2.267 2 2 0-2-0 380.8 6.4 4.447 0.180 3 3 0-7-3-9-0 408.8 7.4 1.284 0.721 4 4 0-4-0 419.2 7.0 1.230 0.714 5 5 0-6-0 88.3 2.7 0.553 0.608 6 6 0-8-0 404.8 6.8 1.463 0.579
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表 3 PPSA的解
Table 3. Solution of PPSA algorithm
客户集 路线 客户顺序 距离/km 旅行时间/h 库存补充时间间隔/d 平均车辆需求/veh 1 1 0-1-5-3-0 447.5 8.7 0.424 2.213 2 0-5-0 399.7 6.6 0.424 3 0-1-5-0 447.2 8.1 0.424 4 0-5-0 399.7 6.6 0.424 5 0-1-5-0 447.2 8.1 0.424 6 0-5-0 399.7 6.6 0.424 7 0-1-5-0 447.2 8.1 0.424 2 1 0-7-9-0 390.8 6.6 1.284 0.711 2 0-2-7-9-0 450.7 8.0 1.284 3 1 0-4-0 419.2 7.0 1.230 0.714 4 1 0-6-0 88.3 2.7 0.553 1.094 2 0-6-0 88.3 2.7 0.553 3 0-6-8-0 407.3 7.4 0.357
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表 4 SIRSA和PPSA敏感性对比
Table 4. Sensitivity comparison of SIRSA and PPSA
RWC=4 RWC=8 RT=5 RT=10 RT=20 RT=5 RT=10 RT=20 SIRSA的ρ 9.508 11.317 13.915 7.827 2 9.859 4 12.619 PPSA的ρ 9.424 10.915 13.105 7.680 7 9.211 2 11.544 ρ减少/% 0.9 3.5 5.8 1.9 6.6 8.5
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