Chinese Journal of Management Science ›› 2026, Vol. 34 ›› Issue (11): 199-209.doi: 10.16381/j.cnki.issn1003-207x.2024.1151
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Jianbin Li1,2, Gong Feng1, Ping Zhou3, Cheng Yang1, Qihuang Mei4(
)
Received:2024-07-12
Revised:2025-01-09
Online:2026-11-25
Published:2026-11-10
Contact:
Qihuang Mei
E-mail:qhmei@wtu.edu.cn
CLC Number:
Jianbin Li,Gong Feng,Ping Zhou, et al. Research on Multi-Period Lot-Sizing Problem Considering Raw Material Substitution[J]. Chinese Journal of Management Science, 2026, 34(11): 199-209.
"
| 参数 | 含义 |
|---|---|
| 集合 | |
| 烟草产品集合, | |
| 烟叶原料集合, | |
| 生产周期集合, | |
| 生产机器集合, | |
| 烟草产品 | |
| 烟草产品 | |
| 烟草产品 | |
| 烟草产品 | |
| 一个足够大的正整数 | |
| 生产机器 | |
| 生产1单位烟草产品 | |
| 生产1单位烟草产品 | |
| 原料 | |
| 原料 | |
| 原料 | |
| 在生产周期 | |
| 生产周期 | |
| 决策变量 | |
| 生产周期 | |
| 在生产周期 | |
| 生产周期 | |
| 在生产周期 |
"
| 算例 | N | T | Gurobi | 贪婪算法 | ALNS | 混合ALNS | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| obj | t/s | obj | t/s | obj | t/s | Gap_AG/% | Gap_AT/% | obj | t/s | Gap_G/% | Gap_T/% | Gap_A/% | |||
| A1 | 2 | 2 | 8023.11 | 0.1 | 10221.78 | 0 | 9047.01 | 6.5 | -12.76 | 11.49 | 8023.11 | 4.73 | 0 | 21.51 | 11.32 |
| A2 | 2 | 8 | 25904.09 | 2.0 | 37343.68 | 0 | 32735.68 | 10.5 | -26.37 | 12.34 | 25904.09 | 5.36 | 0 | 30.63 | 20.87 |
| A3 | 3 | 10 | 45187.81 | 5.0 | 64868.28 | 0.001 | 58742.28 | 14.3 | -30.00 | 9.44 | 45187.81 | 19.07 | 0 | 30.34 | 23.07 |
| A4 | 4 | 12 | 72406.51 | 8.0 | 107658.76 | 0.002 | 97434.75 | 25.6 | -34.57 | 9.50 | 72406.51 | 31.82 | 0 | 32.74 | 25.69 |
| A5 | 5 | 14 | 99676.70 | 20.0 | 153701.28 | 0.002 | 142553.28 | 27.8 | -43.02 | 7.25 | 99676.70 | 32.46 | 0 | 35.15 | 30.08 |
| A6 | 6 | 16 | 119852.47 | 50.0 | 198922.96 | 0.003 | 186145.96 | 30.3 | -55.31 | 6.42 | 119892.48 | 35.38 | -0.03 | 39.73 | 35.59 |
| A7 | 6 | 18 | 134687.29 | 250.0 | 226003.21 | 0.003 | 209806.21 | 122.17 | -55.77 | 7.17 | 136051.29 | 45.83 | -1.00 | 39.80 | 35.15 |
| A8 | 7 | 20 | - | 36000 | 297525.31 | 0.004 | 262508.31 | 130.62 | - | 11.77 | 158213.03 | 46.72 | - | 46.82 | 39.73 |
| A9 | 7 | 22 | - | 36000 | 330394.81 | 0.006 | 273330.81 | 134.13 | - | 17.27 | 167770.66 | 53.41 | - | 49.22 | 38.62 |
| A10 | 8 | 24 | - | 36000 | 419445.59 | 0.006 | 345092.59 | 153.65 | - | 17.73 | 188622.54 | 54.05 | - | 55.03 | 45.34 |
| A11 | 9 | 26 | - | 36000 | 603469.64 | 0.013 | 538536.64 | 291.69 | - | 10.76 | 229053.89 | 57.72 | - | 62.04 | 57.47 |
| A12 | 10 | 28 | - | 36000 | 724157.02 | 0.013 | 628934.02 | 614.36 | - | 13.15 | 273883.39 | 57.74 | - | 62.18 | 56.45 |
| A13 | 11 | 30 | - | 36000 | 835364.14 | 0.013 | 703890.14 | 1027.51 | - | 15.74 | 312184.54 | 281.27 | - | 62.63 | 55.65 |
| A14 | 12 | 32 | - | 36000 | 934261.63 | 0.016 | 807350.63 | 1336.51 | - | 13.58 | 377407.60 | 389.5 | - | 59.60 | 53.25 |
| Avg | - | - | - | - | - | - | - | - | - | 11.69 | - | - | - | 44.82 | 37.73 |
"
| 算例 | N | T | 存在原料替代 | ||||||
|---|---|---|---|---|---|---|---|---|---|
| 总成本 | 生产成本 | 生产准备成本 | 持有成本 | 缺货成本 | 替代成本 | ||||
| B1 | 6 | 8 | 72301.0 | 42240.0 | 11931.0 | 12620.0 | 0.0 | 5510.0 | |
| B2 | 8 | 8 | 94952.3 | 53460.0 | 21861.0 | 13060.0 | 0.0 | 6571.3 | |
| B3 | 10 | 8 | 121973.8 | 71280.0 | 23909.0 | 18720.0 | 0.0 | 8064.8 | |
| B4 | 12 | 8 | 155968.4 | 91740.0 | 30609.0 | 25300.0 | 0.0 | 8319.4 | |
| B5 | 14 | 8 | 167116.6 | 102300.0 | 30845.0 | 26940.0 | 0.0 | 7031.6 | |
| B6 | 16 | 8 | 181483.4 | 107580.0 | 34185.0 | 32120.0 | 0.0 | 7598.4 | |
| 算例 | N | T | 不存在原料替代 | ||||||
| 总成本 | 生产成本 | 生产准备成本 | 持有成本 | 缺货成本 | 替代成本 | ||||
| B1 | 6 | 8 | 104331.0 | 28987.0 | 8566.0 | 7130.0 | 59648.0 | - | |
| B2 | 8 | 8 | 142066.0 | 35996.0 | 13038.0 | 10030.0 | 83002.0 | - | |
| B3 | 10 | 8 | 160274.0 | 52539.0 | 16511.0 | 14080.0 | 77144.0 | - | |
| B4 | 12 | 8 | 196104.0 | 67304.0 | 22008.0 | 17790.0 | 89002.0 | - | |
| B5 | 14 | 8 | 211559.0 | 79558.0 | 24745.0 | 19213.0 | 88043.0 | - | |
| B6 | 16 | 8 | 220265.0 | 85568.0 | 29734.0 | 22561.0 | 82402.0 | - | |
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