碳税政策下生产和销售的选址问题

doi:10.15960/j.cnki.issn.1007-6093.2021.04.004

运筹学学报 ›› 2021, Vol. 25 ›› Issue (4): 45-57.doi: 10.15960/j.cnki.issn.1007-6093.2021.04.004

碳税政策下生产和销售的选址问题

向翀¹, 李小申¹^,*(), 孙广磊²

1. 河南科技大学数学与统计学院, 河南洛阳 471003
2. 河南科技大学信息与工程学院, 河南洛阳 471003

收稿日期:2020-03-09 出版日期:2021-12-15 发布日期:2021-12-11
通讯作者: 李小申 E-mail:hnykli@163.com
作者简介:李小申 E-mail: hnykli@163.com
基金资助:
国家自然科学基金(12071112);国家自然科学基金(11471102);河南省高等学校重点科研项目(20ZX001)

Location problem of production and sales under carbon tax policy

Chong XIANG¹, Xiaoshen LI¹^,*(), Guanglei SUN²

1. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, Henan, China
2. School of Information Engineering, Henan University of Science and Technology, Luoyang 471003, Henan, China

Received:2020-03-09 Online:2021-12-15 Published:2021-12-11
Contact: Xiaoshen LI E-mail:hnykli@163.com

摘要/Abstract

摘要：

本文考虑碳税政策下一个生产型企业生产和销售的选址问题。消费者分布在一条直线上，运输成本是线性的，企业除承担自身产品的运输费用外还承担消费者的运输成本。本文建立了利润最大化模型，分析了利润函数的性质，给出了求解方法。通过数值实验证明了求解方法的有效性，同时得出，即使消费者分布是中心对称的，最优的选址也不一定中心对称，这纠正了人们的错觉。增加碳税可使销售点靠近自己的消费者，增加企业的费用，但不一定起到减排的作用，只有通过灵活的碳税政策才有可能达到减排的目的。

关键词: 选址问题, 碳税政策, 消费者分布, 运输费用比

Abstract:

This paper considers a location problem of production and sales of a production-oriented enterprise under carbon tax policy. Consumers are distributed on a straight line with linear transportation costs. In addition to pay the transportation costs of its own products, the enterprise is also responsible for the transportation costs of consumers. A profit maximization model is established, properties of the profit function are analyzed, and a solving method is given. Numerical experiments prove the effectiveness of the solving method. They show that even if the distribution of consumers is centersymmetric, the optimal location is not necessarily center-symmetric, which corrects the illusion of people. Increasing carbon tax drives the retailers approach their respective customers, increases the enterprise's cost, but may not reduce the carbon emission, which may achieve only by flexible carbon tax policy.

Key words: location problem, carbon tax policy, consumer distribution, transportation cost ratio

中图分类号:

向翀, 李小申, 孙广磊. 碳税政策下生产和销售的选址问题[J]. 运筹学学报, 2021, 25(4): 45-57.

Chong XIANG, Xiaoshen LI, Guanglei SUN. Location problem of production and sales under carbon tax policy[J]. Operations Research Transactions, 2021, 25(4): 45-57.

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参考文献 14

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$ p_{ec} = p_{et} $	$ r $	$ x_1 $	$ x_2 $	$ m $	$ \pi $	$ e $
0	0.394 9	-0.457 9	0.198 5	0.198 5	0.025 3	0.004 1
3.000 0	0.371 7	-0.212 2	0.462 7	-0.212 2	0.041 8	0.004 1
6.000 0	0.362 0	-0.217 9	0.464 7	-0.217 9	0.058 3	0.004 1
9.000 0	0.356 6	-0.465 8	0.220 8	0.220 8	0.074 8	0.004 1
12.000 0	0.353 1	-0.466 4	0.223 2	0.223 2	0.091 3	0.004 1
15.000 0	0.350 8	-0.467 5	0.224 6	0.224 6	0.107 8	0.004 0
18.000 0	0.349 0	-0.225 6	0.467 1	-0.225 6	0.124 3	0.004 0
21.000 0	0.347 7	-0.226 3	0.467 4	-0.226 3	0.140 8	0.004 0
24.000 0	0.346 7	-0.467 8	0.227 2	0.227 2	0.157 4	0.004 0
27.000 0	0.345 8	-0.227 2	0.467 8	-0.227 2	0.173 9	0.004 0
30.000 0	0.345 1	-0.227 2	0.467 8	-0.227 2	0.190 4	0.004 0

$ p_{ec} = p_{et} $	$ r $	$ x_1 $	$ x_2 $	$ m $	$ \pi $	$ e $
0	0.394 9	-0.017 9	0.530 4	0.530 4	0.019 8	0.003 3
3.000 0	0.371 7	-0.024 2	0.537 7	0.537 7	0.032 7	0.003 2
6.000 0	0.362 0	-0.026 8	0.541 1	0.541 1	0.045 6	0.003 2
9.000 0	0.356 6	-0.028 3	0.542 9	0.542 9	0.058 5	0.003 2
12.000 0	0.353 1	-0.028 3	0.542 9	0.542 9	0.071 5	0.003 2
15.000 0	0.350 8	-0.028 3	0.542 9	0.542 9	0.084 4	0.003 2
18.000 0	0.349 0	-0.028 3	0.542 9	0.542 9	0.097 3	0.003 2
21.000 0	0.347 7	-0.028 3	0.542 9	0.542 9	0.110 2	0.003 2
24.000 0	0.346 7	-0.028 3	0.542 9	0.542 9	0.123 2	0.003 2
27.000 0	0.345 8	-0.028 3	0.542 9	0.542 9	0.136 1	0.003 2
30.000 0	0.345 1	-0.028 3	0.542 9	0.542 9	0.149 0	0.003 2

$ p_{et} $	$ r $	$ x_1 $	$ x_2 $	$ m $	$ \pi $	$ e $
0	0.394 9	-0.457 9	0.198 5	0.198 5	0.025 3	0.004 1
3.000 0	0.234 7	-0.300 8	0.485 5	-0.300 8	0.037 1	0.003 8
6.000 0	0.167 0	-0.492 9	0.351 8	0.351 8	0.048 3	0.003 7
9.000 0	0.129 6	-0.495 6	0.382 2	0.382 2	0.059 4	0.003 7
12.000 0	0.105 9	-0.497 3	0.401 9	0.401 9	0.070 3	0.003 7
15.000 0	0.089 5	-0.497 8	0.416 1	0.416 1	0.081 2	0.003 6
18.000 0	0.077 5	-0.498 5	0.426 8	0.426 8	0.092 0	0.003 6
21.000 0	0.068 4	-0.499 0	0.435 0	0.435 0	0.102 9	0.003 6
24.000 0	0.061 2	-0.498 8	0.441 5	0.441 5	0.113 7	0.003 6
27.000 0	0.055 3	-0.499 5	0.447 2	0.447 2	0.124 5	0.003 6
30.000 0	0.050 5	-0.499 2	0.451 2	0.451 2	0.135 3	0.003 6

$ p_{et} $	$ r $	$ x_1 $	$ x_2 $	$ m $	$ \pi $	$ e $
0	0.394 9	-0.017 9	0.530 4	0.530 4	0.019 8	0.003 3
3.000 0	0.234 7	-0.054 2	0.587 1	0.587 1	0.029 2	0.003 1
6.000 0	0.167 0	-0.063 9	0.613 9	0.613 9	0.038 4	0.003 0
9.000 0	0.129 6	-0.063 9	0.613 9	0.613 9	0.047 5	0.003 0
12.000 0	0.105 9	-0.063 9	0.613 9	0.613 9	0.056 5	0.003 0
15.000 0	0.089 5	-0.063 9	0.613 9	0.613 9	0.065 6	0.003 0
18.000 0	0.077 5	-0.063 9	0.613 9	0.613 9	0.074 7	0.003 0
21.000 0	0.068 4	-0.063 9	0.613 9	0.613 9	0.083 8	0.003 0
24.000 0	0.061 2	-0.063 9	0.613 9	0.613 9	0.092 9	0.003 0
27.000 0	0.055 3	-0.063 9	0.613 9	0.613 9	0.102 0	0.003 0
30.000 0	0.050 5	-0.063 9	0.613 9	0.613 9	0.111 1	0.003 0

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[4]	徐大川, 万玮, 吴晨晨, 徐文青. 随机容错设施选址问题的原始-对偶近似算法[J]. 运筹学学报, 2014, 18(2): 17-28.

碳税政策下生产和销售的选址问题

Location problem of production and sales under carbon tax policy

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