需求不确定的修正库存定价模型

doi:10.15960/j.cnki.issn.1007-6093.2023.03.002

摘要/Abstract

摘要：

经济订货量(EOQ)模型的目的是寻找使得总库存成本最小化的最优订货量，从而解决库存管理独立需求的问题。本文在EOQ模型的基础上提出了一种修正的库存定价模型。该模型是用波动需求代替原确定需求。与经典EOQ模型不同，修正模型的研究目标是寻找使总利润最大化的最优价格。由于修正模型中具有波动量$\zeta$，本文通过求解其鲁棒对等模型得到最优解。在低碳的背景下，政府和企业必须采取积极措施来降低碳排放。为实现低碳目标，本文在修正的库存定价模型中添加了碳税变量，进一步分析碳税政策下最优价格的变化情况。最后，通过数值算例说明了在碳税政策下，为获得更多的利润，企业应积极探索节能减排方法，加强节能减排管理。

关键词: EOQ, 波动集, 库存定价, 低碳, 鲁棒对等

Abstract:

The economic order quantity (EOQ) model seeks the optimal order quantity to minimize the total inventory cost, so as to solve the inventory management problem with independent demand. In this work, a modified inventory pricing model based on the EOQ model is proposed. In the presented model, the original certain demand is replaced by a perturbation demand. Different from the classical EOQ model, the goal of modified model is to find the optimal price maximum the total profit. Because the modified model has perturbation set $\zeta$, it is hard to obtain the optimal solution. We get the optimal solution by solving its robust counterpart model. In the context of low carbon, in the meantime, the government and enterprises must take positive measures to reduce carbon emissions. The carbon tax is added to the modified inventory pricing model in order to reduce carbon emission. Finally, numerical examples is provided to support that enterprises should appropriately reduce carbon emissions in order to obtain more profits under the carbon tax policy.

Key words: EOQ, perturbation set, inventory pricing, low-carbon, robust counterpart

中图分类号:

O221.2

苏珂, 任晓慧. 需求不确定的修正库存定价模型[J]. 运筹学学报, 2023, 27(3): 21-36.

Ke SU, Xiaohui REN. A modified inventory pricing model with uncertainty demand[J]. Operations Research Transactions, 2023, 27(3): 21-36.

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文献	需求形式					碳政策	自变量	目标函数
文献	确定	线性	随机	模糊	波动	碳政策	自变量	目标函数
[8]	$ \surd $					None	订单量	成本
[9]	$ \surd $					None	订单量	利润
[10]	$ \surd $					None	销售价格	利润
[11]	$ \surd $					None	订单量	成本
[12]	$ \surd $					None	订单量	成本
[13]		$ \surd $				碳税	订单量	成本
[14]		$ \surd $				碳税、限额交易	订单量	成本
[15]		$ \surd $				碳税、限额交易	订单量	利润
[16]				$ \surd $		None	订单量	成本
[20]			$ \surd $			None	订单量	利润
[21]		$ \surd $				碳税政策	订单量	成本
[22]	$ \surd $					环境因素	订单量	成本
[23]	$ \surd $					限额交易政策	订单量	成本
[25]	$ \surd $					环境因素	采购次数	成本
[27]		$ \surd $				限额交易政策	订单量	成本
本文		$ \surd $			$ \surd $	碳税政策	销售价格	利润

$ D $	市场实际需求量	$ D_{0} $	市场潜在需求量
$ w $	单位产品的批发价格	$ p $	单位产品的销售价格
$ k $	需求的价格敏感系数	$ h $	单位订单的库存持有成本
$ Q $	单位订单的经济订货量	$ Q_{0} $	每订单的最大订货量
$ a $	订单量的价格敏感系数	$ A $	每次补货的固定订购成本
$ t $	单位碳排放征税价格	$ E $	每年总碳排放量
$ e $	单位时间排放水平	$ g $	仓库单位时间可变排放量
$ \pi $	波动需求下零售商的总利润	$ \pi_{t} $	碳税约束下零售商的总利润

参数	(PC$ _{1} $)	(PC$ _{2} $)	(PC$ _{3} $)	(PC$ _{3}' $)
价格$ p $	$ 105.017 $	105.017	$ 105.033 $	$ 105.017 $
利润	26 943.80	$ 30 618.80 $	$ 29 840.48 $	$ 26 373.05 $

	价格$ p $	利润	排放
$ t=0 $	105.017	$ 30\, 618.80 $	145.239
$ t=2 $	105.033	$ 29\, 840.48 $	144.243
$ t=4 $	105.050	$ 29\, 351.44 $	144.242
$ t=8 $	105.107	$ 28\, 390.21 $	144.244
$ t=12 $	105.117	$ 27\, 453.02 $	144.238