The capandoffset regulation is a practical scheme to lessen carbon emissions. The retailer selling fresh products can adopt sustainable technologies to lessen greenhouse gas emissions. We aim to analyze the optimal joint strategies on order quantity and sustainable technology investment when the retailer faces stochastic market demand and can only acquire the mean and variance of distribution information. We construct a distributionally robust optimization model and use the KarushKuhnTucker (KKT) conditions to solve the analytic formula of optimal solutions. By comparing the models with and without investing in sustainable technologies, we examine the effect of sustainable technologies on the operational management decisions of the retailer. Finally, some computational examples are applied to analyze the impact of critical factors on operational strategies, and some managerial insights are given based on the analysis results.
With the intensification of climate warming and enhancement of sustainable awareness, carbon emissions reduction has become one of the critical issues in the world. Carbon dioxide is a major contributor to global warming. Many countries and regions have set shortterm and longterm targets to lessen emissions. In September 2020, the Chinese government promised to lower carbon emissions, and successively released a series of supporting measures to achieve carbon peaking and carbon neutrality goals. Great efforts, such as implementing carbon regulations, have been made to achieve the goal of sustainable development [
In this context, the operational objective of the retailer has been changed to pursue economic benefits and protect environment simultaneously. Many enterprises take active measures to protect the environment. For example, WalMart, the largest department store in the United States, actively adopted new technologies to save energy and has built a lowcarbon distribution center and a lowcarbon supermarket. The development of cold chain market urges retailers to concentrate on the operational management of fresh products. The fresh products have perishable physical properties and are preserved in special temperaturecontrolled equipment that generates higher carbon emissions. Lekkerland, a famous retailer in Germany, implemented a “multitemperature logistics” distribution strategy to sell perishable products. However, using such special multitemperature equipment leads Lekkerland to produce much greenhouse gases compared with standard warehousing and logistics systems [
Affected by market fluctuations and uncertainties, it is more difficult for fresh product retailers to forecast the full distribution information of demand [
To address the major issues mentioned above, we consider the operational strategy of a fresh product retailer under capandoffset regulation. The retailer has to decide whether to invest in sustainable technology to lessen greenhouse gas emissions and find the optimal order quantity only according to the mean and variance of the stochastic demand. In order to give valuable suggestions to the retailer, we construct a distributionally robust optimization model and work out the analytic formula of joint order quantity and lowcarbon technology investment. We further explore the situation without technology investment and compare two distributionally robust optimization models. Finally, some computational studies are conducted to validate the impact of principal factors on the robustness of operational decisions.
Our work has the following research contributions. First, we consider limited distribution information of stochastic demand and lowcarbon technology investment in operational decisions of the fresh product retailer. We use a distributionally robust newsvendor method to work out the analytic formula of joint order quantity and sustainable technology investment. Second, we theoretically and numerically provide some conditions where investing in sustainable technology leads the fresh product retailer to gain higher expected profit and emit lower greenhouse gases under capandoffset regulation. Finally, we numerically investigate how carbon parameters affect the robustness of the optimal joint strategies on order quantity and sustainable technology investment.
The reminders of this paper are arranged as follows.
Two research branches are connected with the considered topic. Operational decisions of the fresh product retailer and robust decisions of the retailer under carbon regulations.
The first branch of research concentrates on operational decisions of the fresh product retailer. This topic has received extensive attentions. In this context, Cai et al. [
The articles mentioned above do not consider the impact of carbon emission reduction on developing models for different types of supply chains with fresh products. However, how to lessen carbon emissions has become a major issue in optimizing the fresh product supply chain. It is due to the fact that employing special packaging, cryogenic devices and other equipment may release more greenhouse gases. Bai et al. [
The second branch of research concentrates on frims’ robust decisions under carbon regulations. This topic is popular in the operational management field. Due to the difficulties of acquiring full information of demand distribution, distributionally robust optimization approach is proposed to work out the optimal tactics with limited distribution information [
The retailer purchases
In
If actual demand
In
The transportation is the main link to emit greenhouse gases. The retailer can reduce carbon emissions by investing in sustainable technologies, equipments or machineries. The marginal reduction amount of carbon emissions deceases as the increment of the investment cost that identifies with the principle of “Increasing Marginal Cost” in economics. Referring to Huang et al. [
Considering the fact that the carbon emissions cannot be completely lessened to 0 even if investing in sustainable technologies, we assume that carbon emissions satisfies
Decision variables  Explanation 

Order quantity  
The investment cost of sustainable technology  
Other parameters  Explanation 
Unit order cost  
Unit transportation cost  
The shortage cost per unit product  
Unit sales price  
Surviving index of fresh products  
Freshness index of fresh products  
Random factor of the market demand. Assuming that the retailer can only acquire the mean 

The stochastic market demand  
The potential sales scale  
The price elasticity of demand  
Carbon emission per unit product before investment  
Total carbon emissions  
Expected profit function without carbon regulations 
This subsection utilizes the distributionally robust optimization approach to analyze the optimal joint strategies on order quantity and sustainable technology investment. The fresh product retailer faces the fact that the probability distribution of demand is difficult to acquire and operation management is constrained by capandoffset regulation.
Referring to Chen et al. [
Based on historical data information, the retailer can only acquire the mean
Here,
We solve the distributionally robust optimization models
Referring to Gallego et al. [
And there exists a distribution function
For the convenience of solving the model, set
To ensure the feasibility of the solution, we assume that
Using
Please refer to
From the proof of Theorem 3.1, we can also draw the following corollary that reflects the conditions of investment and relation between the total carbon emissions and carbon cap for model
When
When
When
Next, we solve the distributionally robust optimization model
Defined
Using
Otherwise, there does not exist optimal solutions.
Above theorem indicates that when carbon emissions are restricted by carbon cap, the optimal joint strategy is easier to determine than in the case where carbon emissions exceed carbon cap. Additionally, the selection of optimal solution only depends on carbon cap
According to Theorem 3.2, we can also draw the following corollary that reflects the conditions of investment and relation between the total carbon emissions and carbon cap for model
When
When
Combining with Theorem 3.1 and Theorem 3.2, we can get Theorem 3.3.
Theorem 3.3 shows that the fresh product retailer can make the distributionally robust optimal decisions to maximize expected profit function when the random demand information is limited to know.
This subsection constructs another distributionally robust optimization model, denoted as
Similar to model
Without investing in sustainable technology,
For Model
For Model
For Model
Theorem 3.4 solves the analytic formula for the optimal solution of
According to Theorem 3.3 and Theorem 3.4, we can obtain the following theorem.
If
If
If
Theorem 3.5 compares the expected profits and carbon emissions between models
In this subsection, the computational examples are reported. We explore the impact of some critical parameters, such as carbon cap
Based on the above situation, we solved the expected profits and carbon emissions of the retailer with only acquiring the mean and variance of stochastic demand. The calculation results are shown in
Ordering quantities  Sustainable technology investments  Expected profits  Carbon emissions  

675.82  57.62  3215.68  3800  
667.76  0  3188.56  4006.54 
From
From the aspect of emissions, if the retailer decides to invest in sustainable technology under capandoffset regulation with limited distribution information, the optimal sustainable technology investments are 57.62, and the carbon emissions are 3800, which are equivalent to the carbon cap stipulated by authorities. When the retailer does not invest in sustainable technology, the carbon emissions are 4006.54 that exceed the carbon cap. It shows that investing in sustainable technologies can effectively lessen releasing greenhouse gases.
Moreover, the expected profits in the case of investing in sustainable technology increase by 0.8% and the carbon emissions decrease by 8.2% compared with the case of no investment. It demonstrates that under the capandoffset regulation, investing in sustainable technology is more conducive for the retailer to achieving higher expected profits and lower carbon emissions.
We further analyze the sensitivity effects of carbon cap
According to the above discussion, the increase of carbon cap could encourage retailer to order and increase operating profit. But the increase of carbon tax could restrict the retailer to ordering less products and lessen operating profit. Under the capandoffset regulation, the optimal order quantity and expected profits after investment are always no less than that without investment. As well as the carbon emissions are always no more than that without investment. This suggests that the capandoffset regulation can effectively promote the retailer to invest in sustainable technology. It is beneficial for the retailer to achieve the target of higher expected profits and lower carbon emissions.
Next, we analyze the impact of surviving index
In addition, we can also find that no matter how the survival and freshness of products affect business operations, investing in sustainable technologies is more profitable and emits fewer emissions than that without investment under the capandoffset policy.
With the enhancement of environmental awareness, the sustainable management concept brings new opportunities and challenges to the operation of fresh product retailers. Based on this background, we combine capandoffset regulation to research the optimal decisions of the fresh product retailer. Firstly, we construct distributionally robust newsvendor models where the information of stochastic factors in the market demand is limited to the mean and variance. We propose the analytic formula of joint decisions on order quantity and lowcarbon technology investment by KKT conditions. A further comparison between the problems with investment and without investment is revealed. Finally, numerical studies are carried out to verify the impact of the critical carbon factors on the robustness of operational tactics. The results show that the capandoffset regulation can effectively encourage the retailer to invest in sustainable technologies and lead to higher expected profits and lower carbon emissions. This is consistent with the retailer’s longterm goals and is conducive to achieving sustainable development. This paper mainly studies the optimal strategies from the angle of a single fresh product retailer. Further research can be conducted from the angle of the whole supply chain with fresh products in the future.
This study is financially supported by the National Natural Science Foundation of China (Grant No. 71702087), the Youth Innovation Science and Technology Support Program of Shandong Province Higher Education (Grant No. 2021RW024), and the Special Funds for Taishan Scholars, Shandong (Grant No. tsqn202103063).
The authors declare that they have no conflicts of interest to report regarding the present study.
Let
Using
KKT conditions are as follows:
In actual operation, the retailer pursues profit maximization, and the stock factor satisfies the condition
Case 1.
Case 2.
Since
If
Case 3.
Substituting
Case 4.
Case 5. Combining with Case 3 and Case 4 in the overlapping interval
Let
Using
KKT conditions are as follows:
Similar to the proof of Theorem 3.1, we assume the stock factor satisfies
Case 1.
Case 2.
Taking the first derivative on
Case 3.
From
Case 4.
(i) Using
According to the aforementioned proof, we know that if
(ii) According to Theorem 3.1 and Theorem 3.4, it is easy to verify the conclusion by taking