The Impacts of Payment Schemes and Carbon Emission Policies on Replenishment and Pricing Decisions for Perishable Products in a Supply Chain
Abstract
:1. Introduction
2. Notations and Assumptions
the portion of the procurement cost that must be paid upfront, | |
the portion of the procurement cost payable upon delivery, | |
the portion of the procurement cost that allows for an acceptable delay from the supplier to the retailer, and | |
the duration of credit extended by the retailer to customers, i.e., the downstream credit period, | |
the duration of credit offered by the supplier to the retailer, i.e., the upstream credit period, | |
the proportion of sales revenue that allows for an acceptable delay from the retailer to customers, | |
the annual compound interest paid per dollar | |
the duration over years for which prepayments are made, > 0 | |
the procurement cost per unit in dollars, | |
the holding cost per unit per year in dollars, excluding interest charges, | |
carbon emissions generated during the purchase of a single unit of the product | |
carbon emissions resulting from inventory holding per unit over a given timeframe | |
carbon emissions generated by an order | |
unit carbon trading emission price or unit carbon tax | |
carbon emission cap for the retailer | |
the annual interest charged by the supplier per dollar | |
the annual interest earned per dollar | |
the duration until the expiration date or shelf life, i.e., the stock age, measured in years, | |
the cost of ordering, expressed in dollars per order, | |
the selling price per unit in dollars, (decision variable) | |
the time in years, | |
the annual demand rate, and | |
the deteriorating rate at time and | |
the inventory level in units at time | |
the order quantity | |
the duration of the cycle period, measured in years, (decision variable) | |
the current value of the overall annual profit in dollars | |
the current value of interest incurred for advance payment per cycle period | |
the current value of interest incurred for cash payment per cycle period | |
the current value of interest incurred for credit payment per cycle period | |
the current value of interest accrued for credit payment per cycle period | |
the current value of capital cost per cycle period |
- (1)
- Shortages are prohibited.
- (2)
- The ending inventory is zero.
- (3)
- The freshness and demand of perishable products are absolutely related to the stock age; hence, the demand rate is assumed as a function of selling price and stock age , that is, , where and .
- (4)
- During the credit period provided by the upstream supplier, the unsettled account allows for the generated sales revenue to be deposited into an interest-bearing account. Once the permissible delay period elapses, the retailer settles the remaining procurement cost and proceeds to pay the accrued interest charges on the items in stock. The downstream credit period, , is offered by the retailer. Consequently, the retailer can amass revenue in an account and acquire earned interest when . There is no interest earned for the retailer when . Because the product cannot be sold after the expiration date, it is assumed that and .
- (5)
- The supplier asks that the retailer (i) prepay percentage of procurement cost in years prior to the time of delivery, (ii) pay another percentage of procurement cost at the time of delivery, and (iii) offer a credit period of years on the remaining percentage of procurement cost (i.e., , and ). Similarly, the retailer extends partial trade credit to customers, allowing them a credit period of years for proportion of sales, while the remaining portion (i.e., proportion of sales) is paid in cash.
- (6)
- Two main policy approaches apply to carbon emission reduction: the carbon cap-and-trade policy and the carbon tax policy. Within the framework of the carbon cap-and-trade policy, the retailer is assigned an initial cap for carbon emissions and has the flexibility to trade or exchange emission rights within this established cap. If the retailer exceeds its carbon cap , it must purchase extra carbon allowances from the compliance carbon trading market to offset the difference between its actual emissions and the established cap. In the scenario where the retailer’s carbon emissions fall below its carbon cap, however, the retailer will have the opportunity to trade its surplus carbon allowances with other businesses on the compliance carbon trading market. In the carbon tax policy, the focus is solely on the amount of tax imposed on total carbon emissions, without considering other factors or mechanisms such as trading or allowances. The carbon emissions of the retailer primarily originate from various operational activities, encompassing tasks such as ordering, purchasing, and storage.
3. Mathematical Model Formulation
4. Theoretical Findings
4.1. Case 1:
4.2. Case 2:
5. Numerical Examples
6. Sensitivity Analysis
- (1)
- When any of the parameters increases, the optimal selling price also increases. Conversely, the optimal selling price decreases when the parameters increase. Furthermore, the ordering cost and the procurement cost exert a notable positive influence on the optimal selling price . However, the impact of other parameters on the optimal selling price is relatively limited.
- (2)
- The influence of parameters on the optimal replenishment time is positive, indicating that an increase in any of these parameters results in a longer optimal replenishment time . Conversely, the influence of parameters on is negative, suggesting that an increase in any of these parameters leads to a shorter optimal replenishment time . Also important to highlight is that the ordering cost , procurement cost , stock age , carbon emissions from an order , and carbon trading price all exert a notable positive effect on the optimal replenishment time . Conversely, the holding cost exhibits a substantial negative impact on the optimal replenishment time . The impact of other parameters on the optimal replenishment time is relatively modest.
- (3)
- A higher value of parameters results in a higher optimal order quantity , while a higher value of parameters leads to a lower . Moreover, the ordering cost , stock age , carbon emissions from an order , and carbon trading price all have a considerable positive impact on the optimal order quantity . Conversely, the procurement cost has a substantial negative effect on the optimal order quantity . The influence of other parameters on the optimal order quantity is relatively minor.
- (4)
- The parameters positively influence the optimal current value of the total annual profit , whereas the parameters negatively affect . Furthermore, the stock age exerts a notable positive impact on the optimal current value of the total annual profit . Conversely, both the ordering cost and procurement cost have a considerable negative effect on the optimal current value of the total annual profit . The impact of other parameters on the optimal current value of the total annual profit is relatively minor.
- (5)
- The impact of parameters on the optimal amount of total annual carbon emissions is positive, indicating that an increase in any of these parameters results in a higher . Conversely, the effect of parameters on is negative, suggesting that an increase in any of these parameters leads to a lower . It is worth noting that the carbon emissions from buying a product and the carbon emissions from an order have a substantial positive impact on the optimal amount of total annual carbon emissions . Conversely, the ordering cost , procurement cost , stock age , and carbon trading price all exert a significant negative effect on the optimal amount of total annual carbon emissions . The influence of other parameters on the optimal is relatively limited.
7. Conclusions
- (1)
- When facing an increase in ordering or procurement costs, the retailer is required to elevate the selling price and prolong the replenishment time. Nevertheless, in this scenario, the optimal current values of total annual profit and the optimal amount of total annual carbon emissions both diminish.
- (2)
- As the stock age rises, the retailer needs to elongate the replenishment time and augment the order quantity. Consequently, the optimal current values of total annual profit are expected to rise, while the optimal amount of total annual carbon emissions is anticipated to decrease.
- (3)
- As carbon emissions increase, the retailer must raise the selling price and extend the replenishment time. Consequently, the optimal amount of total annual carbon emissions will increase, while the optimal current values of the total annual profit will decrease.
- (4)
- When the carbon trading price rises, the retailer needs to raise the selling price, extend the replenishment time, and increase the order quantity. Consequently, both the optimal amount of total annual carbon emissions and the optimal current values of the total annual profit will decline.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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References | Demand Function | Payment Type | Carbon Policy |
---|---|---|---|
Chang et al. [43] | Price | ACC | X |
Cheng et al. [16] | Price | Advance-Credit | Carbon tax |
Feng et al. [39] | Price, Stock Age, and Level | ACC | X |
Jain et al. [17] | Constant | X | Cap-and-trade, Carbon tax, and Carbon offset |
Li and Teng [48] | Price, Stock Age, and Level | Cash | X |
Li et al. [51] | Price and Stock Age | ACC | X |
Li et al. [52] | Price | ACC | X |
Ma et al. [6] | Price and Freshness | X | Cap-and-trade |
Mishra et al. [8] | Price and Stock | X | Cap-and-trade |
Roy and Sana [53]) | Stochastic | Credit | X |
Sabzevar et al. [10] | Price | X | Cap-and-trade |
Shi et al. [12] | Constant | ACC | Carbon tax |
Shi et al. [45] | Time | ACC | X |
Taleizadeh et al. [44] | Constant | Advance-Credit | X |
Tsao et al. [40] | Constant | ACC | X |
Wu et al. [42] | Constant | ACC | X |
This paper | Price and Stock Age | ACC | Cap-and-trade and Carbon tax |
Decision | ||||||
---|---|---|---|---|---|---|
Parameter | ||||||
65.01 | 0.14111 | 53.24 | 11,343.70 | 4797.41 | ||
65.07 | 0.15367 | 57.20 | 11,000.90 | 4545.60 | ||
65.12 | 0.16538 | 60.78 | 10,684.10 | 4342.41 | ||
trend | ↗ | ↗ | ↗ | ↘ | ↘ | |
59.97 | 0.14276 | 62.56 | 13,038.40 | 5082.61 | ||
65.07 | 0.15367 | 57.20 | 11,000.90 | 4545.60 | ||
70.18 | 0.16551 | 52.25 | 9271.16 | 4069.54 | ||
trend | ↗ | ↗ | ↘ | ↘ | ↘ | |
65.02 | 0.15432 | 57.49 | 11,059.10 | 4536.50 | ||
65.07 | 0.15367 | 57.20 | 11,000.90 | 4545.60 | ||
65.12 | 0.15303 | 56.91 | 10,942.80 | 4554.47 | ||
trend | ↗ | ↘ | ↘ | ↘ | ↗ | |
65.14 | 0.15393 | 57.16 | 10,965.60 | 4536.65 | ||
65.07 | 0.15367 | 57.20 | 11,000.90 | 4545.60 | ||
65.00 | 0.15338 | 57.23 | 11,036.90 | 4554.96 | ||
trend | ↘ | ↘ | ↗ | ↗ | ↗ | |
64.96 | 0.15034 | 57.19 | 11,061.90 | 4563.57 | ||
65.07 | 0.15367 | 57.20 | 11,000.90 | 4545.60 | ||
65.18 | 0.15426 | 57.20 | 10,942.60 | 4528.62 | ||
trend | ↗ | ↗ | ↗ | ↘ | ↘ | |
64.99 | 0.15313 | 57.16 | 11,058.50 | 4560.09 | ||
65.07 | 0.15367 | 57.20 | 11,000.90 | 4545.60 | ||
65.15 | 0.15422 | 57.24 | 10,943.40 | 4531.09 | ||
trend | ↗ | ↗ | ↗ | ↘ | ↘ | |
65.00 | 0.15325 | 57.18 | 11,032.20 | 4557.21 | ||
65.07 | 0.15367 | 57.20 | 11,000.90 | 4545.60 | ||
65.13 | 0.15410 | 57.22 | 10,969.60 | 4534.00 | ||
trend | ↗ | ↗ | ↗ | ↘ | ↘ | |
65.00 | 0.15444 | 57.56 | 11,028.10 | 4535.59 | ||
65.07 | 0.15367 | 57.20 | 11,000.90 | 4545.60 | ||
65.14 | 0.15291 | 56.84 | 10,973.90 | 4555.57 | ||
trend | ↗ | ↘ | ↘ | ↘ | ↗ | |
65.04 | 0.14261 | 52.23 | 10,628.10 | 4710.01 | ||
65.07 | 0.15367 | 57.20 | 11,000.90 | 4545.60 | ||
65.09 | 0.16331 | 61.56 | 11,292.90 | 4422.22 | ||
trend | ↗ | ↗ | ↗ | ↗ | ↘ | |
65.02 | 0.15368 | 57.29 | 11,019.40 | 4548.37 | ||
65.07 | 0.15367 | 57.20 | 11,000.90 | 4545.60 | ||
65.12 | 0.15366 | 57.11 | 10,982.40 | 4542.85 | ||
trend | ↗ | ↘ | ↘ | ↘ | ↘ | |
65.13 | 0.15427 | 57.29 | 10,959.70 | 4531.37 | ||
65.07 | 0.15367 | 57.20 | 11,000.90 | 4545.60 | ||
65.01 | 0.15308 | 57.11 | 11,042.20 | 4559.84 | ||
trend | ↘ | ↘ | ↘ | ↗ | ↗ | |
64.87 | 0.15322 | 57.40 | 11,075.60 | 4191.14 | ||
65.07 | 0.15367 | 57.20 | 11,000.90 | 4545.60 | ||
65.27 | 0.15413 | 57.00 | 10,926.70 | 4895.31 | ||
trend | ↗ | ↗ | ↘ | ↘ | ↗ | |
65.06 | 0.15123 | 56.44 | 11,067.20 | 4260.84 | ||
65.07 | 0.15367 | 57.20 | 11,000.90 | 4545.60 | ||
65.08 | 0.15607 | 57.94 | 10,935.60 | 4822.01 | ||
trend | ↗ | ↗ | ↗ | ↘ | ↗ | |
65.05 | 0.15382 | 57.27 | 11,006.30 | 4516.39 | ||
65.07 | 0.15367 | 57.20 | 11,000.90 | 4545.60 | ||
65.08 | 0.15352 | 57.13 | 10,995.50 | 4574.74 | ||
trend | ↗ | ↘ | ↘ | ↘ | ↗ | |
64.50 | 0.14286 | 54.65 | 11,070.20 | 4790.71 | ||
65.07 | 0.15367 | 57.20 | 11,000.90 | 4545.60 | ||
65.64 | 0.16408 | 59.44 | 10,954.50 | 4333.59 | ||
trend | ↗ | ↗ | ↗ | ↘ | ↘ |
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Chang, C.-T.; Tseng, Y.-T. The Impacts of Payment Schemes and Carbon Emission Policies on Replenishment and Pricing Decisions for Perishable Products in a Supply Chain. Mathematics 2024, 12, 1033. https://doi.org/10.3390/math12071033
Chang C-T, Tseng Y-T. The Impacts of Payment Schemes and Carbon Emission Policies on Replenishment and Pricing Decisions for Perishable Products in a Supply Chain. Mathematics. 2024; 12(7):1033. https://doi.org/10.3390/math12071033
Chicago/Turabian StyleChang, Chun-Tao, and Yao-Ting Tseng. 2024. "The Impacts of Payment Schemes and Carbon Emission Policies on Replenishment and Pricing Decisions for Perishable Products in a Supply Chain" Mathematics 12, no. 7: 1033. https://doi.org/10.3390/math12071033
APA StyleChang, C. -T., & Tseng, Y. -T. (2024). The Impacts of Payment Schemes and Carbon Emission Policies on Replenishment and Pricing Decisions for Perishable Products in a Supply Chain. Mathematics, 12(7), 1033. https://doi.org/10.3390/math12071033