Optimizing Pricing, Pre-Sale Incentive, and Inventory Decisions with Advance Sales and Trade Credit under Carbon Tax Policy
Abstract
:1. Introduction
2. Literature Review
3. Notation and Assumptions
Unit purchasing cost. | |
Unit carbon tax. | |
Amount of carbon emissions per unit product purchased by the retailer. | |
Unit holding cost per unit time excluding the interest charges. | |
Amount of carbon emissions per unit per unit of time stored by the retailer. | |
Cost of placing an order. | |
Amount of carbon emissions generated by the retailer per order. | |
Interest charges per TWD investment in stocks per unit time. | |
Interest earned per TWD per unit time. | |
Trade credit period. | |
Advance selling period. | |
The order cancellation rate, where . | |
The prepaid deposit rate, where . | |
Advance sales discount rate, i.e., , is the unit advance sales price, where , a decision variable. | |
p | Unit spot sales price, a decision variable. |
The demand rate, is a function of p. | |
Spot selling period, a decision variable. | |
The order quantity. | |
p* | The optimal unit spot sales price. |
The optimal advance sales discount rate. | |
The optimal spot selling period. | |
The optimal order quantity. | |
Total profit, which is a function of , , and p. | |
Maximum total profit, i.e., . |
- The inventory system here is for a single item in a single season.
- The replenishment occurs instantaneously at an infinite rate.
- Customers who accept an advance sales offer must pre-pay a deposit for the pre-committed orders. For those who cancel their pre-committed orders, no refund is permitted.
- The carbon emissions generated by the retailer mainly come from operational activities such as ordering, purchase, and storage.
- The demand rate, D, is linearly dependent on the selling price, p, and can be expressed as , where a and b are positive constants. We also assume that the demand rate is always positive. That is, .
- The retailer offers an advance sale to its customers with respective discount rate .
- Shortages are not allowed.
4. Model Formulation
- (a)
- The sales revenue is .
- (b)
- The deposit income arising from orders canceled is .
- (c)
- The cost of placing an order is S.
- (d)
- The cost of purchasing is .
- (e)
- The cost of carrying inventory (excluding interest payable) is .
- (f)
- The carbon tax is .
- (g)
- The interest payable and interest earned.
5. Model Solution and Theorical Results
- (a)
- If , the optimal solution is and given in (12) and (13), respectively.
- (b)
- If , the optimal solution is and given in (20) and (21), respectively.
Algorithm
- Step 1.
- Start with j = 0 and the initial value of .
- Step 2.
- Check the values of and .
- Step 2-1.
- If , calculate the values of and , put () into (4) to solve the value of , and go to Step 3.
- Step 2-2.
- If , calculate the values of and , put () into (5) to solve the value of , and go to Step 3.
- Step 3.
- If the difference between and is tiny, set , , and , and is the optimal solution. Otherwise, set and go back to Step 2.
- Step 4.
- Stop.
6. Numerical Examples
- (1)
- When the value of M is higher (for example, in Table 2), the retailer is more likely to choose Alternative 1, which implies the length of the retailer’s inventory period, (), will be less than the length of the trade credit period, .
- (2)
- As the length of advance selling period increases, the optimal spot selling period , the optimal advance sales discount rate , and the optimal spot selling price increase. When Alternative 1 is the optimal decision, the optimal amounts of carbon emissions, order quantity, and total profit increase as the length of advance selling period increases. In contrast, when Alternative 2 is the optimal decision, the optimal amounts of carbon emissions, order quantity, and total profit first increase and then decrease once the length of the advance selling period increases.
- (3)
- With the increase in the length of trade credit period , all the optimal spot selling period , the optimal advance sales discount rate , the amounts of carbon emissions, order quantity, and total profit increase while the optimal spot selling price decreases.
- (4)
- As the carbon tax cr increases, all the optimal spot selling period , the optimal advance sales discount rate , amounts of carbon emissions, order quantity, and total profit decrease while the optimal spot selling price increases. Further, when considering the scenario where cr is 0, the proposed model can be simplified to a special model without carbon policy, which is simpler to Cheng and Ouyang [22].
- (1)
- An increase in autonomous consumption causes an increase in the retailer’s selling price, advance sales discount rate, order quantity, and total profit. In contrast, as induced consumption increases, the retailer’s selling price, advance sales discount rate, order quantity, and total profit decrease.
- (2)
- Regardless of the increase in fixed cost or amount of carbon emissions generated by the retailer per order, it will not affect the optimal solutions, but the total profit will increase accordingly.
- (3)
- The increase in holding cost leads to the decrease in the retailer’s selling price, advance sales discount rate, order quantity, and total profit.
- (4)
- Similar to the holding cost, an increase in purchase cost results in decreases in the retailer’s advance sales discount rate, order quantity, and total profit. The difference is that the increase in purchase cost will be reflected in the selling price increase.
- (5)
- If the unit carbon emissions resulting from the retailer’s purchase or storage of products increase, the retailer’s selling price, advance sales discount rate, order quantity, and total profit will decrease.
7. Conclusions
- (1)
- The holding cost and trade credit period have significant impacts on the alternation of the optimal solution. In particular, when facing high holding cost or long trade credit period offered by the supplier, the retailer keeps the length of inventory period as short as possible to enjoy the benefits of delayed payments. These are similar to the results of Chen and Cheng [20], Cheng and Ouyang [22], and Li et al. [31].
- (2)
- It is known from previous studies on sustainable inventory models that all the optimal decisions, the amount of carbon emission, and total profit will decrease as the tax rate increases. However, what has not been mentioned in the previous literature is that the increase in carbon tax will make the retailer lower the advance sales discount rate to reduce the willingness of customers to pre-order.
- (3)
- An increase in autonomous consumption leads to an increase in the retailer’s selling price, advance sales discount rate, order quantity, the amount of carbon emission, and total profit, while induced consumption has the opposite effect. From an economic perspective, consumers’ spontaneous consumption may gradually decrease under the trend of rising environmental protection awareness. For the retailer, it can respond by lowering price, reducing order quantity, and reducing advance sales discount. In addition, it can also develop towards green products to increase spontaneous consumption.
- (4)
- Although an increase in fixed carbon emissions generated per order does not affect the optimal solutions, it will increase the total profit. On the other hand, an increase in unit carbon emissions from the retailer’s purchasing or holding of products will lead to a decrease in the retailer’s selling price, advance sales discount rate, order quantity, and total profit.
- (5)
- The retailer can suffer negative impacts on its profitability due to an increase in holding or purchase costs, causing it to modify selling prices, advance sales discounts, order quantities, and total profit. Furthermore, while purchase cost increases lead to a rise in selling prices, holding cost increments do not.
- (1)
- (2)
- Furthermore, this study investigates a given advance selling period and trade credit period. It could be of interest to consider the situation in which the retailer determines when to start the advance sales system or faces a conditional trade credit.
- (3)
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
References
- Rout, C.; Paul, A.; Kumar, R.S.; Chakraborty, D.; Goswami, A. Cooperative sustainable supply chain for deteriorating item and imperfect production under different carbon emission regulations. J. Clean. Prod. 2020, 272, 122170. [Google Scholar] [CrossRef]
- Li, R.; Teng, J.T.; Zheng, Y. Optimal credit term, order quantity and pricing policies for perishable products when demand depends on price, expiration date, and credit period. Ann. Oper. Res. 2019, 280, 377–405. [Google Scholar] [CrossRef]
- He, P.; Zhang, W.; Xu, X.; Bian, Y. Production lot-sizing and carbon emissions under cap-and-trade and carbon tax regulations carbon tax regulations. J. Clean. Prod. 2014, 103, 241–248. [Google Scholar] [CrossRef]
- Konur, D. Carbon constrained integrated inventory control and truckload transportation with heterogeneous freight trucks. Int. J. Prod. Econ. 2014, 153, 268–279. [Google Scholar] [CrossRef]
- Battini, D.; Persona, A.; Sgarbossa, F. A sustainable EOQ model: Theoretical formulation and applications. Int. J. Prod. Econ. 2014, 149, 145–153. [Google Scholar] [CrossRef]
- Daryanto, Y.; Wee, H.M. Sustainable Economic Production Quantity Models: An Approach toward a Cleaner Production. Int. J. Adv. Manag. Sci. 2018, 6, 206–212. [Google Scholar] [CrossRef]
- Daryanto, Y.; Wee, H. Low Carbon Economic Production Quantity Model for Imperfect Quality Deteriorating Items. Int. J. Ind. Eng. Eng. Manag. 2019, 1, 1–8. [Google Scholar] [CrossRef]
- Taleizadeh, A.A.; Soleymanfar, V.R.; Govindan, K. Sustainable economic production quantity models for inventory systems with shortage. J. Clean. Prod. 2018, 174, 1011–1020. [Google Scholar] [CrossRef]
- Zhang, R.Y.; Liu, Q. Low carbon constrained EPQ model and computing. In Proceedings of the 2018 Eighth International Conference on Instrumentation & Measurement, Computer, Communication and Control, Harbin, China, 19–21 July 2018. [Google Scholar]
- Xu, X.; He, P.; Xu, H.; Zhang, Q. Supply chain coordination with green technology under cap-and-trade regulation. Int. J. Prod. Econ. 2017, 183, 433–442. [Google Scholar] [CrossRef]
- Tiwari, S.; Daryanto, Y.; Wee, H.M. Sustainable inventory management with deteriorating and imperfect quality items considering carbon emission. J. Clean. Prod. 2018, 192, 281–292. [Google Scholar] [CrossRef]
- Mishra, U.; Wu, J.-Z.; Sarkar, B. A sustainable production-inventory model for a controllable carbon emissions rate under shortages. J. Clean. Prod. 2020, 256, 120268. [Google Scholar] [CrossRef]
- Shen, L.; Lin, F.; Cheng, T.C.E. Low-Carbon Transition Models of High Carbon Supply Chains under the Mixed Carbon Cap-and-Trade and Carbon Tax Policy in the Carbon Neutrality Era. Int. J. Environ. Res. Public Health 2022, 19, 11150. [Google Scholar] [CrossRef] [PubMed]
- Sadigh, A.N.; Chaharsooghi, S.K.; Sheikhmohammady, M. A game theoretic approach to coordination of pricing, advertising, and inventory decisions in a competitive supply chain. J. Ind. Manag. Optim. 2016, 12, 337–355. [Google Scholar] [CrossRef]
- Qi, Q.; Wang, J.; Bai, Q. Pricing decision of a two-echelon supply chain with one supplier and two retailers under a carbon cap regulation. J. Clean. Prod. 2017, 151, 286–302. [Google Scholar] [CrossRef]
- Halat, K.; Hafezalkotob, A. Modeling carbon regulation policies in inventory decisions of a multi-stage green supply chain: A game theory approach. Comput. Ind. Eng. 2019, 128, 807–830. [Google Scholar] [CrossRef]
- Huang, Y.-S.; Fang, C.-C.; Lin, Y.-A. Inventory management in supply chains with consideration of Logistics, green investment and different carbon emissions policies. Comput. Ind. Eng. 2020, 139, 106207. [Google Scholar] [CrossRef]
- Chang, C.-C.; Lu, C.-J.; Yang, C.-T. Multistage supply chain production–inventory model with collaborative preservation technology investment. Sci. Iran. 2022, 29, 2099–2114. [Google Scholar] [CrossRef]
- Tsao, Y.-C. Retailer’s optimal ordering and discounting policies under advance sales discount and trade credits. Comput. Ind. Eng. 2009, 56, 208–215. [Google Scholar] [CrossRef]
- Chen, M.L.; Cheng, M.C. Optimal order quantity under advance sales and permissible delays in payments. Afr. J. Bus. Manag. 2011, 5, 7325–7334. [Google Scholar]
- Dye, C.-Y.; Hsieh, T.-P. Joint pricing and ordering policy for an advance booking system with partial order cancellations. Appl. Math. Model. 2013, 37, 3645–3659. [Google Scholar] [CrossRef]
- Cheng, M.C.; Ouyang, L.Y. Advance sales system with price-dependent demand and an appreciation period under trade credit. Int. J. Inf. Manag. Sci. 2014, 25, 251–262. [Google Scholar]
- Youjun, Z.; Yan, Z.; Liang, C. An inventory model with advance sales and demand rate dependent on price. In Proceedings of the 2015 12th International Conference on Service Systems and Service Management, Guangzhou, China, 22–24 June 2015. [Google Scholar]
- Seref, M.M.H.; Seref, O.; Alptekinoglu, A.; Erengüç, S.S. Advance selling to strategic consumers. Comput. Manag. Sci. 2016, 13, 597–626. [Google Scholar]
- Cheng, M.-C.; Hsieh, T.-P.; Lee, H.-M.; Ouyang, L.-Y. Optimal ordering policies for deteriorating items with a return period and price-dependent demand under two-phase advance sales. Oper. Res. 2020, 20, 585–604. [Google Scholar] [CrossRef]
- Duary, A.; Das, S.; Arif, M.G.; Abualnaja, K.M.; Khan, M.A.A.; Zakarya, M.; Shaikh, A.A. Advance and delay in payments with the price-discount inventory model for deteriorating items under capacity constraint and partially back-logged shortages. Alex. Eng. J. 2022, 61, 1735–1745. [Google Scholar] [CrossRef]
- Lou, K.-R.; Wang, L. Optimal lot-sizing policy for a manufacturer with defective items in a supply chain with up-stream and down-stream trade credits. Comput. Ind. Eng. 2013, 66, 1125–1130. [Google Scholar] [CrossRef]
- Tsao, Y.-C. Joint location, inventory, and preservation decisions for non-instantaneous deterioration items under delay in payments. Int. J. Syst. Sci. 2016, 47, 572–585. [Google Scholar] [CrossRef]
- Zhong, Y.; Shu, J.; Xie, W.; Zhou, Y.-W. Optimal trade credit and replenishment policies for supply chain network design. Omega 2018, 81, 26–37. [Google Scholar] [CrossRef]
- Chang, C.T.; Ouyang, L.Y.; Teng, J.T.; Lai, K.K.; Cárdenas-Barrón, L.E. Manufacturer’s pricing and lot-sizing decisions for perishable goods under various payment terms by a discounted cash flow analysis. Int. J. Prod. Econ. 2019, 218, 83–95. [Google Scholar] [CrossRef]
- Li, R.; Liu, Y.; Teng, J.-T.; Tsao, Y.-C. Optimal pricing, lot-sizing and backordering decisions when a seller demands an advance-cash-credit payment scheme. Eur. J. Oper. Res. 2019, 278, 283–295. [Google Scholar] [CrossRef]
- Tsao, Y.-C. Coordinating contracts under default risk control-based trade credit. Int. J. Prod. Econ. 2019, 212, 168–175. [Google Scholar] [CrossRef]
- Shi, Y.; Zhang, Z.; Chen, S.C.; Cárdenas Barrón, L.E.; Skouri, K. Optimal replenishment decisions for perishable products under cash, advance, and credit payments considering carbon tax regulations. Int. J. Prod. Econ. 2020, 223, 107514. [Google Scholar] [CrossRef]
- Mallick, R.K.; Patra, K.; Mondal, S.K. Mixture inventory model of lost sale and back-order with stochastic lead time demand on permissible delay in payments. Ann. Oper. Res. 2020, 292, 341–369. [Google Scholar] [CrossRef]
- Li, R.; Yang, H.-L.; Shi, Y.; Teng, J.-T.; Lai, K.-K. EOQ-based pricing and customer credit decisions under general supplier payments. Eur. J. Oper. Res. 2021, 289, 652–665. [Google Scholar] [CrossRef]
- Li, R.; Skouri, K.; Teng, J.T.; Yang, W.G. Seller’s optimal replenishment policy and payment term among advance, cash, and credit payments. Int. J. Prod. Econ. 2018, 197, 35–42. [Google Scholar] [CrossRef]
- Chung, K.J.; Liao, J.J.; Srivastava, H.M.; Lee, S.F.; Lin, S.D. The EOQ model for deteriorating items with a conditional trade credit linked to order quantity in a supply chain system. Mathematics 2021, 9, 2311. [Google Scholar] [CrossRef]
- Jani, M.Y.; Betheja, M.R.; Bhadoriya, A.; Chaudhari, U.; Abbas, M.; Alqahtani, M.S. Optimal Pricing Policies with an Allowable Discount for Perishable Items under Time-Dependent Sales Price and Trade Credit. Mathematics 2022, 10, 1948. [Google Scholar] [CrossRef]
- Ouyang, L.Y.; Wu, K.S.; Yang, C.T. Coordinating replenishment and pricing policies for non-instantaneous deteriorating items with price sensitive demand. Int. J. Syst. Sci. 2009, 40, 1273–1281. [Google Scholar] [CrossRef]
Authors (Year) | Model Type | Advance Sales | Trade Credit | Carbon Tax | Price-Dependent Demand Rate |
---|---|---|---|---|---|
Battini et al. [5] | EOQ | V | |||
Daryanto & Wee [7] | EPQ | V | |||
Tiwari et al. [11] | Production–inventory | V | |||
Mishra et al. [12] | EPQ | V | |||
Shen et al. [13] | Production–inventory | V | |||
Cheng & Ouyang [22] | EOQ | V | V | V | |
Cheng et al. [25] | EOQ | V | V | ||
Duary et al. [26] | EOQ | V | V | V | |
Li et al. [35] | EOQ | V | V | ||
Jani et al. [38] | EOQ | V | V | ||
Present model | EOQ | V | V | V | V |
cr | M | Alternatives | |||||||
0 | 1 | 1 | Alternative2 | 2.7932 | 0.1235 | 273.101 | 371.507 | 644.960 | 24,760 |
2 | Alternative2 | 3.7932 | 0.1247 | 273.101 | 534.064 | 888.796 | 40,032 | ||
3 | Alternative2 | 7.4251 | 0.3791 | 333.755 | 524.444 | 769.328 | 32,909 | ||
2 | 1 | Alternative1 | 2.8116 | 0.1236 | 271.809 | 381.817 | 662.263 | 26,204 | |
2 | Alternative1 | 3.8116 | 0.1247 | 271.809 | 546.640 | 909.497 | 42,133 | ||
3 | Alternative1 | 4.8116 | 0.1259 | 271.809 | 712.703 | 1158.590 | 58,429 | ||
3 | 1 | Alternative1 | 2.8708 | 0.1249 | 270.949 | 395.212 | 685.736 | 27,775 | |
2 | Alternative1 | 3.8708 | 0.1261 | 270.948 | 562.236 | 936.271 | 44,368 | ||
3 | Alternative1 | 4.8708 | 0.1272 | 270.948 | 730.465 | 1188.610 | 61,331 | ||
0.5 | 1 | 1 | Alternative2 | 2.7800 | 0.1231 | 273.347 | 368.214 | 639.275 | 24,439 |
2 | Alternative2 | 3.7800 | 0.1243 | 273.347 | 530.123 | 882.137 | 39,589 | ||
3 | Alternative2 | 7.5381 | 0.3873 | 334.090 | 532.016 | 775.482 | 31,480 | ||
2 | 1 | Alternative1 | 2.7990 | 0.1232 | 272.057 | 378.540 | 656.599 | 25,874 | |
2 | Alternative1 | 3.7990 | 0.1244 | 272.057 | 542.723 | 902.873 | 41,680 | ||
3 | Alternative1 | 4.7990 | 0.1255 | 272.057 | 708.152 | 1151.020 | 57,852 | ||
3 | 1 | Alternative1 | 2.8581 | 0.1246 | 271.193 | 391.883 | 679.949 | 27,434 | |
2 | Alternative1 | 3.8581 | 0.1257 | 271.193 | 558.276 | 929.539 | 43,902 | ||
3 | Alternative1 | 4.8581 | 0.1268 | 271.193 | 725.880 | 1180.940 | 60,739 | ||
1 | 1 | 1 | Alternative2 | 2.7669 | 0.1227 | 273.594 | 364.943 | 633.634 | 24,121 |
2 | Alternative2 | 3.7669 | 0.1239 | 273.594 | 526.203 | 875.524 | 39,150 | ||
3 | Alternative2 | 7.6498 | 0.3955 | 334.394 | 539.784 | 781.877 | 30,003 | ||
2 | 1 | Alternative1 | 2.7864 | 0.1228 | 272.305 | 375.284 | 650.978 | 25,547 | |
2 | Alternative1 | 3.7864 | 0.1240 | 272.305 | 538.828 | 896.293 | 41,230 | ||
3 | Alternative1 | 4.7864 | 0.1251 | 272.305 | 703.622 | 1143.480 | 57,278 | ||
3 | 1 | Alternative1 | 2.8454 | 0.1242 | 271.437 | 388.575 | 674.207 | 27,095 | |
2 | Alternative1 | 3.8454 | 0.1253 | 271.437 | 554.338 | 922.851 | 43,439 | ||
3 | Alternative1 | 4.8454 | 0.1264 | 271.437 | 721.316 | 1173.320 | 60,150 |
Parameters | Values | ||||||
---|---|---|---|---|---|---|---|
a | 640 | 373.910 | |||||
720 | 606.275 | ||||||
800 | 918.094 | ||||||
880 | 1314.84 | ||||||
960 | 1803.66 | ||||||
b | 2 | 1677.86 | |||||
2.25 | 1233.03 | ||||||
2.5 | 918.094 | ||||||
2.75 | 689.432 | ||||||
3 | 521.688 | ||||||
S | 40 | 918.094 | |||||
45 | 918.094 | ||||||
50 | 918.094 | ||||||
55 | 918.094 | ||||||
60 | 918.094 | ||||||
h | 24 | 1090.58 | |||||
27 | 994.045 | ||||||
30 | 918.094 | ||||||
33 | 856.849 | ||||||
36 | 806.456 | ||||||
c | 145.6 | 4.7123 | 1373.16 | 54,893 | |||
163.8 | 4.3144 | 1130.24 | 42,436 | ||||
182 | 3.9204 | 918.094 | 32,128 | ||||
200.2 | 3.5303 | 734.762 | 23,743 | ||||
218.4 | 3.1432 | 578.376 | 17,057 | ||||
40 | 908.094 | ||||||
45 | 913.094 | ||||||
50 | 918.094 | ||||||
55 | 923.094 | ||||||
60 | 928.094 | ||||||
0.16 | 3.9222 | 0.124080 | 272.329 | 898.193 | 32,138 | ||
0.18 | 3.9213 | 0.124079 | 272.329 | 908.150 | 32,133 | ||
0.2 | 3.9204 | 0.124079 | 272.329 | 918.094 | 32,128 | ||
0.22 | 3.9195 | 0.124078 | 272.329 | 928.026 | 32,123 | ||
0.24 | 3.9186 | 0.124077 | 272.329 | 937.946 | 32,118 | ||
1.2 | 3.9236 | 0.12416 | 272.280 | 766.164 | 32,205 | ||
1.35 | 3.9220 | 0.12412 | 272.305 | 842.194 | 32,166 | ||
1.5 | 3.9204 | 0.12408 | 272.329 | 918.094 | 32,128 | ||
1.65 | 3.9188 | 0.12404 | 272.353 | 993.866 | 32,090 | ||
1.8 | 3.9172 | 0.12400 | 272.378 | 1069.51 | 32,052 |
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Cheng, M.-C.; Lo, H.-C.; Yang, C.-T. Optimizing Pricing, Pre-Sale Incentive, and Inventory Decisions with Advance Sales and Trade Credit under Carbon Tax Policy. Mathematics 2023, 11, 2534. https://doi.org/10.3390/math11112534
Cheng M-C, Lo H-C, Yang C-T. Optimizing Pricing, Pre-Sale Incentive, and Inventory Decisions with Advance Sales and Trade Credit under Carbon Tax Policy. Mathematics. 2023; 11(11):2534. https://doi.org/10.3390/math11112534
Chicago/Turabian StyleCheng, Mei-Chuan, Hui-Chiung Lo, and Chih-Te Yang. 2023. "Optimizing Pricing, Pre-Sale Incentive, and Inventory Decisions with Advance Sales and Trade Credit under Carbon Tax Policy" Mathematics 11, no. 11: 2534. https://doi.org/10.3390/math11112534