Optimal Pricing, Advertising, Production, Inventory and Investing Policies in a Multi-Stage Sustainable Supply Chain
Abstract
:1. Introduction
2. Literature Overview
2.1. Sustainable Production–Inventory Models
2.2. Inventory Model with Price and Advertisement Effect
2.3. Research Gap and Contribution
3. Notation and Assumptions
- (1)
- A single vendor, single buyer, and single commodity is involved in the proposed supply chain system.
- (2)
- In reality, the vendor’s productivity of finished products is usually greater than the demand rate (i.e., ) and finite.
- (3)
- The supply chain members mutually agree that the buyer orders Q units and allows the supplier to ship in n times with q (=Q/n) units where the delivery cost is paid by the buyer.
- (4)
- The demand is affected by advertisement efforts and selling price of product. That is, the demand rate is , where a is constant scale demand parameter, b is price elasticity factor, and denote advertisement effectiveness factors.
- (5)
- The buyer’s carbon emissions originate from ordering, holding inventory, shipping, advertising, and purchasing activities while the vendor’s carbon emissions originate from purchasing the materials, setting, production, and holding of materials.
- (6)
- Based on the study of [22,23], the model assumes that carbon emissions can be decreased by investing in carbon-reduction technologies. The carbon emission reduction rate, , is the increasing function of carbon emission reduction, , where . Further, the carbon emission reduction investment is shared by the buyer and vendor through an agreement where the capital investment ratios of buyer and vendor are and , respectively.
- (7)
- Whether it is the finished products and materials of the buyer or the vendor, shortages are not permitted.
4. Mathematical Model Formulation and Solution
4.1. Total Profit and Carbon Emissions for the Buyer
- (a)
- The sale revenue of buyer is
- (b)
- The ordering cost of buyer is A.
- (c)
- The purchase cost of buyer is vq.
- (d)
- The transportation cost (includes fixed and variable costs) of buyer is .
- (e)
- The promotional cost of buyer is .
- (f)
- The holding cost of buyer is
- (g)
- The investment for carbon emission reduction of buyer is .
4.2. Total Profit and Carbon Emissions for the Vendor
- (a)
- The vendor’s sale revenue is vQ = vnq.
- (b)
- The vendor’s ordering cost for raw materials is .
- (c)
- The vendor’s setup cost is S.
- (d)
- The vendor’s materials cost is
- (e)
- The vendor’s production cost is
- (f)
- Holding cost:
- (g)
- The carbon emission reduction technology investment shared by suppliers is ().
- (1)
- Carbon cap-and-trade
- (2)
- Carbon tax
Algorithm 1. Solving procedures under various carbon emission policies |
1: For , let 2: Identify the values of , , and by setting , , and 3: Substitute , , and into to obtain 4: Set , and repeat Step 2 to find 5: If , then , and hence is the optimal solution. Otherwise, return to Step 4 |
5. Numerical Illustration and Sensitivity Analysis
- (1)
- Increasing the production rate or deteriorating rate of finished product reduces the vendor’s shipping quantity of order quantities, the buyers’ order quantities of finished products, unit selling price, and investment for carbon emissions reduction while increasing the buyer’s unit promotional cost and the integrated total profit. The results indicate that when the productivity or the deteriorating rate of finished product increases, the demand can be increased by lowering prices and increasing advertising investment, thereby increasing the integrated total profit. It’s worth noting that when considering pricing and advertising effectiveness, productivity increases will reduce the vendor’s shipping quantity, which is different from the result of [21,22]. Further, the influence of the deteriorating rate of the finished product changing to the optimal solutions is particularly significant.
- (2)
- Increasing the vendor’s set up cost, ordering cost of raw materials, the buyer’s ordering cost of finished products or fixed shipping cost increases their shipping quantity of order quantities, the buyers’ order quantities of finished products, unit selling price, and investment for carbon emissions reduction but decreases the buyer’s unit promotional cost and the integrated total profit. It is intuitive that the quantity of production and delivery will increase while the integrated total profit will decrease as fixed costs increase. However, investment for carbon emissions reduction and the selling price will increase while the advertising investment will decrease with increasing fixed costs.
- (3)
- Increasing the unit cost parameters , v, , , , , deteriorating rate of raw material or amount of raw materials used per unit of finished good decreases the vendor’s shipping quantity of order quantities, the buyers’ order quantities of finished products, unit promotional cost, investment in reducing carbon emissions reduction, and the integrated total profit, but increases the buyer’s selling price.
- (4)
- Although these results are intuitive, it’s worth noting that when the change of vendor’s production cost or supply price is large enough (for example, the vendor’s production cost decreases by 20% or the vendor’s supply price increases by 20% in Table 2), the optimal number of shipments will change.
- (5)
- With the increase in scale demand parameter or the decrease in price elasticity factor b, all the vendor’s shipping quantity of order quantities, the buyers’ order quantities of finished products, unit selling price, unit promotional cost, and the investment in carbon emissions reduction and integrated total profit will increase under the fixed number of shipments. In addition, Benjaafar et al. [7] emphasized that determining the frequency of delivery is very important in mitigating carbon emissions, this study finds that the changes in demand parameters are relatively sensitive to the number of shipments.
- (6)
- As to the advertisement effectiveness factors, all the vendor’s shipping quantity of order quantities, the buyers’ order quantities of finished products, investment for carbon emissions reduction, and the integrated total profit will increase with the increase in or . The difference is that the selling price and the advertising investment will increase as the value of increases, but they will decrease as the value of increases. This result is different from [25,26,28] because this study treats advertising cost as a decision variable.
- (1)
- As the amount of fixed carbon emissions , , , or increases, the vendor’s shipping quantity of order quantities, the buyers’ order quantities of finished products, unit selling price, and the investment in carbon emissions reduction increase, but the unit promotional cost of buyer and the integrated total profit decreases.
- (2)
- As the amount of unit carbon emissions , , , , , or increases, the vendor’s shipping quantity of order quantities, the buyers’ order quantities of finished products, unit promotional cost and the integrated total profit decrease, but the unit selling price and the investment in carbon emissions reduction increases.
- (3)
- With the increase in carbon emissions of vendor’s unit raw material, the vendor’s order quantity shipment, the buyer’s finished product order quantity, unit promotional cost, the investment in carbon emissions reduction and the integrated total profit will decrease, but the unit selling price will increase.
- (4)
- With the increase in carbon emissions, market price , the vendor’s shipping quantity of order quantities, the buyers’ order quantities of finished products, unit selling price, the investment in carbon emissions reduction and the integrated total profit will increase, but the unit promotional cost will increase.
6. Conclusions
- (1)
- Whether the productivity or the deteriorating rate of finished product increases, supply chain members will reduce selling price and increase advertising investment in the demand, thereby increasing the integrated total profit. The effect is more significant when the deteriorating rate of finished product changes.
- (2)
- Benjaafar et al. [7] claimed that the frequency of vendor ‘s delivery is very important in mitigating carbon emissions, and this study finds that the optimal the number of shipments is not easily affected by parameter changes, except for the vendor’s production cost, supply price, and demand parameters.
- (3)
- Different from the research of [25,26,28], this study treats advertising costs as a decision variable. Changes in the advertisement effectiveness factors have the same effects on the vendor’s shipping quantity of order quantities, the buyers’ order quantities of finished products, investment for carbon emissions reduction, and the integrated total profit. However, their changes have opposite effects on the selling price and the advertising investment.
- (4)
- When pricing, advertising and carbon emissions are considered in the model simultaneously and it is found that the increase in carbon emission parameter or mark price of carbon will increase the price, but will reduce the advertising investment.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Notation
Production rate for the vendor | |
Demand rate for the buyer, a function of the selling price and advertisement cost | |
Buyer’s replenishment cost per order | |
Buyer’s fixed carbon emissions per order | |
Vendor’s ordering cost of raw material per order | |
The fixed carbon emissions per order by the vendor | |
Quantity of raw materials used per unit of finished good | |
Vendor’s setup cost per setup | |
Vendor’s fixed carbon emissions per setup | |
Product cost per unit for the vendor | |
Material cost per unit for the vendor | |
The relative carbon emissions per unit of produced by the vendor | |
The relative carbon emissions per unit of material by the vendor | |
The supply price per unit by the vendor | |
The carbon emissions associated with each unit purchased by the buyer | |
Amount of associated carbon emissions per unit of advertising for the buyer | |
Deteriorating rate of raw materials | |
Deteriorating rate of finished goods | |
Buyer’s carrying cost per unit of time | |
Carbon emissions per unit of inventory held by the buyer per unit of time | |
The carrying cost per finished product per unit of time by vendor | |
The carbon emissions per finished product per unit of time by vendor | |
The holding cost per unit of material per unit of time by vendor | |
The carbon emissions per unit of raw material per unit of time by vendor | |
The fixed transportation cost per shipment by buyer | |
Buyer’s fixed carbon emissions per shipment | |
Buyer’s variable transportation cost per unit | |
Buyer’s associated carbon emissions per unit of transport | |
C | Unit carbon emission tax rate |
Buyer’s carbon emission quota per unit time | |
Vendor’s carbon emission quota per unit time | |
Carbon emissions reduction investment, a decision variable | |
Carbon emissions reduction ratio, as a function of | |
Buyer’s retail price per unit, a decision variable | |
Buyer’s order quantity of finish products, a decision variable | |
Length of time for the vendor to ship the finished products to the buyer for the first time, a decision variable | |
Length of the replenishment cycle by the buyer, a decision variable | |
Length of the production cycle by the vendor, a decision variable | |
Length of the period of production by the vendor, a decision variable | |
Buyer’s promotional cost per unit, a decision variable | |
Number of shipments from vendor to buyer, a decision variable | |
Quantity per each transport from vendor to buyer, a decision variable | |
Qm | Vendor’s order quantity of materials, a decision variable |
* | Superscript represents optimal value |
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References | Model | Carbon Emission Effect | Multistage | Carbon Emission Reduction Technology | Pricing Strategy | Advertising Effect |
---|---|---|---|---|---|---|
[1,12] | EOQ | Carbon cost | ||||
[7,11] | EOQ | (1) Carbon cap (2) Carbon tax (3) Carbon cap-and-trade (4) Carbon offsets | ||||
[10] | EOQ | (1) Direct accounting (2) Carbon cap (3) Carbon tax (4) Carbon cap-and-trade (5) Carbon offsets | ||||
[13] | EOQ | (1) Carbon cap (2) Carbon tax (3) Carbon cap-and-trade | V | |||
[14] | EPQ | Carbon cost | ||||
[15] | Production–inventory | (1) Carbon cap (2) Carbon tax | ||||
[16] | Production–inventory | Carbon tax | V | |||
[17] | Production–inventory | Carbon cost | ||||
[18] | Production–inventory | Carbon tax | ||||
[19,20] | Production–inventory | |||||
[21] | Production–inventory | Carbon cost | V | |||
[22,23] | Production–inventory | (1) Carbon cap-and-trade (2) Carbon offsets | V | |||
[24] | Production–inventory | Carbon cap-and-trade | V | V | ||
[25] | Production–inventory | V | V | |||
[26,27,28,29,30,31] | EOQ | V | V | |||
[32] | EPQ | V | ||||
This paper | Production–inventory | (1) Carbon cap-and-trade (2) Carbon tax | V | V | V | V |
Parameters | Changing in % | Changing in % | ||||||
---|---|---|---|---|---|---|---|---|
P | −20 | 3 | 0.1240 | 0.1233 | 0.0556 | 0.1820 | −1.3736 | −0.6021 |
−10 | 3 | 0.0543 | 0.0540 | 0.0248 | 0.0823 | −0.6210 | −0.2717 | |
+10 | 3 | −0.0436 | −0.0443 | −0.0203 | −0.0692 | 0.5215 | 0.2266 | |
+20 | 3 | −0.0795 | −0.0800 | −0.0373 | −0.1281 | 0.9654 | 0.4191 | |
S | −20 | 3 | −2.0051 | −2.0050 | −0.3708 | −0.0187 | 0.2801 | 0.4608 |
−10 | 3 | −0.9963 | −0.9962 | −0.1836 | −0.0094 | 0.1394 | 0.2290 | |
+10 | 3 | 0.9842 | 0.9837 | 0.1801 | 0.0092 | −0.1379 | −0.2271 | |
+20 | 3 | 1.9568 | 1.9568 | 0.3566 | 0.0184 | −0.2745 | −0.4514 | |
A | −20 | 3 | −1.5990 | −1.5994 | −0.2953 | −0.0188 | 0.2529 | 0.3708 |
−10 | 3 | −0.7954 | −0.7958 | −0.1464 | −0.0094 | 0.1259 | 0.1844 | |
+10 | 3 | 0.7876 | 0.7872 | 0.1443 | 0.0094 | −0.1247 | −0.1830 | |
+20 | 3 | 1.5675 | 1.5676 | 0.2862 | 0.0186 | −0.2484 | −0.3646 | |
−20 | 3 | −1.2472 | −1.2477 | −0.2300 | −0.0117 | 0.1744 | 0.2868 | |
−10 | 3 | −0.6211 | −0.6214 | −0.1143 | −0.0058 | 0.0870 | 0.1427 | |
+10 | 3 | 0.6165 | 0.6157 | 0.1129 | 0.0058 | −0.0863 | −0.1422 | |
+20 | 3 | 1.2284 | 1.2284 | 0.2245 | 0.0116 | −0.1722 | −0.2835 | |
−20 | 4 | −6.4231 | 24.7688 | 0.1756 | −1.0488 | 8.2970 | 7.0439 | |
−10 | 3 | 3.8116 | 3.8115 | 0.6810 | −0.4318 | 2.9752 | 3.4643 | |
+10 | 3 | −3.5824 | −3.5831 | −0.6586 | 0.4348 | −3.0101 | −3.3852 | |
+20 | 3 | −6.9607 | −6.9609 | −1.2975 | 0.8729 | −6.0549 | −6.6912 | |
−20 | 3 | 1.5900 | 1.5897 | 0.2867 | −0.1761 | 1.2100 | 1.3901 | |
−10 | 3 | 0.7891 | 0.7891 | 0.1428 | −0.0882 | 0.6058 | 0.6932 | |
+10 | 3 | −0.7781 | −0.7785 | −0.1415 | 0.0882 | −0.6071 | −0.6903 | |
+20 | 3 | −1.5452 | −1.5454 | −0.2818 | 0.1765 | −1.2155 | −1.3768 | |
−20 | 3 | 1.3539 | 1.3537 | 0.2402 | −0.3803 | 2.7578 | 1.3569 | |
−10 | 3 | 0.6694 | 0.6696 | 0.1191 | −0.1884 | 1.3670 | 0.6718 | |
+10 | 3 | −0.6555 | −0.6561 | −0.1171 | 0.1853 | −1.3435 | −0.6590 | |
+20 | 4 | −14.6055 | 13.8585 | −1.4455 | 0.1476 | −0.0851 | −1.2920 | |
−20 | 3 | 2.8109 | 2.8104 | 0.4938 | −0.9146 | 6.6646 | 6.4347 | |
−10 | 3 | 1.4044 | 1.4038 | 0.2482 | −0.4576 | 3.3345 | 3.1785 | |
+10 | 3 | −1.4027 | −1.4028 | −0.2503 | 0.4583 | −3.3394 | −3.1016 | |
+20 | 3 | −2.8037 | −2.8037 | −0.5031 | 0.9173 | −6.6840 | −6.1270 | |
−20 | 3 | 0.9666 | 0.9664 | 0.1765 | −0.0127 | 0.0275 | 0.1887 | |
−10 | 3 | 0.4798 | 0.4798 | 0.0878 | −0.0063 | 0.0139 | 0.0939 | |
+10 | 3 | −0.4729 | −0.4731 | −0.0867 | 0.0062 | −0.0141 | −0.0939 | |
+20 | 3 | −0.9391 | −0.9394 | −0.1726 | 0.0125 | −0.0284 | −0.1873 | |
−20 | 3 | 0.0902 | 0.0896 | 0.0166 | −0.0030 | 0.0158 | 0.0137 | |
−10 | 3 | 0.0451 | 0.0443 | 0.0083 | −0.0015 | 0.0080 | 0.0066 | |
+10 | 3 | −0.0451 | −0.0453 | −0.0082 | 0.0015 | −0.0078 | −0.0071 | |
+20 | 3 | −0.0902 | −0.0906 | −0.0165 | 0.0029 | −0.0157 | −0.0137 | |
−20 | 3 | 10.2138 | 10.2137 | 13.3196 | 2.9028 | −20.9241 | −18.2249 | |
−10 | 3 | 5.1539 | 5.1536 | 6.2303 | 1.1960 | −8.5922 | −7.8361 | |
+10 | 3 | −4.8131 | −4.8135 | −5.4609 | −0.8776 | 6.2581 | 6.0065 | |
+20 | 3 | −9.1718 | −9.1722 | −10.2543 | −1.5449 | 10.9740 | 10.6879 | |
−20 | 3 | 0.1000 | 0.0992 | 0.0171 | −0.0033 | 0.0174 | 0.0152 | |
−10 | 3 | 0.0500 | 0.0491 | 0.0086 | −0.0017 | 0.0088 | 0.0076 | |
+10 | 3 | −0.0500 | −0.0501 | −0.0085 | 0.0017 | −0.0087 | −0.0076 | |
+20 | 3 | −0.1003 | −0.1002 | −0.0170 | 0.0032 | −0.0173 | −0.0152 | |
−20 | 3 | −0.3969 | −0.3969 | −0.0729 | −0.0047 | 0.0628 | 0.0920 | |
−10 | 3 | −0.1983 | −0.1985 | −0.0364 | −0.0023 | 0.0314 | 0.0460 | |
+10 | 3 | 0.1977 | 0.1975 | 0.0364 | 0.0023 | −0.0312 | −0.0460 | |
+20 | 3 | 0.3948 | 0.3941 | 0.0724 | 0.0047 | −0.0625 | −0.0920 | |
−20 | 3 | 0.9602 | 0.9596 | 0.1706 | −0.2770 | 2.0101 | 1.9221 | |
−10 | 3 | 0.4795 | 0.4788 | 0.0854 | −0.1385 | 1.0057 | 0.9577 | |
+10 | 3 | −0.4789 | −0.4788 | −0.0854 | 0.1385 | −1.0059 | −0.9506 | |
+20 | 3 | −0.9567 | −0.9567 | −0.1710 | 0.2772 | −2.0124 | −1.8946 | |
a | −20 | 2 | −6.0704 | −37.3805 | −3.4529 | −18.1491 | −70.2065 | −47.6204 |
−10 | 3 | −12.3056 | −12.3061 | −2.2821 | −9.1802 | −33.4552 | −27.3336 | |
+10 | 3 | 11.9053 | 11.9046 | 2.0144 | 9.2413 | 33.0271 | 34.9256 | |
+20 | 4 | 8.2677 | 44.3560 | 2.6941 | 18.2633 | 68.5639 | 79.0129 | |
b | −20 | 4 | 0.2835 | 33.7107 | 1.3254 | 22.7981 | 85.0788 | 66.3446 |
−10 | 4 | −7.1315 | 23.8236 | −0.0109 | 10.0422 | 39.0021 | 26.9306 | |
+10 | 3 | −6.3806 | −6.3810 | −1.1520 | −8.3458 | −30.1238 | −19.2054 | |
+20 | 3 | −12.2481 | −12.2483 | −2.2646 | −15.2819 | −55.3401 | −33.2534 | |
−20 | 3 | −5.2730 | −5.2733 | −0.9594 | 1.5436 | 22.3392 | −10.1721 | |
−10 | 3 | −2.6493 | −2.6495 | −0.4771 | 0.7707 | 11.1783 | −5.1930 | |
+10 | 3 | 2.6759 | 2.6755 | 0.4721 | −0.7686 | −11.1935 | 5.4096 | |
+20 | 3 | 5.3802 | 5.3800 | 0.9394 | −1.5354 | −22.4016 | 11.0412 | |
−20 | 3 | −5.4704 | −5.4707 | −0.9835 | −1.9722 | −28.3606 | −5.7472 | |
−10 | 3 | −2.7572 | −2.7574 | −0.4909 | −0.8790 | −12.5963 | −3.0343 | |
+10 | 3 | 2.7635 | 2.7632 | 0.4826 | 0.7235 | 10.2867 | 3.2610 | |
+20 | 3 | 5.5111 | 5.5110 | 0.9533 | 1.3310 | 18.8360 | 6.6878 | |
r | −20 | 3 | 1.8212 | 1.8209 | 0.2038 | −0.1938 | 1.3277 | 1.5219 |
−10 | 3 | 0.9024 | 0.9018 | 0.1013 | −0.0970 | 0.6645 | 0.7591 | |
+10 | 3 | −0.8868 | −0.8874 | −0.0998 | 0.0970 | −0.6660 | −0.7548 | |
+20 | 3 | −1.7585 | −1.7593 | −0.1986 | 0.1942 | −1.3337 | −1.5058 |
Parameters | Changing in % | Changing in % | ||||||
---|---|---|---|---|---|---|---|---|
−20 | 3 | −2.7147 | −2.7150 | −1.1827 | −0.0315 | 0.4255 | 0.6254 | |
−10 | 3 | −1.3452 | −1.3460 | −0.5814 | −0.0157 | 0.2111 | 0.3101 | |
+10 | 3 | 1.3224 | 1.3219 | 0.5628 | 0.0154 | −0.2079 | −0.3063 | |
+20 | 3 | 2.6228 | 2.6226 | 1.1081 | 0.0307 | −0.4129 | −0.6078 | |
−20 | 3 | −0.0835 | −0.0838 | −0.0356 | −0.0008 | 0.0117 | 0.0190 | |
−10 | 3 | −0.0419 | −0.0424 | −0.0177 | −0.0004 | 0.0058 | 0.0095 | |
+10 | 3 | 0.0416 | 0.0414 | 0.0179 | 0.0004 | −0.0057 | −0.0095 | |
+20 | 3 | 0.0832 | 0.0829 | 0.0356 | 0.0007 | −0.0116 | −0.0194 | |
−20 | 3 | −0.1252 | −0.1253 | −0.0534 | −0.0012 | 0.0174 | 0.0284 | |
−10 | 3 | −0.0627 | −0.0626 | −0.0266 | −0.0006 | 0.0088 | 0.0142 | |
+10 | 3 | 0.0624 | 0.0617 | 0.0268 | 0.0006 | −0.0087 | −0.0147 | |
+20 | 3 | 0.1249 | 0.1243 | 0.0534 | 0.0011 | −0.0173 | −0.0289 | |
−20 | 3 | 0.4867 | 0.4866 | −0.4050 | −0.0579 | 0.4003 | 0.4599 | |
−10 | 3 | 0.2428 | 0.2428 | −0.2010 | −0.0290 | 0.2003 | 0.2295 | |
+10 | 3 | −0.2419 | −0.2428 | 0.1983 | 0.0289 | −0.2004 | −0.2295 | |
+20 | 3 | −0.4830 | −0.4837 | 0.3939 | 0.0579 | −0.4008 | −0.4585 | |
−20 | 3 | 0.1023 | 0.1021 | −0.2092 | −0.0309 | 0.2244 | 0.2134 | |
−10 | 3 | 0.0512 | 0.0511 | −0.1042 | −0.0154 | 0.1122 | 0.1067 | |
+10 | 3 | −0.0512 | −0.0520 | 0.1038 | 0.0154 | −0.1122 | −0.1067 | |
+20 | 3 | −0.1023 | −0.1031 | 0.2068 | 0.0308 | −0.2244 | −0.2134 | |
−20 | 3 | 0.1289 | 0.1281 | −0.1000 | −0.0147 | 0.1014 | 0.1157 | |
−10 | 3 | 0.0645 | 0.0636 | −0.0498 | −0.0074 | 0.0508 | 0.0578 | |
+10 | 3 | −0.0645 | −0.0646 | 0.0499 | 0.0073 | −0.0507 | −0.0583 | |
+20 | 3 | −0.1286 | −0.1291 | 0.0994 | 0.0147 | −0.1014 | −0.1162 | |
−20 | 3 | 0.1023 | 0.1021 | −0.2092 | −0.0309 | 0.2244 | 0.2134 | |
−10 | 3 | 0.0512 | 0.0511 | −0.1042 | −0.0154 | 0.1122 | 0.1067 | |
+10 | 3 | −0.0512 | −0.0520 | 0.1038 | 0.0154 | −0.1122 | −0.1067 | |
+20 | 3 | −0.1023 | −0.1031 | 0.2068 | 0.0308 | −0.2244 | −0.2134 | |
−20 | 3 | 1.0307 | 1.0299 | −2.2330 | −0.3117 | 2.2657 | 2.1714 | |
−10 | 3 | 0.5154 | 0.5145 | −1.0823 | −0.1558 | 1.1335 | 1.0810 | |
+10 | 3 | −0.5156 | −0.5155 | 1.0209 | 0.1558 | −1.1334 | −1.0720 | |
+20 | 3 | −1.0310 | −1.0319 | 1.9863 | 0.3118 | −2.2672 | −2.1349 | |
−20 | 3 | 0.0107 | 0.0106 | −0.0002 | −0.00014 | 0.0004 | 0.0019 | |
−10 | 3 | 0.0052 | 0.0048 | −0.0001 | −0.00007 | 0.0002 | 0.0009 | |
+10 | 3 | −0.0052 | −0.0058 | 0.0002 | 0.00007 | −0.0001 | −0.0009 | |
+20 | 3 | −0.0107 | −0.0106 | 0.0003 | 0.00014 | −0.0003 | −0.0024 | |
−20 | 3 | 0.0030 | 0.0030 | 0.0004 | −0.00010 | 0.0005 | 0.0005 | |
−10 | 3 | 0.0015 | 0.0015 | 0.00001 | −0.00005 | 0.0003 | 0.0002 | |
+10 | 3 | −0.0015 | −0.0015 | −0.00006 | 0.00005 | −0.0003 | −0.0002 | |
+20 | 3 | −0.0030 | −0.0030 | −0.00009 | 0.00010 | −0.0005 | −0.0005 | |
−20 | 3 | −0.8044 | −0.8045 | −0.3464 | −0.0094 | 0.1263 | 0.1854 | |
−10 | 3 | −0.4012 | −0.4018 | −0.1724 | −0.0047 | 0.0630 | 0.0925 | |
+10 | 3 | 0.3992 | 0.3989 | 0.1708 | 0.0047 | −0.0627 | −0.0925 | |
+20 | 3 | 0.7960 | 0.7958 | 0.3398 | 0.0092 | −0.1251 | −0.1844 | |
−20 | 3 | 0.1023 | 0.1021 | −0.2092 | −0.0309 | 0.2244 | 0.2134 | |
−10 | 3 | 0.0512 | 0.0511 | −0.1042 | −0.0154 | 0.1122 | 0.1067 | |
+10 | 3 | −0.0512 | −0.0520 | 0.1038 | 0.0154 | −0.1122 | −0.1067 | |
+20 | 3 | −0.1023 | −0.1031 | 0.2068 | 0.0308 | −0.2244 | −0.2134 | |
−20 | 3 | −1.8889 | −1.8894 | −5.3529 | −0.5186 | 4.0178 | −0.4547 | |
−10 | 3 | −0.8989 | −0.8989 | −2.5284 | −0.2596 | 2.0081 | −0.2442 | |
+10 | 3 | 0.8139 | 0.8132 | 2.2873 | 0.2601 | −2.0082 | 0.2769 | |
+20 | 3 | 1.5487 | 1.5483 | 4.3740 | 0.5208 | −4.0166 | 0.5855 |
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Pan, J.-L.; Chiu, C.-Y.; Wu, K.-S.; Yang, C.-T.; Wang, Y.-W. Optimal Pricing, Advertising, Production, Inventory and Investing Policies in a Multi-Stage Sustainable Supply Chain. Energies 2021, 14, 7544. https://doi.org/10.3390/en14227544
Pan J-L, Chiu C-Y, Wu K-S, Yang C-T, Wang Y-W. Optimal Pricing, Advertising, Production, Inventory and Investing Policies in a Multi-Stage Sustainable Supply Chain. Energies. 2021; 14(22):7544. https://doi.org/10.3390/en14227544
Chicago/Turabian StylePan, Jia-Liang, Chui-Yu Chiu, Kun-Shan Wu, Chih-Te Yang, and Yen-Wen Wang. 2021. "Optimal Pricing, Advertising, Production, Inventory and Investing Policies in a Multi-Stage Sustainable Supply Chain" Energies 14, no. 22: 7544. https://doi.org/10.3390/en14227544