Sustainable Supply Chain System for Defective Products with Different Carbon Emission Strategies
Abstract
:1. Introduction
1.1. Literature Review
1.2. Research Motivations and Contributions
2. Notation and Assumptions
Assumptions
- (i)
- A single form of an item is used for the production–inventory model. The buyer can place order Q to be shipped in n number of equal-sized deliveries once the inventory reaches r.
- (ii)
- The lead-time demand X follows a normal probability distribution function , with mean and standard deviation . The r is defined as r , where signifies the safety component. The L comprises m jointly autonomous modules, whereby the ith module has a normal period , a least period , and a crashing cost . These are rearranged conveniently to give , such that . constituents are crashed at some point in time, beginning with the first element due to its lowest unit-crashing cost, followed by the next element, and then the subsequent elements afterwards.
- (iii)
- Let and be the span of with modules crashed to their lowest period; then can be stated as and the crashing cost for per cycle is B .
- (iv)
- The manufacturing sector produces defective items due to use of a long-run system. Thus, after a certain time, this system starts to produce defective items. The fraction of faulty items is found in all lots, and, thus, all lots are immediately screened at a constant rate , which is higher than .
- (v)
- Carbon emissions arise in the process of manufacturing, transportation, and storage. To reduce emissions from the system, additional investment is used. According to Huang et al. [25], to reduce carbon emissions, investment in green technology can be utilized. The green technology function for reducing emissions is presented as .
3. Model Development
3.1. Model without Considering Carbon Emissions
3.1.1. Modeling for Buyer
3.1.2. Modeling for Vendor
3.2. Carbon Emission Policies with Green Investments
3.2.1. Carbon Taxation
Algorithm 1. Optimal solutions for carbon taxation scenario |
Step 1.. |
Step 2., perform steps (2.1) and (2.2). |
Step 2.1. from Equations (3) and (5), respectively. |
Step 2.2. into Equation (1). |
Step 3.. |
Step 4.= Min j = 0, 1, 2, 3…, n, is an optimal solution. |
Step 5.. |
Step 6. If 〖, then turn back to step 5; otherwise turn to step 7. |
Step 7. is the optimal solution. |
3.2.2. Limited Carbon Emission
Algorithm 2 Optimal solutions for limited carbon emissions scenario |
Step 1. Put . |
Step 2. For each , perform steps (2.1) and (2.2). |
Step 2.1. Find the values of , by solving Equations (8), (9), and (11), respectively. |
Step 2.2. Calculate the subsequent , by putting and in Equation (1). |
Step 3. Find Min j = 0, 1, 2, …, n, . |
Step 4. Set = Min j = 0, 1, 2, 3…, n, , then for a fixed value of , the set is an optimal solution. |
Step 5. Set and repeat steps 2 to 4, to obtain 〖. |
Step 6. If , then turn back to step 5, otherwise move to step 7. |
Step 7. Put , then set is the optimal solution. |
4. Numerical and Sensitivity Study
4.1. Numerical Study
4.2. Sensitivity Study
4.3. Academic and Managerial Implications
- (1)
- The increase in the backlogged parameters and brings a loss in profit, which is a higher total cost as the selling price of the items becomes higher.
- (2)
- Total cost increases with the increase in and because increasing these values enhances the carbon emissions, and the transportation costs also increase.
- (3)
- (4)
- (5)
- The costs incurred by the vendor increase due to the increase in S, which leads to an increased joint total cost. The vendor’s setup cost is also highly sensitive to Q and n.
- (6)
- As the customer demands increase, the vendor will plan a larger number of shipments, thus resulting in higher emissions. One solution to curtail emissions is to reduce delivery frequency, which will result in a longer lead time.
- (7)
- Table 8 indicates that with an increase in the vendor’s limited carbon emission quantity , an increase in is also recorded. The high limited carbon emissions allowed by governments may lead to the vendor producing more products. Nonetheless, increasing carbon emissions limits are not always a positive option for reducing carbon emissions. Defining appropriate carbon emission strategies that align economic development with ecological protection is important for governments.
- (8)
- The suggested technique lets managers change the rate of production by managing production allocation. When the rate of production has a significant influence on the quantity of the emissions that are produced, the plan of a adjustment becomes vital. Our findings show that adjusting the to a suitable level can benefit the system by balancing the supply with the demand and cutting emissions. Regrettably, prior inventory models did not take such restrictions into account; hence, this benefit was unavailable.
- (9)
- This study evaluates the consequences of carbon control depending on emissions, the goal function of the suggested inventory system, and inventory cost. The cost of the system among different scenarios (carbon taxation and limited carbon emission) are compared. The results indicate that limited carbon emission is less than carbon taxation for the inventory cost system.
- (10)
- The comparison between carbon taxation and limited carbon policies reveals that subsequent costs to the buyer exert varying effects on the vendors’ total costs and carbon emissions.
- (11)
- With the help of green technology, the vendor has more chances to cut the emissions caused by the production activity. Although the use of green technology needs a greater cost, the vendor will obtain the benefits from the reduced emissions.
- (12)
- Purchasing power allowances can be reduced by investment in decreasing carbon outflows, even for a lesser limit for carbon emissions.
- (13)
- Managers can only invest in renewable methods that lead to a reduction in carbon discharges and meet the requirements for lower pollution levels, which leads to a maximum aggregate inventory cost. The total cost for inventory then decreases as the carbon-release cap slowly rises. The aggregate inventory cost is retained at a given cost when the carbon emission limit rises above a threshold, which makes the SC limited by the carbon emission limit.
- (14)
- According to our findings, transitioning to green production has a significant influence on the inventory system. In order to comply with carbon tax legislation, the producer can use green technology to reduce emissions from the activities of production, transportation, and storage. Unfortunately, with various types of green technology available, picking which one to employ in production may be challenging. Green technology includes renewable energy, green chemistry, and recycling technology (100% recycled tin, precious metals). Consequently, administrators must cautiously select the most appropriate green technology. In addition to cost reasons, managers must evaluate other variables when selecting the appropriate technology.
- (15)
- The proposed model gives flexibility to a manager to adjust the production rate by controlling the production allocation. In a situation where the level of production emissions is very much influenced by the production rate, the policy on production-rate adjustment becomes important. Our study shows that by adjusting the production rate to an appropriate level, the system can obtain benefits, balancing the production with demand and decreasing the production’s emissions.
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Notations
Parameters | |
D | demand rate (units/time) |
P | production rate (units/time) |
crashing cost of lead time | |
S | setup cost (USD/setup) |
A | ordering cost (USD/order) |
r | reorder point |
storage cost for vendor (USD/unit/unit time) | |
storage cost for buyer (USD/unit/unit time) | |
d | delivery distance (unit) |
F | transport cost per unit (USD/unit distance) |
emissions from storage per unit (gallon/unit) | |
emissions from transportation per unit (gallon/unit distance) | |
emissions from production per unit (gallon/unit) | |
emissions during manufacturing setup (gallon/setup) | |
G | green investment amount (USD) |
ability factor to reduce emissions | |
offset factor to reduce emissions | |
U | emissions upper limit (gallon) |
unit carbon emission tax (USD/gallon) | |
rate of screening | |
cost for screening per unit (USD/unit) | |
scraping cost per unit (USD/unit) | |
cost for wrongly accepting an imperfect item per unit (USD/unit) | |
cost for wrongly rejecting a perfect item per unit (USD/unit) | |
the fraction of Type I error (a random variable) | |
the fraction of Type II error (a random variable) | |
y | the proportion of imperfect items that were received by the buyer from the vendor |
the proportion of imperfect items observed by the buyer | |
backorder ratio | |
backorder price per unit (USD/unit) | |
penalty cost of a loss of sale (USD/unit) | |
the standard deviation of lead-time demand | |
Decision variables | |
Q | order quantity (USD/time) |
n | number of deliveries |
L | inventory lead time |
R(G) | green investment amount (USD) |
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Author(s) | Multi-Echelon Model | Human Error | Carbon Emission | Green Investment | Limited Carbon Emission and Carbon Taxation | Controllable Lead Time |
---|---|---|---|---|---|---|
Khanra et al. [3] | ✓ | |||||
Das et al. [4] | ✓ | |||||
Priyan and Mala [6] | ✓ | ✓ | ||||
Priyan and Uthayakumar [8] | ✓ | ✓ | ||||
Khan et al. [10] | ✓ | ✓ | ||||
Taheri-Tolgari et al. [11] | ✓ | ✓ | ||||
Tiwari et al. [12] | ✓ | ✓ | ||||
Pan and Yang [17] | ✓ | ✓ | ||||
Hoque [18] | ✓ | ✓ | ||||
Hammami et al. [21] | ✓ | ✓ | ✓ | |||
Li et al. [22] | ✓ | ✓ | ✓ | |||
Tang et al. [23] | ✓ | |||||
Halat and Hafezalkoto [24] | ✓ | ✓ | ||||
Huang et al. [25] | ✓ | ✓ | ✓ | ✓ | ||
Yang et al. [28] | ✓ | ✓ | ||||
Md. Rakibul [29] | ✓ | ✓ | ✓ | |||
Biswajit et al. [30] | ✓ | ✓ | ✓ | |||
Yuqiang et al. [31] | ✓ | ✓ | ||||
This paper | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
Parameter | Value | Parameter | Value |
---|---|---|---|
8000/cycle | USD 1.2/gallon | ||
12,000/year | 6000 gallons | ||
USD 75/order | USD 0.5/unit | ||
175,200 | USD 0.5/unit | ||
USD 1.3 unit/unit time | USD 150/unit | ||
USD 10 unit/unit time | USD 200/unit | ||
USD 10/km | USD 50/unit | ||
200 km | 7 | ||
4 gallons/unit | 0.02 | ||
5 gallons/km | 0.02 | ||
2 gallons/cycle | 0.02 | ||
10 gallons/setup | USD 1200/setup | ||
15 | 0.2 | ||
0.01 | USD 100/unit | ||
0.2 | 0.75 |
Lead-Time Module | Normal Period (Days) | Minimum Period (Days) | Unit-Crashing Cost (USD/Days) |
---|---|---|---|
1 | 20 | 6 | 0.4 |
2 | 20 | 6 | 1.2 |
3 | 16 | 9 | 5.0 |
(Week) | B (L) |
---|---|
8 | 0 |
6 | 5.6 |
4 | 22.4 |
3 | 57.4 |
n | ||||||||
---|---|---|---|---|---|---|---|---|
Q | Q | Q | Q | |||||
1 | 2397 | 70,565 | 2352 | 69,794 | 2300 | 69,678 | 2274 | 69,092 |
2 | 2165 | 70,708 | 2120 | 69,745 | 2067 | 68,619 | 2040 | 68,280 |
3 | 2029 | 72,081 | 1986 | 71,055 | 1934 | 69,853 | 1908 | 68,033 |
4 | 1927 | 73,708 | 1884 | 72,627 | 1835 | 71,362 | 1810 | 68,409 |
5 | 1905 | 73,614 | 1794 | 73,412 | 1798 | 72,005 | 1795 | 69,121 |
n | Q | Q | Q | Q | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 6637 | 0.2 | 61,178 | 6486 | 0.2 | 60,867 | 6309 | 0.2 | 60,134 | 6219 | 0.2 | 59,895 |
2 | 6381 | 0.2 | 60,466 | 6224 | 0.2 | 60,143 | 6040 | 0.2 | 59,874 | 5945 | 0.2 | 59,177 |
3 | 6246 | 0.3 | 62,529 | 6285 | 0.3 | 61,270 | 6092 | 0.3 | 59,775 | 5987 | 0.3 | 58,962 |
4 | 6446 | 0.3 | 65,122 | 6291 | 0.3 | 63,813 | 6108 | 0.3 | 62,259 | 6014 | 0.3 | 59,217 |
5 | 6536 | 0.3 | 67,317 | 6350 | 0.3 | 64,526 | 6219 | 0.3 | 63,591 | 6251 | 0.3 | 60,021 |
Parameters | % Changes | Q* | L* | n* | Parameters | % Changes | Q* | L* | n* | ||
---|---|---|---|---|---|---|---|---|---|---|---|
D | +50% | 2189 | 4 | 4 | 70,701 | +50% | 2193 | 4 | 3 | 69,874 | |
+25% | 2126 | 3 | 3 | 69,784 | +25% | 2115 | 3 | 3 | 69,312 | ||
0% | 1908 | 3 | 3 | 68,038 | 0% | 1908 | 3 | 3 | 68,038 | ||
−25% | 2012 | 3 | 3 | 67,753 | −25% | 1986 | 3 | 3 | 67,211 | ||
−50% | 1986 | 3 | 3 | 65,857 | −50% | 1915 | 3 | 3 | 67,043 | ||
P | +50% | 2116 | 8 | 4 | 71,575 | +50% | 2265 | 4 | 4 | 68,587 | |
+25% | 2095 | 8 | 4 | 69,519 | +25% | 2187 | 4 | 4 | 68,346 | ||
0% | 1908 | 3 | 3 | 68,038 | 0% | 1908 | 4 | 3 | 68,038 | ||
−25% | 2011 | 3 | 3 | 67,954 | −25% | 2016 | 4 | 3 | 67,854 | ||
−50% | 1954 | 3 | 2 | 67,123 | −50% | 1995 | 4 | 3 | 67,532 | ||
A | +50% | 2214 | 4 | 3 | 72,294 | +50% | 2206 | 3 | 4 | 69,018 | |
+25% | 2158 | 4 | 3 | 71,456 | +25% | 2152 | 3 | 4 | 68,542 | ||
0% | 1908 | 3 | 3 | 68,038 | 0% | 1908 | 3 | 3 | 68,038 | ||
−25% | 2002 | 3 | 3 | 67,157 | −25% | 1989 | 3 | 3 | 67,816 | ||
−50% | 1973 | 3 | 2 | 66,548 | −50% | 1931 | 3 | 3 | 67,524 | ||
+50% | 2190 | 8 | 3 | 70,051 | S | +50% | 2243 | 4 | 2 | 69,339 | |
+25% | 2137 | 8 | 3 | 68,986 | +25% | 2194 | 4 | 2 | 68,756 | ||
0% | 1908 | 3 | 3 | 68,038 | 0% | 1908 | 3 | 3 | 68,038 | ||
−25% | 2012 | 3 | 3 | 67,423 | −25% | 2009 | 3 | 3 | 67,727 | ||
−50% | 1969 | 3 | 2 | 67,108 | −50% | 1899 | 3 | 4 | 67,501 |
Parameters | % Changes | Q | L | n | Parameters | % Changes | Q | L | n | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
D | +50% | 6153 | 0.3 | 3 | 2 | 60,992 | +50% | 6127 | 0.3 | 6 | 4 | 59,424 | |
+25% | 6089 | 0.3 | 3 | 2 | 59,644 | +25% | 6045 | 0.3 | 6 | 3 | 59,110 | ||
0% | 5987 | 0.3 | 3 | 3 | 58,962 | 0% | 5987 | 0.3 | 3 | 3 | 58,962 | ||
−25% | 5478 | 0.3 | 3 | 3 | 57,571 | −25% | 5876 | 0.3 | 3 | 2 | 58,681 | ||
−50% | 5122 | 0.4 | 6 | 4 | 56,401 | −50% | 5743 | 0.3 | 3 | 1 | 58,448 | ||
P | +50% | 6248 | 0.2 | 8 | 3 | 60,491 | +50% | 6143 | 0.3 | 4 | 3 | 59,853 | |
+25% | 6107 | 0.2 | 8 | 3 | 59,847 | +25% | 6084 | 0.3 | 4 | 3 | 59,412 | ||
0% | 5987 | 0.3 | 3 | 3 | 58,962 | 0% | 5987 | 0.3 | 3 | 3 | 58,962 | ||
−25% | 5627 | 0.3 | 3 | 2 | 57,246 | −25% | 5813 | 0.3 | 3 | 3 | 58,611 | ||
−50% | 5431 | 0.3 | 3 | 2 | 56,312 | −50% | 5897 | 0.3 | 3 | 3 | 58,323 | ||
A | +50% | 6230 | 0.3 | 3 | 3 | 60,821 | +50% | 6150 | 0.4 | 6 | 3 | 59,540 | |
+25% | 6152 | 0.3 | 3 | 3 | 59,731 | +25% | 6091 | 0.4 | 6 | 3 | 59,215 | ||
0% | 5987 | 0.3 | 3 | 3 | 58,962 | 0% | 5987 | 0.3 | 3 | 3 | 58,962 | ||
−25% | 5148 | 0.3 | 3 | 3 | 57,576 | −25% | 5873 | 0.3 | 3 | 2 | 58,613 | ||
−50% | 5019 | 0.3 | 3 | 3 | 56,521 | −50% | 5987 | 0.3 | 3 | 2 | 58,318 | ||
+50% | 6211 | 0.4 | 6 | 4 | 59,123 | S | +50% | 6230 | 0.3 | 3 | 3 | 60,481 | |
+25% | 6068 | 0.3 | 6 | 3 | 59,031 | +25% | 6121 | 0.3 | 3 | 3 | 59,843 | ||
0% | 5987 | 0.3 | 3 | 3 | 58,962 | 0% | 5987 | 0.3 | 3 | 3 | 58,962 | ||
−25% | 5903 | 0.3 | 3 | 3 | 58,815 | −25% | 5843 | 0.3 | 3 | 3 | 57,760 | ||
−50% | 5894 | 0.3 | 3 | 2 | 58,687 | −50% | 5725 | 0.3 | 3 | 2 | 56,877 | ||
U | +50% | 6254 | 0.3 | 3 | 3 | 59,374 | |||||||
+25% | 6009 | 0.3 | 3 | 3 | 59,195 | ||||||||
0% | 5987 | 0.3 | 3 | 3 | 58,962 | ||||||||
−25% | 5502 | 0.3 | 3 | 3 | 58,749 | ||||||||
−50% | 5491 | 0.3 | 3 | 3 | 58,539 |
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Mala, P.; Palanivel, M.; Priyan, S.; Jirawattanapanit, A.; Rajchakit, G.; Kaewmesri, P. Sustainable Supply Chain System for Defective Products with Different Carbon Emission Strategies. Sustainability 2022, 14, 16082. https://doi.org/10.3390/su142316082
Mala P, Palanivel M, Priyan S, Jirawattanapanit A, Rajchakit G, Kaewmesri P. Sustainable Supply Chain System for Defective Products with Different Carbon Emission Strategies. Sustainability. 2022; 14(23):16082. https://doi.org/10.3390/su142316082
Chicago/Turabian StyleMala, Pitchaikani, Muthusamy Palanivel, Siluvayan Priyan, Anuwat Jirawattanapanit, Grienggrai Rajchakit, and Pramet Kaewmesri. 2022. "Sustainable Supply Chain System for Defective Products with Different Carbon Emission Strategies" Sustainability 14, no. 23: 16082. https://doi.org/10.3390/su142316082