Multi-Stage Production and Process Outsourcing in Automobile-Part Supply Chain Considering a Carbon Tax Strategy Using Sequential Quadratic Optimization Technique
Abstract
:1. Introduction
2. Literature Review and Conceptual Framework
3. Mathematical Model
3.1. Assumptions
- The model considered multiple types of items. The production system outsourced operations due to limited constraints. The imperfect products were produced, after which reworking was done and inspection cost was incurred.
- Production and demand rates were constant and known throughout the supply chain. There were no shortages produced in the system (Pa > ∑ Pbi > Pc > D to avoid shortages). The demand rate was equal in all three phases.
- Production and reworking were done in the same manufacturing system at the same production rate. Inventory holding costs were based on the average inventory.
- There was no scrap during the rework process. The rework process was 100% perfect. All products were screened and the screening cost was negligible. Transportation cost was not considered the total cost of the supply chain.
3.2. Decision Variables
- Q, production quantity for manufacturer.
- (Qb1, Qb2, Qb3, …, Qbn) Production Quantity for n outsourcers.
3.3. Notation
3.4. Model Formulation
3.4.1. Cost of Manufacturer
Setup Cost
Manufacturing and Rework Cost
Holding Cost
Transportation Cost
Carbon Tax
Inspection Cost
Total Manufacturing Cost
3.4.2. Total Cost of Outsourcers
3.4.3. Total Cost of the Supply Chain
3.4.4. Constraints
- Production Constraints:
- Demand Constraints:
- Space Constraints:
- To avoid shortage:
4. Methodology
Sequential Quadratic Programming (SQP)
5. Numerical Experiment
5.1. Numerical Example 01
5.2. Numerical Example 02
6. Numerical Results (Case1 & 2) and Managerial Insights
7. Sensitivity Analysis
- The marginal cost had a higher impact on the total cost. Changing the marginal cost by ±50% caused ±29% variation in the total cost.
- A second significant parameter with a high impact on TC was manufacturing cost, Ma. Changing Ma ± 50% varied TC by ±4%. Similarly, inspection cost was the next most significant variable, with a reduction of 3.5% in TC.
- Some variables (MR, Ia, Ic, Ibi, em, ebi, Ma, Mc, and Mbi) had no impact on decision variables, but had a direct impact on the total cost.
- The production rates of manufacturers and outsourcers both had low impacts on the total cost. Comparatively, for any production system, the setup cost and holding cost were the main costs.
- With all costs fixed, increasing these costs had a direct impact on the overall cost. It was observed that the setup cost was more sensitive than the holding cost, meaning that the industry could further reduce overall costs by using initial investment to decrease their setup cost.
- In a traditional production system, inspection cost is controlled through human inspection. An increase in inspection costs could cause an increase in total costs. This could be minimized by replacing physical human inspection with machine inspection
- em and ebi were variables for carbon emission, per unit item of production, for manufacturer and ith outsourcers, respectively. It was noted that em had a high impact on total cost, as compared to ebi. Carbon emission had a direct relationship with total cost, and would thus be of major concern for managers; government policy and customers increasingly demand environmentally friendly products. Therefore, to be competitive in the market, a business must minimize the overall carbon emissions in their supply chain.
- In the case of outsourcers, the most impactful parameters on TC were inspection cost Ib1, manufacturing cost Mb1, carbon emission per unit item eb1, and setup cost Sb1.
- A minor change in these two led to high impacts on the total cost. The other variables also impacted the total cost, albeit minorly. Abrupt changes in the total cost occurred only when the marginal and demand rates were changed slightly. All other variables’ lines merged into each other, showing that there was little or no impact on the percentage of the total cost. The results clearly showed that the marginal rate and demand had a significant impact on output.
- Similarly, the manufacturing cost line had the second-highest impact on total cost; a small change in this was able to change the total cost. The third-highest impact in this category was the inspection cost, which had little impact on the objective function.
8. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix A.1. Inventory Diagram of the First Phase of Manufacture
Appendix A.2. Inventory Diagrams of 2nd Phase of Outsourcers
Appendix A.3. Inventory Diagram of 2nd Phase of Outsourcer 2
Appendix A.4. Inventory Diagram of 2nd Phase of Outsourcer 3
Appendix A.5. Inventory Diagram of 2nd Phase of the ith Outsourcer
Appendix A.6. Inventory Diagram of the Last Phase of Manufacturer
Appendix B
Appendix B.1. Mathematical Modeling
Appendix B.2. Phase A
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Authors | Outsourcing | Supply Chain | Optimization | Methodology | Imperfection | Carbon Policy | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Process | Product | Logistic | Centralized | Decentralize | NLP | LP and IP | SQP | Analytical | Carbon Tax | Carbon Cap | Carbon Trad | ||
Yang et al. (2005) [51] | √ | √ | |||||||||||
YangPeng (2016) [52] | √ | √ | √ | √ | |||||||||
Xiao-Ying Bao (2018) [53] | √ | √ | √ | √ | √ | ||||||||
Mingzhou Jin (2014) [54] | √ | √ | √ | √ | |||||||||
Lhoussaine ameknassi (2016) [30] | √ | √ | √ | √ | √ | ||||||||
Alex coman (2000) [55] | √ | √ | √ | ||||||||||
M.N Qureshi, Dinesh Kumar (2007) [56] | √ | √ | √ | ||||||||||
Jian Li, Qin Su (2017) [57] | √ | √ | √ | √ | √ | √ | √ | √ | |||||
Saif benjaafar, Mark daskin (2010) [58] | √ | √ | √ | √ | √ | ||||||||
Abolfazl Gharaei (2019) [59] | √ | √ | √ | √ | |||||||||
Yuwan Shyi Peter Chiu et al. (2020) [60] | √ | √ | √ | √ | |||||||||
Proposed Work | √ | √ | √ | √ | √ | √ |
Notation | Description |
---|---|
M | Index for manufacturer |
I | Index for outsourcers |
J | Index for item |
TCj | Total cost of the supply chain |
TCmj | Total cost of manufacturer |
TCoij | Total cost of ith outsourcer |
HCmj | Holding cost of manufacturer |
HCoij | Holding cost of outsourcer i |
Hmj | Holding cost per unit item of manufacturer |
Hoij | Holding cost per unit item of ith outsourcer |
SCmj | Setup cost of manufacturer |
SCoij | Setup cost of outsourcer i |
Smj | Setup cost per unit item of manufacturer |
Soij | Setup cost per unit item of ith outsourcer |
PCmj | Production cost of manufacturer |
PCoij | Production cost of outsourcer i |
Maj | Production cost per unit item of Phase A for manufacturer |
Mcj | Production cost per unit item of Phase C for manufacturer |
Moi | Production cost per unit item of ith outsourcer |
Dj | Constant rate of demand |
Paj | Production rate of phase A |
Pcj | Production rate of phase C |
Pbij | Production rate of phase B for ith outsourcer |
CEmj | Carbon emission cost for the manufacturer |
CEoij | Carbon emission cost for outsourcer i |
fmj | Carbon emission cost per ton CO2 emission for manufacturer |
emj | Carbon emission per unit item production for the manufacturer |
fbij | Carbon emission cost per ton CO2 emission for outsourcer i |
ebij | Carbon emission per unit item production for outsourcer i |
ftj | Carbon emission cost per ton CO2 emission in transportation |
etmj | Carbon emission per unit item transportation of manufacturer |
etoij | Carbon emission per unit item transportation of oustourcer i |
αj | Rate of rework of phase A for the manufacturer |
αcj | Rate of rework of phase C for manufacturer |
αbij | Rate of rework for the ith outsourcer |
MR | Marginal cost of outsourcers |
Iaj | Inspection cost per unit item at phase A |
Icj | Inspection cost per unit item at phase C |
Ibij | Inspection cost per unit item at phase B for ith outsourcer |
Fmj | Fixed transportation cost of manufacturer |
Foij | Fixed transportaiotn cost of outsourcer i |
Vmj | Variable transportation cost of manufacturer |
Voij | Variable transportaion cost of outsourcer i |
Manufacturer | Demand | Production Rate | Manufacturing Cost | Holding Cost | Setup Cost | Inspection Cost | Carbon Tax | CO2 Emission/Item | Defectives | Transportation Cost |
---|---|---|---|---|---|---|---|---|---|---|
Phase A | 300 | 600 | 12 | 50 | 50 | 10 | 23 | 0.8 | 0.05 | Fixed = 03 Variable = 15 CO2 Cost = 6 |
Phase C | 300 | 400 | 8 | 50 | 9 | 23 | 0.02 |
Phase B | Outsourcers | Production Rate | Manufacturing Cost | Holding Cost | Setup Cost | Rework Cost | Inspection Cost | Carbon Emission Cost | Defectives | CO2 Emission/Item | Transporation Cost |
1 | 450 | 6 | 56 | 45 | 6 | 9.5 | 23 | 0.04 | 0.18 | Fixed = 03 Variable = 15 CO2 Cost = 6 | |
2 | 550 | 7 | 50 | 50 | 7 | 10 | 23 | 0.04 | 0.2 | ||
3 | 580 | 8 | 47 | 55 | 8 | 10.5 | 23 | 0.04 | 0.22 |
Manufacturer | Demand | Production Rate | Manufacturing Cost | Holding Cost | Setup Cost | Inspection Cost | Carbon Emission Cost | CO2 Emission/kg | Defectives | Transportation Cost |
---|---|---|---|---|---|---|---|---|---|---|
Phase A | 2,160,000 | 3,854,400 | 30 | 50 | 8 | 1.6 | 23 | 0.8 | 0.05 | Fixed = 03 Variable = 15 CO2 Cos t = 6 |
Phase C | 2,160,000 | 3,854,400 | 30 | 50 | 1 | 23 | 0.02 |
Phase B | Outsourcers | Production Rate | Manufacturing Cost | Holding Cost | Setup Cost | Rework Cost | Inspection Cost | Carbon Emission Cost | Defectives | CO2 Emission/Item | Transportation Cost |
1 | 450 | 6 | 80 | 15 | 6 | 1.2 | 23 | 0.04 | 0.18 | Fixed = 03 Variable = 15 CO2 Cost = 6 | |
2 | 550 | 7 | 50 | 10 | 7 | 1.2 | 23 | 0.04 | 0.2 | ||
3 | 580 | 8 | 40 | 5 | 8 | 1.2 | 23 | 0.04 | 0.22 |
Case | Total Cost (TC) | Manufacturer Optimal Quantity (Q) | 1st Outsourcer Optimal Quantity (Qb1) | 2nd Outsourcer Optimal Quantity (Qb2) | 3rd Outsourcer Optimal Quantity (Qb3) |
---|---|---|---|---|---|
Case 1 | USD 93,362.8$ | 87.6 parts | 28.1 parts | 29.4 parts | 30.3 parts |
Case 2 | SAR 350,233.46 | 1606.9 kg | 469.9 kg | 526.5 kg | 610.6 kg |
Parameters | % Change in Values | Decision Variables | % Change in the Total Cost | |||
---|---|---|---|---|---|---|
Q | Qb1 | Qb2 | Qb3 | |||
Sm | −50 | 50.4 | 15.5 | 16.8 | 17.9 | −0.3 |
−25 | 51 | 15.7 | 17 | 18.1 | −0.15 | |
25 | 52.1 | 16 | 17.4 | 18.6 | 0.15 | |
50 | 52.7 | 16.2 | 17.6 | 18.8 | 0.3 | |
Hm | −50 | 60.4 | 18.4 | 20.2 | 21.7 | −2 |
−25 | 55.5 | 17 | 18.6 | 19.8 | −0.9 | |
25 | 48.4 | 14.9 | 16.2 | 17.2 | 0.9 | |
50 | 46.2 | 14.3 | 15.4 | 16.4 | 1.6 | |
MR | −50 | 43.3 | 13.1 | 14.5 | 15.3 | −29.2 |
−25 | 48.1 | 14.9 | 16.1 | 17.1 | −14.5 | |
25 | 54.1 | 16.7 | 18.1 | 17.3 | 14.5 | |
50 | 56.2 | 17.2 | 18.8 | 20.1 | 29 | |
Ma | −50 | 51.6 | 15.9 | 17.2 | 18.4 | −4 |
−25 | 51.6 | 15.9 | 17.2 | 18.4 | −2 | |
25 | 51.6 | 15.9 | 17.2 | 18.4 | 2 | |
50 | 51.6 | 15.9 | 17.2 | 18.4 | 3.9 | |
Mc | −50 | 51.6 | 15.9 | 17.2 | 18.4 | −2.3 |
−25 | 51.6 | 15.9 | 17.2 | 18.4 | 1.3 | |
25 | 51.6 | 15.9 | 17.2 | 18.4 | 1.3 | |
50 | 51.6 | 15.9 | 17.2 | 18.4 | 2.6 | |
Ia | −50 | 51.6 | 15.9 | 17.2 | 18.4 | −3.2 |
−25 | 51.6 | 15.9 | 17.2 | 18.4 | −1.6 | |
25 | 51.6 | 15.9 | 17.2 | 18.4 | 1.6 | |
50 | 51.6 | 15.9 | 17.2 | 18.4 | 3.2 | |
Ic | −50 | 51.6 | 15.9 | 17.2 | 18.4 | −2.9 |
−25 | 51.6 | 15.9 | 17.2 | 18.4 | −2.1 | |
25 | 51.6 | 15.9 | 17.2 | 18.4 | 1.4 | |
50 | 51.6 | 15.9 | 17.2 | 18.4 | 2.9 |
Parameters | % Change in Values | Decision Variables | % Change in the Total Cost | |||
---|---|---|---|---|---|---|
Q | Qb1 | Qb2 | Qb3 | |||
Sb1 | −50 | 47.3 | 11.36 | 17.4 | 18.5 | −1.2 |
−25 | 49.6 | 13.8 | 17.3 | 18.4 | −0.5 | |
25 | 53.3 | 17.7 | 17.2 | 18.3 | 0.4 | |
50 | 54.8 | 19.4 | 17.1 | 18.3 | 0.9 | |
hb1 | −50 | 54 | 18.4 | 17.2 | 18.3 | −0.5 |
−25 | 52.6 | 17 | 17.2 | 18.3 | −0.2 | |
25 | 50.7 | 14.9 | 17.3 | 18.4 | 0.2 | |
50 | 49.9 | 15.9 | 15.5 | 18.4 | 0.5 | |
Mb1 | −50 | 51.6 | 15.9 | 17.2 | 18.4 | −2.3 |
−25 | 51.6 | 15.9 | 17.2 | 18.4 | −1.1 | |
25 | 51.6 | 15.9 | 17.2 | 18.4 | 1.1 | |
50 | 51.6 | 15.9 | 17.2 | 18.4 | 2.3 | |
Ib1 | −50 | 51.6 | 15.9 | 17.2 | 18.4 | −3.5 |
−25 | 51.6 | 15.9 | 17.2 | 18.4 | −1.5 | |
25 | 51.6 | 15.9 | 17.2 | 18.4 | 1.5 | |
50 | 51.6 | 15.9 | 17.2 | 18.4 | 3.1 | |
eb1 | −50 | 51.6 | 15.9 | 17.2 | 18.4 | −1.5 |
−25 | 51.6 | 15.9 | 17.2 | 18.4 | −0.8 | |
25 | 51.6 | 15.9 | 17.2 | 18.4 | 1.0 | |
50 | 51.6 | 15.9 | 17.2 | 18.4 | 1.5 |
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Alkahtani, M.; Hidri, L.; Mrad, M. Multi-Stage Production and Process Outsourcing in Automobile-Part Supply Chain Considering a Carbon Tax Strategy Using Sequential Quadratic Optimization Technique. Mathematics 2023, 11, 1191. https://doi.org/10.3390/math11051191
Alkahtani M, Hidri L, Mrad M. Multi-Stage Production and Process Outsourcing in Automobile-Part Supply Chain Considering a Carbon Tax Strategy Using Sequential Quadratic Optimization Technique. Mathematics. 2023; 11(5):1191. https://doi.org/10.3390/math11051191
Chicago/Turabian StyleAlkahtani, Mohammed, Lofti Hidri, and Mehdi Mrad. 2023. "Multi-Stage Production and Process Outsourcing in Automobile-Part Supply Chain Considering a Carbon Tax Strategy Using Sequential Quadratic Optimization Technique" Mathematics 11, no. 5: 1191. https://doi.org/10.3390/math11051191
APA StyleAlkahtani, M., Hidri, L., & Mrad, M. (2023). Multi-Stage Production and Process Outsourcing in Automobile-Part Supply Chain Considering a Carbon Tax Strategy Using Sequential Quadratic Optimization Technique. Mathematics, 11(5), 1191. https://doi.org/10.3390/math11051191