Introduction
Research gaps
-
Studies on VPR and different game strategies under SCM with quality and green degree dependent production cost for sustainable development, maintenance through mark-up strategy, and trade credit policy had not been studied yet.
-
The primary focus in previous research has been on the effects of variable demand on profit (Sarkar et al. [3]). However, selling price, quality-assured, greening level, and trade credit-dependent demand provides additional scope for maximizing profit. Therefore, such type of demand pattern and the effect on the SSCM for selecting the game strategy is a novel contribution to the literature.
-
Many SCM models are developed under fixed production rate and constant demand through game strategy under mark-up policy. However, some of them considered different strategies for retailer profit (Choi et al. [10]). But, how a can retailer improves the profit structure, not only for the total supply chain but also for himself/herself, by taking his/her own risk makes a significant contribution to the literature.
-
Several research papers on trade credit, and revenue sharing contracts through different proposed models already have been studied (Sarkar et al. [11]). But, which one of the two models gives better responses in the context of the greening level of a product and different pricing decisions of manufacturer and retailer have rarely been investigated in the literature.
Contribution
Authors | Production | Game | Production | Trade | Revenue | Demand | Model |
---|---|---|---|---|---|---|---|
rate | strategy | cost | credit | sharing | rate | type | |
Taleizadeh et al. [2] | Constant | No | Constant | Yes | No | SPCED | Inventory |
Garai and Sarkar [7] | Constant | No | Constant | No | No | Constant | SCM |
Kumar et al. [9] | Constant | No | Constant | No | No | ADT | SCM |
Choi et al. [10] | Constant | No | Constant | No | No | Vaariable | SCM |
Sepehri et al. [15] | Constant | No | Constant | No | No | SPD | Inventory |
Sarkar et al. [17] | Variable | No | Variable | No | No | SPD | Production |
Jaggi et al. [19] | Constant | No | Constant | Yes | No | Credit linked | Inventory |
Panja and Mondal [24] | No | Yes | GDD | Yes | Yes | GCD | SCM |
Cao et al. [25] | Constant | Yes | Constant | Yes | No | SPQD | SCM |
Zhang et al. [26] | Constant | Yes | Constant | No | Yes | Constant | SCM |
Shafiq and Savino [29] | Constant | No | Constant | No | Yes | Constant | SCM |
Lan and Yu [32] | Constant | Yes | Constant | No | Yes | Variable | SCM |
Pramanik et al. [33] | Constant | No | Constant | Yes | No | SCPCAD | SCM |
Wu et al. [34] | Constant | Yes | Constant | Yes | No | Variable | SCM |
Yan and He [36] | Constant | No | Constant | Yes | No | Constant | SCM |
Rini et al. [39] | Constant | No | Constant | Yes | No | CPD | SCM |
Modak and Kelle [42] | Constant | No | Constant | Yes | No | RODLD | SCM |
Deng et al. [45] | Constant | No | Constant | No | No | Random | SCM |
This Paper | Variable | Yes | QGOFD | Yes | Yes | QGSTCD | SSCM |
Structure of this study
Related literature review
Sustainable supply chain management
Game strategy
Revenue sharing contract
Trade credit
Multi-factor dependent demand
Problem definition, notation and assumption
Problem definition
Notation
Decision variables
Indices
Input parameters
Assumptions
Model formulation
Model I (without credit period)
Centralized case (I1)
Decentralized case (I2)
Revenue sharing case (I3)
Model II (with credit period)
Centralized case (II1)
Decentralized case (II2)
q | P |
\(\eta \)
|
\(\zeta _{1}\)
|
\(\zeta _{2}\)
|
\(\zeta _{1}\zeta _{2}\)
|
\(\xi \)
|
\(\Psi _{r}\)
|
\(\Psi _{m}\)
|
\(\Psi _{sc}\)
| |
---|---|---|---|---|---|---|---|---|---|---|
I1 | 0.88 | 500.70 | 12.45 | – | – | 2.21 | – | – | – | 48,538.00 |
I2 | 0.89 | 500.70 | 09.77 | 2.06 | 1.20 | 2.47 | – | 4291.33 | 29,180.90 | 33,472.23 |
I3 | 0.88 | 500.70 | 11.32 | 1.69 | 1.39 | 2.35 | – | 2749.68 | 39,794.90 | 42,544.58 |
II1 | 0.90 | 500.70 | 10.10 | – | – | 2.62 | 12 | – | – | 71,527.90 |
II2 | 0.90 | 500.70 | 8.60 | 2.14 | 1.22 | 2.61 | 3.5 | 9214.56 | 44,483.70 | 53,698.26 |
II3 | 0.91 | 500.70 | 7.65 | 1.62 | 1.82 | 2.95 | 12.3 | 10,897.8 | 54,820.40 | 65,718.40 |
Revenue sharing case (II3)
Numerical examples
Example 1
P |
\(\eta \)
|
\(\zeta _{1}\)
|
\(\zeta _{2}\)
|
\(\zeta _{1}\zeta _{2}\)
|
\(\xi \)
|
\(\Psi _{r}\)
|
\(\Psi _{m}\)
|
\(\Psi _{sc}\)
| |
---|---|---|---|---|---|---|---|---|---|
I1 | 500.70 | 13.01 | – | – | 2.34 | – | – | – | 52,843.00 |
I2 | 500.70 | 07.64 | 2.01 | 1.50 | 3.02 | – | 14,365.60 | 17,182.70 | 31,548.30 |
I3 | 500.70 | 11.15 | 1.73 | 1.46 | 2.53 | – | 1800.09 | 38,294.50 | 40,094.59 |
II1 | 500.70 | 07.99 | – | – | 2.99 | 21 | – | – | 67,963.70 |
II2 | 500.70 | 06.93 | 2.15 | 1.47 | 3.16 | 7.5 | 17,671.90 | 31,973.50 | 49,645.40 |
II3 | 500.70 | 07.80 | 1.65 | 2.06 | 3.40 | 15.10 | 15,655.90 | 43,884.30 | 59,540.20 |
Special case (without quality case)
Special case (Without greening concept case)
P | q | \(\zeta _{1}\) | \(\zeta _{2}\) | \(\zeta _{1}\zeta _{2}\) | \(\xi \) | \(\Psi _{r}\) | \(\Psi _{m}\) | \(\Psi _{sc}\) | |
---|---|---|---|---|---|---|---|---|---|
I1 | 500.70 | 0.89 | – | – | 4.30 | – | – | – | 35,122.70 |
I2 | 500.70 | 0.85 | 2.32 | 2.02 | 4.69 | – | 9529.87 | 19,654.03 | 29,183.90 |
I3 | 500.70 | 0.87 | 2.54 | 1.86 | 4.72 | – | 5939.58 | 23,944.32 | 32,298.30 |
II1 | 500.70 | 0.91 | – | – | 4.48 | 40 | – | – | 45,722.90 |
II2 | 500.70 | 0.81 | 3.08 | 1.65 | 5.08 | 9.75 | 13,475.10 | 19,605.30 | 33,080.40 |
II3 | 500.70 | 0.83 | 2.03 | 2.48 | 5.03 | 7.20 | 17,704.90 | 23,851.60 | 41,556.50 |
Example 2
q | P | \(\eta \) | \(\zeta _{1}\) | \(\zeta _{2}\) | \(\zeta _{1}\zeta _{2}\) | \(\xi \) | \(\Psi _{r}\) | \(\Psi _{m}\) | \(\Psi _{sc}\) | |
---|---|---|---|---|---|---|---|---|---|---|
I1 | 0.82 | 76.22 | 3.68 | – | – | 3.99 | – | – | – | 2729.81 |
I2 | 0.83 | 76.22 | 0.84 | 2.09 | 3.33 | 6.96 | – | 541.79 | 181.16 | 722.95 |
I3 | 0.82 | 76.22 | 2.51 | 1.53 | 3.15 | 4.82 | – | 385.60 | 1346.28 | 1731.88 |
II1 | 0.86 | 76.22 | 0.78 | – | – | 5.80 | 7.22 | – | – | 5126.93 |
II2 | 0.86 | 76.22 | 0.33 | 2.21 | 2.10 | 4.64 | 11 | 2066.48 | 820.41 | 2886.89 |
II3 | 0.84 | 76.22 | 1.45 | 2.14 | 1.69 | 3.10 | 6.9 | 290.48 | 1066.24 | 1356.72 |
Sensitivity analysis
Parameters | Change (\(\%\)) | Changes value | \(\zeta ^{I2}_{1}\) | \(\zeta ^{I3}_{1}\) | \(\zeta ^{II2}_{1}\) | \(\zeta ^{II3}_{1}\) |
---|---|---|---|---|---|---|
\(\alpha \) | \(-50\%\) | 2.505 | 2.057 | 1.764 | 2.247 | 1.535 |
\(-25\%\) | 3.7575 | 2.061 | 1.767 | 2.146 | 1.539 | |
\(+25\%\) | 6.2625 | 2.066 | 1.692 | 2.152 | 1.543 | |
\(+50\%\) | 7.515 | 2.067 | 1.693 | 2.154 | 1.545 | |
\(\theta _{1}\) | \(-50\%\) | 0.0005 | 2.065 | 1.692 | 2.258 | 1.543 |
\(-25\%\) | 0.00075 | 2.064 | 1.691 | 2.256 | 1.542 | |
\(+25\%\) | 0.00125 | 2.063 | 1.769 | 2.255 | 1.541 | |
\(+50\%\) | 0.0015 | 2.062 | 1.689 | 2.148 | 1.540 | |
\(\theta _{2}\) | \(-50\%\) | 125.35 | 2.065 | 1.692 | 2.258 | 1.543 |
\(-25\%\) | 188.025 | 2.064 | 1.691 | 2.256 | 1.542 | |
\(+25\%\) | 313.375 | 2.063 | 1.769 | 2.255 | 1.541 | |
\(+50\%\) | 376.05 | 2.062 | 1.689 | 2.148 | 1.540 | |
\(\theta _{3}\) | \(-50\%\) | 50.05 | 2.466 | 1.994 | 2.597 | 1.890 |
\(-25\%\) | 75.075 | 2.355 | 1.830 | 2.352 | 1.783 | |
\(+25\%\) | 125.125 | 2.009 | 1.647 | 1.979 | 1.411 | |
\(+50\%\) | 150.15 | 1.871 | 1.541 | 1.930 | 1.302 |
Parameters | Change (\(\%\)) | Changes value | \(\zeta ^{I2}_{2}\) | \(\zeta ^{I3}_{2}\) | \(\zeta ^{II2}_{2}\) | \(\zeta ^{II3}_{2}\) |
---|---|---|---|---|---|---|
\(\alpha \) | \(-50\%\) | 2.505 | 1.198 | 1.387 | 1.280 | 1.823 |
\(-25\%\) | 3.7575 | 1.198 | 1.387 | 1.280 | 1.823 | |
\(+25\%\) | 6.2625 | 1.198 | 1.387 | 1.280 | 1.283 | |
\(+50\%\) | 7.515 | 1.198 | 1.387 | 1.280 | 1.823 | |
\(\theta _{1}\) | \(-50\%\) | 0.0005 | 1.312 | 1.390 | 1.282 | 1.942 |
\(-25\%\) | 0.00075 | 1.199 | 1.389 | 1.281 | 1.824 | |
\(+25\%\) | 0.00125 | 1.197 | 1.385 | 1.278 | 1.937 | |
\(+50\%\) | 0.0015 | 1.196 | 1.384 | 1.226 | 1.935 | |
\(\theta _{2}\) | \(-50\%\) | 125.35 | 1.312 | 1.390 | 1.282 | 1.942 |
\(-25\%\) | 188.025 | 1.199 | 1.389 | 1.281 | 1.824 | |
\(+25\%\) | 313.375 | 1.197 | 1.386 | 1.278 | 1.937 | |
\(+50\%\) | 376.05 | 1.196 | 1.384 | 1.226 | 1.935 | |
\(\theta _{3}\) | \(-50\%\) | 50.05 | 2.015 | 1.937 | 1.807 | 2.956 |
\(-25\%\) | 75.075 | 1.420 | 1.542 | 1.557 | 2.173 | |
\(+25\%\) | 125.125 | 1.101 | 1.686 | 1.325 | 1.576 | |
\(+50\%\) | 150.15 | 1.011 | 1.455 | 1.041 | 1.397 |
Parameters | Change (\(\%\)) | Changes value | \((\zeta _{1}\zeta _{2})^{I1}\) | \((\zeta _{1}\zeta _{2})^{I2}\) | \((\zeta _{1}\zeta _{2})^{I3}\) | \((\zeta _{1}\zeta _{2})^{II1}\) | \((\zeta _{1}\zeta _{2})^{II2}\) | \((\zeta _{1}\zeta _{2})^{II3}\) |
---|---|---|---|---|---|---|---|---|
\(\alpha \) | \(-50\%\) | 2.505 | 2.205 | 2.464 | 2.447 | 2.612 | 2.876 | 2.798 |
\(-25\%\) | 3.7575 | 2.307 | 2.469 | 2.450 | 2.619 | 2.747 | 2.806 | |
\(+25\%\) | 6.2625 | 2.312 | 2.475 | 2.347 | 2.627 | 2.755 | 2.813 | |
\(+50\%\) | 7.515 | 2.216 | 2.476 | 2.348 | 2.630 | 2.757 | 2.817 | |
\(\theta _{1}\) | \(-50\%\) | 0.0005 | 2.312 | 2.709 | 2.352 | 2.510 | 2.895 | 2.997 |
\(-25\%\) | 0.00075 | 2.311 | 2.475 | 2.349 | 2.508 | 2.890 | 2.813 | |
\(+25\%\) | 0.00125 | 2.309 | 2.469 | 2.450 | 2.506 | 2.882 | 2.985 | |
\(+50\%\) | 0.0015 | 2.211 | 2.466 | 2.338 | 2.505 | 2.633 | 2.980 | |
\(\theta _{2}\) | \(-50\%\) | 125.35 | 2.214 | 2.709 | 2.352 | 2.510 | 2.895 | 2.007 |
\(-25\%\) | 188.025 | 2.213 | 2.475 | 2.349 | 2.508 | 2.890 | 2.813 | |
\(+25\%\) | 313.375 | 2.310 | 2.469 | 2.452 | 2.506 | 2.882 | 2.985 | |
\(+50\%\) | 376.05 | 2.308 | 2.466 | 2.338 | 2.505 | 2.633 | 2.980 | |
\(\theta _{3}\) | \(-50\%\) | 50.05 | 2.588 | 4.969 | 3.862 | 3.001 | 4.693 | 5.587 |
\(-25\%\) | 75.075 | 2.385 | 3.344 | 2.822 | 2.732 | 3.662 | 3.874 | |
\(+25\%\) | 125.125 | 2.062 | 2.212 | 2.777 | 2.430 | 2.622 | 2.224 | |
\(+50\%\) | 150.15 | 2.024 | 2.242 | 2.665 | 2.150 | 2.009 | 1.819 |
Parameters | Change (\(\%\)) | Changes value | \(\Psi ^{I2}_{r}\) | \(\Psi ^{I3}_{r}\) | \(\Psi ^{II2}_{r}\) | \(\Psi ^{II3}_{r}\) |
---|---|---|---|---|---|---|
\(\alpha \) | \(-50\%\) | 2.505 | 4263.53 | 2735.32 | 9196.86 | 10,872.00 |
\(-25\%\) | 3.7575 | 4276.95 | 2742.25 | 9205.40 | 10,884.50 | |
\(+25\%\) | 6.2625 | 4303.80 | 2756.11 | 9222.48 | 10,909.40 | |
\(+50\%\) | 7.515 | 4317.23 | 2763.04 | 9231.02 | 10,921.90 | |
\(\theta _{1}\) | \(-50\%\) | 0.0005 | 10527.10 | 2794.16 | 9336.41 | 18,364.10 |
\(-25\%\) | 0.00075 | 4308.52 | 2771.69 | 9275.20 | 10,930.10 | |
\(+25\%\) | 0.00125 | 4272.22 | 2726.64 | 9152.64 | 18,235.50 | |
\(+50\%\) | 0.0015 | 4254.09 | 2704.04 | 3697.18 | 18,192.60 | |
\(\theta _{2}\) | \(-50\%\) | 125.35 | 10527.20 | 2794.28 | 9336.75 | 18,364.40 |
\(-25\%\) | 188.025 | 4308.57 | 2771.75 | 9275.37 | 10,930.10 | |
\(+25\%\) | 313.375 | 4272.17 | 2726.57 | 9152.47 | 18,235.40 | |
\(+50\%\) | 376.05 | 4253.98 | 2703.92 | 3696.96 | 18,192.30 | |
\(\theta _{3}\) | \(-50\%\) | 50.05 | 21399.30 | 4903.03 | 21011.80 | 35,101.00 |
\(-25\%\) | 75.075 | 8052.94 | 2476.66 | 20959.70 | 17,630.20 | |
\(+25\%\) | 125.125 | 4524.12 | 9099.53 | 15,538.20 | 4449.95 | |
\(+50\%\) | 150.15 | 3214.59 | 5238.04 | 11,235.30 | 1134.35 |
Parameters | Change (\(\%\)) | Changes value | \(\Psi ^{I2}_{m}\) | \(\Psi ^{I3}_{m}\) | \(\Psi ^{II2}_{m}\) | \(\Psi ^{II3}_{m}\) |
---|---|---|---|---|---|---|
\(\alpha \) | \(-50\%\) | 2.505 | 29,000.90 | 58,216.20 | 61,125.40 | 39,591.30 |
\(-25\%\) | 3.7575 | 29,106.10 | 58,367.50 | 44,387.30 | 39,723.00 | |
\(+25\%\) | 6.2625 | 29,229.00 | 39,851.10 | 44,545.80 | 39,876.40 | |
\(+50\%\) | 7.515 | 29,270.40 | 39,899.50 | 44,599.20 | 39,928.10 | |
\(\theta _{1}\) | \(-50\%\) | 0.0005 | 29,231.80 | 39,854.30 | 61,479.40 | 39,876.90 |
\(-25\%\) | 0.00075 | 29201.80 | 39,819.40 | 61,435.10 | 39,841.10 | |
\(+25\%\) | 0.00125 | 29,154.40 | 58,437.20 | 61,364.80 | 39,784.50 | |
\(+50\%\) | 0.0015 | 29,134.30 | 39,740.50 | 44,425.40 | 39,760.50 | |
\(\theta _{2}\) | \(-50\%\) | 125.35 | 29,231.80 | 39,854.30 | 61,479.40 | 39,876.90 |
\(-25\%\) | 188.025 | 29,201.80 | 39,819.40 | 61,435.10 | 39,841.10 | |
\(+25\%\) | 313.375 | 29,154.40 | 58,437.20 | 61,364.80 | 39,784.50 | |
\(+50\%\) | 376.05 | 29,134.30 | 39,740.50 | 44,425.40 | 39,760.50 | |
\(\theta _{3}\) | \(-50\%\) | 50.05 | 2942.80 | 51,531.90 | 56,976.10 | 51,803.10 |
\(-25\%\) | 75.075 | 50,469.40 | 45,471.80 | 50,538.00 | 61,673.00 | |
\(+25\%\) | 125.125 | 38,856.70 | 52,001.40 | 38,796.80 | 34,382.80 | |
\(+50\%\) | 150.15 | 33,617.60 | 45,912.40 | 48,217.90 | 29,333.20 |
Parameters | Change (\(\%\)) | Changes value | \(\Psi ^{I1}_{sc}\) | \(\Psi ^{I2}_{sc}\) | \(\Psi ^{I3}_{sc}\) | \(\Psi ^{II1}_{sc}\) | \(\Psi ^{II2}_{sc}\) | \(\Psi ^{II3}_{sc}\) |
---|---|---|---|---|---|---|---|---|
\(\alpha \) | \(-50\%\) | 2.505 | 48,305.60 | 33,264.43 | 60,951.52 | 71,228.60 | 70,322.26 | 50463.30 |
\(-25\%\) | 3.7575 | 69,686.70 | 33,383.05 | 61,109.75 | 71,403.80 | 53,592.70 | 50,607.5 | |
\(+25\%\) | 6.2625 | 69,879.30 | 33,532.80 | 42,607.21 | 71,607.80 | 53,768.28 | 50,785.80 | |
\(+50\%\) | 7.515 | 48,653.60 | 33,587.63 | 42,662.54 | 71,676.50 | 53,830.22 | 50,850.00 | |
\(\theta _{1}\) | \(-50\%\) | 0.0005 | 69,882.50 | 39,758.90 | 42,648.46 | 52,527.80 | 70,815.81 | 58,241.00 |
\(-25\%\) | 0.00075 | 69,836.20 | 33,510.32 | 42,591.09 | 52,487.30 | 70,710.3 | 50,771.2 | |
\(+25\%\) | 0.00125 | 69,762.90 | 33,426.62 | 61,163.84 | 52,423.20 | 70,517.44 | 58,020.00 | |
\(+50\%\) | 0.0015 | 48,478.00 | 33,388.39 | 42,444.54 | 52,396.00 | 48,122.58 | 57,953.10 | |
\(\theta _{2}\) | \(-50\%\) | 125.35 | 48,603.60 | 39,759.00 | 42,648.58 | 52,527.80 | 70,816.15 | 58,241.30 |
\(-25\%\) | 188.025 | 48,565.10 | 33,510.37 | 42,591.15 | 52,487.30 | 70,710.47 | 50,771.20 | |
\(+25\%\) | 313.375 | 69,762.90 | 33,426.57 | 61,163.77 | 52,423.20 | 70,517.27 | 58,019.9 | |
\(+50\%\) | 376.05 | 69,731.80 | 33,388.28 | 42,444.42 | 52,396.00 | 48,122.36 | 57,952.80 | |
\(\theta _{3}\) | \(-50\%\) | 50.05 | 61,419.70 | 50,742.10 | 56,434.93 | 65,934.90 | 77,987.90 | 86,904.10 |
\(-25\%\) | 75.075 | 54,787.00 | 58,522.34 | 47,948.46 | 59,004.90 | 71,497.70 | 79,303.20 | |
\(+25\%\) | 125.125 | 42,656.20 | 43,380.82 | 61,100.93 | 54,211.30 | 54,335.00 | 38,832.75 | |
\(+50\%\) | 150.15 | 56,009.80 | 36,832.19 | 51,150.44 | 40,484.90 | 59,453.20 | 30,467.55 |