# Supply Chain Coordination and Consumer Awareness for Pollution Reduction

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Differential Game Models and Analysis Outcome

## 4. Theorems

**Theorem**

**1.**

**Proof.**

**Theorem**

**2.**

**Proof.**

**Theorem**

**3.**

**Proof.**

**Theorem**

**4.**

**Proof.**

## 5. Numerical Examples

_{1}= 50) and the unit production cost of a smartphone is about $200 per unit (c = 20); (2) one unit of manufacturer capacity emits 0.01 ton of pollution (l = 0.01); and (3) the potential market size is about 2,000,000 units per month (α = 200,000. Accordingly, the major variables are interpreted as follow: the measure of manufacturer’s pollution accumulation (y) is 10 tons, the measure of sales price is $10 per unit, and the measure of manufacturer’s pollution abatement effort (v) is ton per unit capacity.

## 6. Discussion and Conclusions

## Author Contributions

## Conflicts of Interest

## Appendix A. Analysis for Model 2

## Appendix B. Proofs of Theorems

**Proof**

**of**

**Theorem**

**1.**

**Proof**

**of**

**Theorem**

**2.**

**Proof**

**of**

**Theorem**

**3.**

**Proof**

**of**

**Theorem**

**4**

## References

- Kleindorfer, P.R.; Singhal, K.; Wassenhove, L.N. Sustainable operations management. Prod. Oper. Manag.
**2005**, 14, 482–492. [Google Scholar] [CrossRef] - Linton, J.D.; Klassen, R.; Jayaraman, V. Sustainable supply chains: An introduction. J. Oper. Manag.
**2007**, 25, 1075–1082. [Google Scholar] [CrossRef] - Seuring, S.; Müller, M. From a literature review to a conceptual framework for sustainable supply chain management. J. Clean. Prod.
**2008**, 16, 1699–1710. [Google Scholar] [CrossRef] - Srivastava, S.K. Green supply-chain management: A state-of-the-art literature review. Int. J. Manag. Rev.
**2007**, 9, 53–80. [Google Scholar] [CrossRef] - Benchekroun, H.; Van Long, N. Efficiency inducing taxation for polluting oligopolists. J. Public Econ.
**1998**, 70, 325–342. [Google Scholar] [CrossRef] - Chen, Y.J.; Sheu, J.-B. Environmental-regulation pricing strategies for green supply chain management. Transp. Res. E Logist. Transp. Rev.
**2009**, 45, 667–677. [Google Scholar] [CrossRef] [Green Version] - Jung, C.; Krutilla, K.; Boyd, R. Incentives for advanced pollution abatement technology at the industry level: An evaluation of policy alternatives. J. Environ. Econ. Manag.
**1996**, 30, 95–111. [Google Scholar] [CrossRef] - Li, S. Emission permit banking, pollution abatement and production-inventory control of the firm. Int. J. Prod. Econ.
**2013**, 146, 679–685. [Google Scholar] [CrossRef] - Li, J.; Du, W.; Yang, F.; Hua, G. The carbon subsidy analysis in remanufacturing closed-loop supply chain. Sustainability
**2014**, 6, 3861–3877. [Google Scholar] [CrossRef] - Krass, D.; Nedorezov, T.; Ovchinnikov, A. Environmental taxes and the choice of green technology. Prod. Oper. Manag.
**2013**, 22, 1035–1055. [Google Scholar] [CrossRef] - Milliman, S.R.; Prince, R. Firm incentives to promote technological change in pollution control. J. Environ. Econ. Manag.
**1989**, 17, 247–265. [Google Scholar] [CrossRef] - Subramanian, R.; Gupta, S.; Talbot, B. Compliance strategies under permits for emissions. Prod. Oper. Manag.
**2007**, 16, 763–779. [Google Scholar] [CrossRef] - Tang, C.S.; Zhou, S. Research advances in environmentally and socially sustainable operations. Eur. J. Oper. Res.
**2012**, 223, 585–594. [Google Scholar] [CrossRef] - Zhang, L.; Wang, J.; You, J. Consumer environmental awareness and channel coordination with two substitutable products. Eur. J. Oper. Res.
**2015**, 241, 63–73. [Google Scholar] [CrossRef] - Handfield, R.B.; Walton, S.V.; Seegers, L.K.; Melnyk, S.A. “Green” value chain practices in the furniture industry. J. Oper. Manag.
**1997**, 15, 293–315. [Google Scholar] [CrossRef] - Hollos, D.; Blome, C.; Foerstl, K. Does sustainable supplier co-operation affect performance? Examining implications for the triple bottom line. Int. J. Prod. Res.
**2012**, 50, 2968–2986. [Google Scholar] [CrossRef] - Simpson, D. Use of supply relationships to recycle secondary materials. Int. J. Prod. Res.
**2010**, 48, 227–249. [Google Scholar] [CrossRef] - Ni, D.; Li, K.W.; Tang, X. Social responsibility allocation in two-echelon supply chains: Insights from wholesale price contracts. Eur. J. Oper. Res.
**2010**, 207, 1269–1279. [Google Scholar] [CrossRef] - Lou, G.X.; Xia, H.Y.; Zhang, J.Q.; Fan, T.J. Investment strategy of emission-reduction technology in a supply chain. Sustainability
**2015**, 7, 10684–10708. [Google Scholar] [CrossRef] - Klassen, R.D.; Vachon, S. Collaboration and evaluation in the supply chain: The impact on plant-level environmental investment. Prod. Oper. Manag.
**2003**, 12, 336–352. [Google Scholar] [CrossRef] - Lee, H.L. Don’t tweak your supply chain: Rethink it end to end. Harv. Bus. Rev.
**2010**, 88, 62–69. [Google Scholar] - Conrad, K. Price competition and product differentiation when consumers care for the environment. Environ. Resour. Econ.
**2005**, 31, 1–19. [Google Scholar] [CrossRef] - Du, S.; Zhu, J.; Jiao, H.; Ye, W. Game-theoretical analysis for supply chain with consumer preference to low carbon. Int. J. Prod. Res.
**2015**, 53, 3753–3768. [Google Scholar] [CrossRef] - Ghosh, D.; Shah, J. A comparative analysis of greening policies across supply chain structures. Int. J. Prod. Econ.
**2012**, 135, 568–583. [Google Scholar] [CrossRef] - Wang, K.; Zhao, Y.; Cheng, Y.; Choi, T.-M. Cooperation or competition? Channel choice for a remanufacturing fashion supply chain with government subsidy. Sustainability
**2014**, 6, 7292–7310. [Google Scholar] [CrossRef] - Bagnoli, M.; Watts, S.G. Selling to socially responsible consumers: Competition and the private provision of public goods. J. Econ. Manag. Strategy
**2003**, 12, 419–445. [Google Scholar] [CrossRef] - Yalabik, B.; Fairchild, R.J. Customer, regulatory, and competitive pressure as drivers of environmental innovation. Int. J. Prod. Econ.
**2011**, 131, 519–527. [Google Scholar] [CrossRef] - Liu, Z.L.; Anderson, T.D.; Cruz, J.M. Consumer environmental awareness and competition in two-stage supply chains. Eur. J. Oper. Res.
**2012**, 218, 602–613. [Google Scholar] [CrossRef] - Chung, S.H.; Weaver, R.D.; Friesz, T.L. Strategic response to pollution taxes in supply chain networks: Dynamic, spatial, and organizational dimensions. Eur. J. Oper. Res.
**2013**, 231, 314–327. [Google Scholar] [CrossRef] - Grant, D.S.; Bergesen, A.J.; Jones, A.W. Organizational size and pollution: The case of the US chemical industry. Am. Sociol. Rev.
**2002**, 67, 389–407. [Google Scholar] - Gray, W.B.; Shadbegian, R.J. “Optimal” pollution abatement—Whose benefits matter, and how much? J. Environ. Econ. Manag.
**2004**, 47, 510–534. [Google Scholar] [CrossRef] - Laplante, B.; Rilstone, P. Environmental inspections and emissions of the pulp and paper industry in quebec. J. Environ. Econ. Manag.
**1996**, 31, 19–36. [Google Scholar] [CrossRef] - Ludwig, L. The US acid rain program and its effect on SO
_{2}emission levels. Issues Political Econ.**2004**, 13, 11–22. [Google Scholar] - Vachon, S.; Klassen, R.D. Green project partnership in the supply chain: The case of the package printing industry. J. Clean. Prod.
**2006**, 14, 661–671. [Google Scholar] [CrossRef] - Klassen, R.D. Plant-level environmental management orientation: The influence of management views and plant characteristics. Prod. Oper. Manag.
**2001**, 10, 257–275. [Google Scholar] [CrossRef] - Adida, E.; Bakshi, N.; DeMiguel, V. Supplier capacity and intermediary profits: Can less be more? Prod. Oper. Manag.
**2016**, 25, 630–646. [Google Scholar] [CrossRef] - Ha, A.Y.; Tong, S.; Zhang, H. Sharing demand information in competing supply chains with production diseconomies. Manag. Sci.
**2011**, 57, 566–581. [Google Scholar] [CrossRef] - Anand, K.S.; Mendelson, H. Information and organization for horizontal multimarket coordination. Manag. Sci.
**1997**, 43, 1609–1627. [Google Scholar] [CrossRef] - Eliashberg, J.; Steinberg, R. Marketing-production decisions in an industrial channel of distribution. Manag. Sci.
**1987**, 33, 981–1000. [Google Scholar] [CrossRef] - El Ouardighi, F.; Jørgensen, S.; Pasin, F. A dynamic game with monopolist manufacturer and price-competing duopolist retailers. OR Spectr.
**2013**, 35, 1059–1084. [Google Scholar] [CrossRef] - El Ouardighi, F.; Sim, J.E.; Kim, B. Pollution accumulation and abatement policy in a supply chain. Eur. J. Oper. Res.
**2016**, 248, 982–996. [Google Scholar] [CrossRef] - Weil, D. Implementing Employment Regulations: Insights on the Determinants of Regulatory Performance; Industrial Relations Research Association: Madison, WI, USA, 1997; pp. 429–474. [Google Scholar]
- Wong, E. Fines total $26 million for polluters in China. The New York Times, 1 January 2015; A10. [Google Scholar]
- He, L.; Zhao, D.; Xia, L. Game theoretic analysis of carbon emission abatement in fashion supply chains considering vertical incentives and channel structures. Sustainability
**2015**, 7, 4280–4309. [Google Scholar] [CrossRef] - Bertinelli, L.; Camacho, C.; Zou, B. Carbon capture and storage and transboundary pollution: A differential game approach. Eur. J. Oper. Res.
**2014**, 237, 721–728. [Google Scholar] [CrossRef] - Tidball, M.; Zaccour, G. A differential environmental game with coupling constraints. Optim. Control Appl. Methods
**2009**, 30, 197–207. [Google Scholar] [CrossRef] - Hovelaque, V.; Bironneau, L. The carbon-constrained EOQ model with carbon emission dependent demand. Int. J. Prod. Econ.
**2015**, 164, 285–291. [Google Scholar] [CrossRef] - Bernstein, F.; Kök, A.G. Dynamic cost reduction through process improvement in assembly networks. Manag. Sci.
**2009**, 55, 552–567. [Google Scholar] [CrossRef] - Gerchak, Y.; Wang, Y. Revenue-sharing vs. Wholesale-price contracts in assembly systems with random demand. Prod. Oper. Manag.
**2004**, 13, 23–33. [Google Scholar] [CrossRef] - Wang, Y.; Niu, B.; Guo, P. On the advantage of quantity leadership when outsourcing production to a competitive contract manufacturer. Prod. Oper. Manag.
**2013**, 22, 104–119. [Google Scholar] [CrossRef] - Jørgensen, S. Optimal production, purchasing and pricing: A differential game approach. Eur. J. Oper. Res.
**1986**, 24, 64–76. [Google Scholar] [CrossRef]

**Figure 3.**Pollution dynamics of consumer-aware competitive vs. consumer-ignorant supply chain. (Region 1 implies ${p}_{1}>{\tilde{p}}_{1}$, thus ${y}_{LR}^{II}<{y}_{LR}^{I}={y}_{LR}^{IV}$ and ${v}_{LR}^{II}>{v}_{LR}^{I}={v}_{LR}^{IV}$ hold. In contrast, Region 2 implies ${p}_{1}<{\tilde{p}}_{1}$, thus ${y}_{LR}^{II}>{y}_{LR}^{I}={y}_{LR}^{IV}$ and ${v}_{LR}^{II}<{v}_{LR}^{I}={v}_{LR}^{IV}$ hold.)

**Figure 4.**Pollution dynamics of consumer-aware cooperative vs. consumer-ignorant supply chain. (Region 1 implies $\alpha >\tilde{\alpha}$, thus ${y}_{LR}^{III}<{y}_{LR}^{I}={y}_{LR}^{IV}$ and ${v}_{LR}^{III}>{v}_{LR}^{I}={v}_{LR}^{IV}$ hold. In contrast, Region 2 implies $\alpha <\tilde{\alpha}$, thus ${y}_{LR}^{III}>{y}_{LR}^{I}={y}_{LR}^{IV}$ and ${v}_{LR}^{III}<{v}_{LR}^{I}={v}_{LR}^{IV}$ hold.)

**Figure 5.**Long-term pollution related equilibrium depending on the consumer’s awareness: (

**a**) cumulative pollution; and (

**b**) abatement effort.

Notation | Definition |
---|---|

$y\left(t\right)$ | Cumulative pollution at time t |

$v\left(t\right)$ | The level of effort by the manufacturer to reduce the emission of pollutants |

f | Cost parameter associated with the government penalty on the cumulative pollution |

e | Cost parameter associated with the manufacturer’s pollution abatement effort |

$\overline{U}$ | Manufacturer’s plant capacity |

l | Pollution emission per unit manufacturing capacity |

${p}_{2}\left(t\right)$ | Retail price charged by the retailer at time t |

${p}_{1}\left(t\right)$ | Transfer price paid to the manufacturer at time t |

c | Unit production cost of the manufacturer |

${c}_{1}$ | Cost parameter associated with the deviation from the manufacturing capacity $\overline{U}$ |

${c}_{2}$ | Cost parameter associated with the retailer’s processing the product |

$D\left(t\right)$ | Demand for the product at time t, i.e., $D\left(t\right)=\alpha -\beta {p}_{2}\left(t\right)$ or $D\left(t\right)=\alpha -\beta {p}_{2}\left(t\right)-\gamma y\left(t\right)$ |

α | Potential market size |

β | Coefficient in the demand function associated with the sales price ${p}_{2}\left(t\right)$ |

γ | Coefficient in the demand function associated with the cumulative pollution $y\left(t\right)$ |

δ | Decay rate of the cumulative pollution |

r | Discount rate |

${y}_{LR}^{i}$ | Long-run equilibrium of cumulative pollution in model i, $i=\mathrm{I},\text{II},\text{III},\text{IV}$ |

${v}_{LR}^{i}$ | Long-run equilibrium of the manufacturer’s pollution abatement effort in model i, $i=\mathrm{I},\text{II},\text{III},\text{IV}$ |

${{p}_{2}}_{LR}^{i}$ | Long-run equilibrium of the sales price in model i, $i=\mathrm{I},\text{II},\text{III},\text{IV}$ |

$J,{J}^{m},{J}^{r}$ | Objective function (net profit) of the whole supply chain, manufacturer, or retailer for $t\in \left[0,\infty \right)$ |

Model | Variables | Long-Run Equilibrium |
---|---|---|

Model 1 | ${v}_{LR}^{I}$ | $-\frac{\overline{U}}{2e}{K}_{11}$ |

${y}_{LR}^{I}$ | $-\frac{1}{2f}{K}_{11}\left(r+\delta \right)$ | |

${{p}_{2}}_{LR}^{I}$ | $\frac{\alpha \left(1+2\beta {c}_{2}\right)+\beta {p}_{1}}{2\beta \left(1+\beta {c}_{2}\right)}$ | |

Model 2 | ${v}_{LR}^{II}$ | $-\frac{1}{\overline{U}}\left(\delta {K}_{21}-\overline{U}l\right)$ |

${y}_{LR}^{II}$ | ${K}_{21}$ | |

${{p}_{2}}_{LR}^{II}$ | $\frac{\alpha \left(1+2\beta {c}_{2}\right)+\beta {p}_{1}}{2\beta \left(1+\beta {c}_{2}\right)}-\frac{\gamma \left(1+2\beta {c}_{2}\right)}{2\beta \left(1+\beta {c}_{2}\right)}{K}_{21}$ | |

Model 3 | ${v}_{LR}^{III}$ | $-\frac{1}{\overline{U}}\left(\mathsf{\delta}{K}_{32}-\overline{U}l\right)$ |

${y}_{LR}^{III}$ | ${K}_{32}$ | |

${{p}_{2}}_{LR}^{III}$ | $\frac{\alpha \left(1+2\beta {c}_{1}+2\beta {c}_{2}\right)-2\beta {c}_{1}\overline{U}+\beta c}{2\beta \left(1+\beta {c}_{1}+\beta {c}_{2}\right)}-\frac{\gamma \left(1+2\beta {c}_{1}+2\beta {c}_{2}\right)}{2\beta \left(1+\beta {c}_{1}+\beta {c}_{2}\right)}{K}_{32}$ | |

Model 4 | ${v}_{LR}^{IV}$ | $-\frac{\overline{U}}{2e}{K}_{41}$ |

${y}_{LR}^{IV}$ | $-\frac{1}{2f}{K}_{41}\left(r+\delta \right)$ | |

${{p}_{2}}_{LR}^{IV}$ | $\frac{\alpha +\beta c+2\beta {c}_{1}\left(\alpha -\overline{U}\right)+2\alpha \beta {c}_{2}}{2\beta \left(1+\beta {c}_{1}+\beta {c}_{2}\right)}$ | |

Constants | ${K}_{11}$ | $-\frac{2ef\overline{U}l}{f{\overline{U}}^{2}+e\delta \left(r+\delta \right)}$ |

${K}_{21}$ | $\frac{{\overline{U}}^{2}\left\{\gamma \left(1+\beta {c}_{2}\right)\left[-\left({p}_{1}-c\right)+2{c}_{1}\left(\alpha -\overline{U}\right)\right]-\gamma {c}_{1}\left(\alpha +2\alpha \beta {c}_{2}+\beta {p}_{1}\right)\right\}+2el\overline{U}\left(r+\delta \right)\left(1+\beta {c}_{2}\right)}{2\left(1+\beta {c}_{2}\right)\left[f{\overline{U}}^{2}+e\delta \left(r+\delta \right)\right]+{\gamma}^{2}{\overline{U}}^{2}{c}_{1}}$ | |

${K}_{31}$ | $\frac{4\beta \left(1+\beta {c}_{1}+\beta {c}_{2}\right)\left[f{U}^{2}+e\delta \left(r+\delta \right)\right]-{\gamma}^{2}{U}^{2}}{4e\beta \left(1+\beta {c}_{1}+\beta {c}_{2}\right)}$ | |

${K}_{32}$ | $\frac{4\beta el\overline{U}\left(1+\beta {c}_{1}+\beta {c}_{2}\right)\left(r+\delta \right)-\gamma {\overline{U}}^{2}\left(\alpha -\beta c+2\beta {c}_{1}\overline{U}\right)}{4\beta \left(1+\beta {c}_{1}+\beta {c}_{2}\right)\left[f{\overline{U}}^{2}+e\delta \left(r+\delta \right)\right]-{\gamma}^{2}{\overline{U}}^{2}}$ | |

${K}_{41}$ | $-\frac{2ef\overline{U}l}{f{\overline{U}}^{2}+e\delta \left(r+\delta \right)}$ |

r | p_{1} | c | c_{1} | c_{2} | e | f | l | δ | α | β | γ | $\overline{U}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|

0.004 | 50 | 20 | 10^{−5} | 10^{−5} | 10^{9} | 0.01 | 0.01 | 0.1 | 200,000 | 2000 | 0.1 | 100,000 |

Variable | Model 1 | Model 2 | Model 3 | Model 4 |
---|---|---|---|---|

Pollution accumulation ( y) | 942.0 | 801.5 | 763.6 | 942.0 |

Pollution abatement effort ( v) | 0.00906 | 0.00920 | 0.00924 | 0.00906 |

Sales price (
p_{2}) | 75.49 | 75.47 | 60.56 | 60.58 |

Market demand per period | 49,020 | 48,980 | 78,809 | 78,846 |

Supply chain profit for entire periods | 6.44942 × 10^{8} | 6.44102 × 10^{8} | 7.59763 × 10^{8} | 7.60593 × 10^{8} |

Manufacturer profit for entire periods | 3.38570 × 10^{8} | 3.38215 × 10^{8} | - | - |

Retailer profit for entire periods | 3.06373 × 10^{8} | 3.05887 × 10^{8} | - | - |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kim, B.; Sim, J.E.
Supply Chain Coordination and Consumer Awareness for Pollution Reduction. *Sustainability* **2016**, *8*, 365.
https://doi.org/10.3390/su8040365

**AMA Style**

Kim B, Sim JE.
Supply Chain Coordination and Consumer Awareness for Pollution Reduction. *Sustainability*. 2016; 8(4):365.
https://doi.org/10.3390/su8040365

**Chicago/Turabian Style**

Kim, Bowon, and Jeong Eun Sim.
2016. "Supply Chain Coordination and Consumer Awareness for Pollution Reduction" *Sustainability* 8, no. 4: 365.
https://doi.org/10.3390/su8040365