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Outsourcing contract design for the green transformation of manufacturing systems under asymmetric information
Business School, SiChuan University, Chengdu 610065, China 
Accepting that suppliers' capability for green transformation of manufacturing systems is private information and that the efforts made in the process of transformation invisibly involve private actions of buyers, we construct an outsourcing model including transformation services before project delivery and maintenance services within the warranty period after project delivery and research the optimal outsourcing contract design for buyers. We find that the buyer can design a set of contract menus, including fixed compensation and variable compensation related to the quantity of energy conservation and emission reduction (ECER), to identify suppliers with different transformation capabilities and encourage them to make the best efforts under asymmetric information. Second, to identify the suppliers' transformation capability, the buyer needs to pay information rent to the supplier with high transformation ability. Meanwhile, the existence of asymmetric information will make the supplier with low transformation ability exert insufficient effort, and the existence of asymmetric information will always reduce the buyer's expected utility. In addition, the example analysis shows that asymmetric information always reduces the expected number of ECERs of the buyer. Therefore, it is suggested that the government should consider screening the transformation ability of green technology suppliers, disclose to the market and recommend suppliers with high transformation ability to reduce the negative impact caused by asymmetric information.
References:
[1] 
L. Athias and S. Saussier, Are public private partnerships that rigid? And why? Evidence from price provisions in French toll road concession contracts, Transportation Research Part A: Policy and Practice, 111 (2018), 174186. doi: 10.1016/j.tra.2018.02.011. 
[2] 
S. P. Chuang and C. L. Yang, Key success factors when implementing a greenmanufacturing system, Production Planning and Control, 25 (2014), 923937. doi: 10.1080/09537287.2013.780314. 
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B. Cao and J. Gao, Quality incentive contract with asymmetric process design quality information, Chinese Journal of Management Science, 26 (2018), 145153. 
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A. M. Deif, A system model for green manufacturing, Journal of Cleaner Production, 19 (2011), 15531559. doi: 10.1016/j.jclepro.2011.05.022. 
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A. Goli, E. B. Tirkolaee and N. S. Aydin, Fuzzy integrated cell formation and production scheduling considering automated guided vehicles and human factors, IEEE Transactions on Fuzzy Systems, (2021). doi: 10.1109/TFUZZ.2021.3053838. 
[6] 
A. Goli and M. Alinaghian, A new mathematical model for production and delivery scheduling problem with common cycle in a supply chain with openshop system, International Journal of Manufacturing Technology and Management, 34 (2020), 174187. doi: 10.1504/IJMTM.2020.10027948. 
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K. L. Hui, P. F. Ke, Y. X. Yao and W. T. Yue, Bilateral liabilitybased contracts in information security outsourcing, Information Systems Research, 30 (2019), 411429. doi: 10.1287/isre.2018.0806. 
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H. Huang and M. H. Hu, Contract design for IT outsourcing under asymmetric information, Chinese Journal of Management Science, (2020). 
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H. Huang, L. M. Liu, G. Parker, Y. Tan and H. Y. Xu, Multiattribute procurement auctions in the presence of satisfaction risk, Production and Operations Management, 28 (2019), 12061221. doi: 10.1111/poms.12979. 
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T. Jain, J. Hazra and T. C. E. Cheng, IT outsourcing and vendor cost improvement strategies under asymmetric information, Decision Sciences, (2020). doi: 10.1111/deci.12446. 
[11] 
K. Li, X. Zhang, Y. T. Leung and S. L. Yang, Parallel machine scheduling problems in green manufacturing industry, Journal of Manufacturing Systems, 38 (2016), 98106. doi: 10.1016/j.jmsy.2015.11.006. 
[12] 
G. Li, M. K. Lim and Z. Wang, Stakeholders, green manufacturing, and practice performance: Empirical evidence from Chinese fashion businesses, Annals of Operations Research, 290 (2020), 961982. doi: 10.1007/s10479019031577. 
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H. M. Liu, X. Y. Zhang and M. Y. Hu, Gametheorybased analysis of Energy Performance Contracting for building retrofits, Journal of Cleaner Production, 231 (2019), 10891099. 
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C. Liu, W. Chen and J. Mu, Retailer's multitier green procurement contract in the presence of suppliers' reference point effect, Production and Operations Management, 131 (2019), 242258. doi: 10.1016/j.cie.2019.03.013. 
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R. Lotfi, G. W. Weber, S. M. Sajadifar and N. Mardani, Interdependent demand in the twoperiod newsvendor problem, Journal of Industrial and Management Optimization, 16 (2016), 117140. doi: 10.3934/jimo.2018143. 
[17] 
R. Lotfi, Z. Yadegari, S. H. Hosseini, A. H. Khameneh and G. W. Weber, A robust timecostqualityenergyenvironment tradeoff with resourceconstrained in project management: A case study for a bridge construction project, Journal of Industrial and Management Optimization, 13 (2020), 122. 
[18] 
R. Lotfi, Y. Z. Mehrjerdi, M. S. Pishvaee, A. Sadegheih and G. W. Weber, A robust optimization model for sustainable and resilient closedloop supply chain network design considering conditional value at risk, Numer. Algebra Control Optim., 11 (2021), 221253. doi: 10.3934/naco.2020023. 
[19] 
R. Lotfi, Y. Z. Mehrjerdi and N. Mardani, A multiobjective and multiproduct advertising billboard location model with attraction factor mathematical modeling and solutions, International Journal of Applied Logistics, 7 (2017), 6487. doi: 10.4018/IJAL.2017010104. 
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J. J. Laffont and J. Tirole, A Theory of Incentives in Procurement and Regulation, MIT Press Books, 1993. 
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V. MartínezdeAlbéniz and D. SimchiLevi, A portfolio approach to procurement contracts, Production and Operations Management, 14 (2010), 90114. 
[22] 
A. Maccormack and A. Mishra, Managing the performance tradeoffs from partner integration: Implications of contract choice in R & D Projects, Production and Operations Management, 24 (2015), 15521569. doi: 10.1111/poms.12374. 
[23] 
T. Paksoy and E. Ozceylan, Environmentally conscious optimization of supply chain networks, Journal of the Operational Research Society, 65 (2014), 855872. doi: 10.1057/jors.2012.95. 
[24] 
T. Paksoy, N. Y. Pehlivan and E. Ozceylan, Fuzzy multiobjective optimization of a green supply chain network with risk management that includes environmental hazards, Human and Ecological Risk Assessment, 18 (2012), 11201151. doi: 10.1080/10807039.2012.707940. 
[25] 
Q. Qiu, L. Cui, J. Y. Shen and Y. Li, Optimal maintenance policy considering maintenance errors for systems operating under performancebased contracts, Computers and Industrial Engineering, 112 (2017), 147155. doi: 10.1016/j.cie.2017.08.025. 
[26] 
W. H. Tsai, H. C. Chen, J. Y. Liu, S. P. Chen and Y. S. Shen, Using activitybased costing to evaluate capital investments for green manufacturing systems, International Journal of Production Research, 49 (2011), 72757292. doi: 10.1080/00207543.2010.537389. 
[27] 
E. B. Tirkolaee and N. S. Aydn, A sustainable medical waste collection and transportation model for pandemics, Waste Management and Research, (2021). doi: 10.1177/0734242X211000437. 
[28] 
E. B. Tirkolaee, P. Abbasian and G. W. Weber, Sustainable fuzzy multitrip locationrouting problem for medical waste management during the COVID19 outbreak, Science of The Total Environment, 10 (2020), 143607. 
[29] 
C. Wang, G. Schmidt and V. D. R. Bo, Stagegate contracts to screen agents with inside information, Decision Sciences, 49 (2018), 11561186. doi: 10.1111/deci.12308. 
show all references
References:
[1] 
L. Athias and S. Saussier, Are public private partnerships that rigid? And why? Evidence from price provisions in French toll road concession contracts, Transportation Research Part A: Policy and Practice, 111 (2018), 174186. doi: 10.1016/j.tra.2018.02.011. 
[2] 
S. P. Chuang and C. L. Yang, Key success factors when implementing a greenmanufacturing system, Production Planning and Control, 25 (2014), 923937. doi: 10.1080/09537287.2013.780314. 
[3] 
B. Cao and J. Gao, Quality incentive contract with asymmetric process design quality information, Chinese Journal of Management Science, 26 (2018), 145153. 
[4] 
A. M. Deif, A system model for green manufacturing, Journal of Cleaner Production, 19 (2011), 15531559. doi: 10.1016/j.jclepro.2011.05.022. 
[5] 
A. Goli, E. B. Tirkolaee and N. S. Aydin, Fuzzy integrated cell formation and production scheduling considering automated guided vehicles and human factors, IEEE Transactions on Fuzzy Systems, (2021). doi: 10.1109/TFUZZ.2021.3053838. 
[6] 
A. Goli and M. Alinaghian, A new mathematical model for production and delivery scheduling problem with common cycle in a supply chain with openshop system, International Journal of Manufacturing Technology and Management, 34 (2020), 174187. doi: 10.1504/IJMTM.2020.10027948. 
[7] 
K. L. Hui, P. F. Ke, Y. X. Yao and W. T. Yue, Bilateral liabilitybased contracts in information security outsourcing, Information Systems Research, 30 (2019), 411429. doi: 10.1287/isre.2018.0806. 
[8] 
H. Huang and M. H. Hu, Contract design for IT outsourcing under asymmetric information, Chinese Journal of Management Science, (2020). 
[9] 
H. Huang, L. M. Liu, G. Parker, Y. Tan and H. Y. Xu, Multiattribute procurement auctions in the presence of satisfaction risk, Production and Operations Management, 28 (2019), 12061221. doi: 10.1111/poms.12979. 
[10] 
T. Jain, J. Hazra and T. C. E. Cheng, IT outsourcing and vendor cost improvement strategies under asymmetric information, Decision Sciences, (2020). doi: 10.1111/deci.12446. 
[11] 
K. Li, X. Zhang, Y. T. Leung and S. L. Yang, Parallel machine scheduling problems in green manufacturing industry, Journal of Manufacturing Systems, 38 (2016), 98106. doi: 10.1016/j.jmsy.2015.11.006. 
[12] 
G. Li, M. K. Lim and Z. Wang, Stakeholders, green manufacturing, and practice performance: Empirical evidence from Chinese fashion businesses, Annals of Operations Research, 290 (2020), 961982. doi: 10.1007/s10479019031577. 
[13] 
H. M. Liu, X. Y. Zhang and M. Y. Hu, Gametheorybased analysis of Energy Performance Contracting for building retrofits, Journal of Cleaner Production, 231 (2019), 10891099. 
[14] 
C. Liu, W. Chen and J. Mu, Retailer's multitier green procurement contract in the presence of suppliers' reference point effect, Production and Operations Management, 131 (2019), 242258. doi: 10.1016/j.cie.2019.03.013. 
[15]  D. Li and L. B. Zhu, Guidelines for Cleaner Production in Industrial Enterprises, Science Press, Beijing, 2019. 
[16] 
R. Lotfi, G. W. Weber, S. M. Sajadifar and N. Mardani, Interdependent demand in the twoperiod newsvendor problem, Journal of Industrial and Management Optimization, 16 (2016), 117140. doi: 10.3934/jimo.2018143. 
[17] 
R. Lotfi, Z. Yadegari, S. H. Hosseini, A. H. Khameneh and G. W. Weber, A robust timecostqualityenergyenvironment tradeoff with resourceconstrained in project management: A case study for a bridge construction project, Journal of Industrial and Management Optimization, 13 (2020), 122. 
[18] 
R. Lotfi, Y. Z. Mehrjerdi, M. S. Pishvaee, A. Sadegheih and G. W. Weber, A robust optimization model for sustainable and resilient closedloop supply chain network design considering conditional value at risk, Numer. Algebra Control Optim., 11 (2021), 221253. doi: 10.3934/naco.2020023. 
[19] 
R. Lotfi, Y. Z. Mehrjerdi and N. Mardani, A multiobjective and multiproduct advertising billboard location model with attraction factor mathematical modeling and solutions, International Journal of Applied Logistics, 7 (2017), 6487. doi: 10.4018/IJAL.2017010104. 
[20] 
J. J. Laffont and J. Tirole, A Theory of Incentives in Procurement and Regulation, MIT Press Books, 1993. 
[21] 
V. MartínezdeAlbéniz and D. SimchiLevi, A portfolio approach to procurement contracts, Production and Operations Management, 14 (2010), 90114. 
[22] 
A. Maccormack and A. Mishra, Managing the performance tradeoffs from partner integration: Implications of contract choice in R & D Projects, Production and Operations Management, 24 (2015), 15521569. doi: 10.1111/poms.12374. 
[23] 
T. Paksoy and E. Ozceylan, Environmentally conscious optimization of supply chain networks, Journal of the Operational Research Society, 65 (2014), 855872. doi: 10.1057/jors.2012.95. 
[24] 
T. Paksoy, N. Y. Pehlivan and E. Ozceylan, Fuzzy multiobjective optimization of a green supply chain network with risk management that includes environmental hazards, Human and Ecological Risk Assessment, 18 (2012), 11201151. doi: 10.1080/10807039.2012.707940. 
[25] 
Q. Qiu, L. Cui, J. Y. Shen and Y. Li, Optimal maintenance policy considering maintenance errors for systems operating under performancebased contracts, Computers and Industrial Engineering, 112 (2017), 147155. doi: 10.1016/j.cie.2017.08.025. 
[26] 
W. H. Tsai, H. C. Chen, J. Y. Liu, S. P. Chen and Y. S. Shen, Using activitybased costing to evaluate capital investments for green manufacturing systems, International Journal of Production Research, 49 (2011), 72757292. doi: 10.1080/00207543.2010.537389. 
[27] 
E. B. Tirkolaee and N. S. Aydn, A sustainable medical waste collection and transportation model for pandemics, Waste Management and Research, (2021). doi: 10.1177/0734242X211000437. 
[28] 
E. B. Tirkolaee, P. Abbasian and G. W. Weber, Sustainable fuzzy multitrip locationrouting problem for medical waste management during the COVID19 outbreak, Science of The Total Environment, 10 (2020), 143607. 
[29] 
C. Wang, G. Schmidt and V. D. R. Bo, Stagegate contracts to screen agents with inside information, Decision Sciences, 49 (2018), 11561186. doi: 10.1111/deci.12308. 
Reference  Objective  Solution  Conclusion  
Deif [4]  Design and improve green manufacturing systems  A new model  A comprehensive qualitative answer to the question.  
Tsai et al. [26]  Assist the justification of capital investments for green manufacturing systems (GMSs)  Activitybased costing  Provide insight into the value of capital investments for a GMS based ABC  
Chuang et al. [2]  Evaluate the performance of a green manufacturing system  A new model  The threelayer assessment model is practical  
Li et al. [11]  Scheduling problems that arise in green manufacturing companies  Efficient heuristics  Find a schedule that minimizes the total completion time  
Li et al. [12]  Enhance environmental awareness and green manufacturing practices  Questionnaire investigation  The importance of corporate stakeholders should be promoted  
Lotfi et al. [16,17,18,19]  Considers a closedloop supply chain by taking into account sustainability, resilience, robustness, and risk aversion.  Two stage mixedinteger linear programming model  The robust counterpart provides a better estimation of related factors.  
Goli et al. [5,6]  Design a flexibleresponsive manufacturing system with automatic material handling systems.  A fuzzy mixed integer linear programming model  Proposed algorithms have a high performance compared to CPLEX and other two wellknown algorithms  
Paksoy et al. [23,24]  The optimization of supply chain structures considering both economic and environmental performances  An integer nonlinear programming model  Help decision makers find the optimal solution  
Tirkolaee et al. [27,28]  Try to explain and formulate the sustainable medical waste management problem for pandemics  Proposed a biobjective MILP model  Discuss the practical implications of the results  
Cao et al. [3]  Solve asymmetry information in outsourcing of production  Contract theory  Design a quality incentive contract  
Wang et al. [29]  Solve asymmetry information in outsourcing of R & D  Stagegate contracts  The stagegate contract can help offset the information asymmetry  
Hui et al. [7]  Solve asymmetry information in outsourcing of managed security services  Bilateral liabilitybased contracts  Bilateral liabilitybased contracts can work in the real world  
Huang et al. [8]  Contract design problem of IT service outsourcing  Contract theory  The optimal contract is designed to regulate IT suppliers effectively  
This research  Contract design problem of green transformation of manufacturing system outsourcing  Outsourcing contract design  Design a set of contract menus to resolve asymmetric information 
Reference  Objective  Solution  Conclusion  
Deif [4]  Design and improve green manufacturing systems  A new model  A comprehensive qualitative answer to the question.  
Tsai et al. [26]  Assist the justification of capital investments for green manufacturing systems (GMSs)  Activitybased costing  Provide insight into the value of capital investments for a GMS based ABC  
Chuang et al. [2]  Evaluate the performance of a green manufacturing system  A new model  The threelayer assessment model is practical  
Li et al. [11]  Scheduling problems that arise in green manufacturing companies  Efficient heuristics  Find a schedule that minimizes the total completion time  
Li et al. [12]  Enhance environmental awareness and green manufacturing practices  Questionnaire investigation  The importance of corporate stakeholders should be promoted  
Lotfi et al. [16,17,18,19]  Considers a closedloop supply chain by taking into account sustainability, resilience, robustness, and risk aversion.  Two stage mixedinteger linear programming model  The robust counterpart provides a better estimation of related factors.  
Goli et al. [5,6]  Design a flexibleresponsive manufacturing system with automatic material handling systems.  A fuzzy mixed integer linear programming model  Proposed algorithms have a high performance compared to CPLEX and other two wellknown algorithms  
Paksoy et al. [23,24]  The optimization of supply chain structures considering both economic and environmental performances  An integer nonlinear programming model  Help decision makers find the optimal solution  
Tirkolaee et al. [27,28]  Try to explain and formulate the sustainable medical waste management problem for pandemics  Proposed a biobjective MILP model  Discuss the practical implications of the results  
Cao et al. [3]  Solve asymmetry information in outsourcing of production  Contract theory  Design a quality incentive contract  
Wang et al. [29]  Solve asymmetry information in outsourcing of R & D  Stagegate contracts  The stagegate contract can help offset the information asymmetry  
Hui et al. [7]  Solve asymmetry information in outsourcing of managed security services  Bilateral liabilitybased contracts  Bilateral liabilitybased contracts can work in the real world  
Huang et al. [8]  Contract design problem of IT service outsourcing  Contract theory  The optimal contract is designed to regulate IT suppliers effectively  
This research  Contract design problem of green transformation of manufacturing system outsourcing  Outsourcing contract design  Design a set of contract menus to resolve asymmetric information 
Symbols  Definition 
Decision variables  
Fixed remuneration provided by the employer to the contractor  
Unit reward of ECER exceeding the benchmark after system transformation  
Parameters  
Capability parameters of the contractor's transformation system  
The types of contractors: high type (with higher transformation capacity 

The probability that the contractor is high  
Contractor's efforts to transform the system  
Number of ECERs achieved after system transformation  
The benchmark number of ECERs required by the employer according to relevant government or industry standards  
Failure number in warranty period after system transformation  
The maximum number of failures in the warranty period after the completion of system transformation  
Total cost of the contractor's modification of the system  
The single maintenance cost  
Value coefficient of ECER quantity to the employer  
Sensitivity coefficient of the employer to the number of failures in the warranty period 
Symbols  Definition 
Decision variables  
Fixed remuneration provided by the employer to the contractor  
Unit reward of ECER exceeding the benchmark after system transformation  
Parameters  
Capability parameters of the contractor's transformation system  
The types of contractors: high type (with higher transformation capacity 

The probability that the contractor is high  
Contractor's efforts to transform the system  
Number of ECERs achieved after system transformation  
The benchmark number of ECERs required by the employer according to relevant government or industry standards  
Failure number in warranty period after system transformation  
The maximum number of failures in the warranty period after the completion of system transformation  
Total cost of the contractor's modification of the system  
The single maintenance cost  
Value coefficient of ECER quantity to the employer  
Sensitivity coefficient of the employer to the number of failures in the warranty period 
Situations  High type  Low type  
Symmetric information  
Asymmetric information  
^{1} Among them, $f_{L1}^{A{\rm{*}}}{\rm{ = }}0$, $f_{L2}^{A{\rm{*}}}{\rm{ = }}\frac{{\left({1  \rho } \right){\beta _L}\left({u{\rm{ + }}v} \right)  \rho \left({{\beta _H}{\rm{ + }}w{\beta _H}  {\beta _L}  w{\beta _L}} \right)}}{{\left({1  \rho } \right){\beta _L}{\rm{ + }}\rho {\beta _H}  \rho {\beta _L}}}$, $x = \frac{{\rho {\beta _L}\left({{\beta _H}{\rm{ + }}w{\beta _H}  {\beta _L}  w{\beta _L}} \right)}}{{1  \rho }}$ 
Situations  High type  Low type  
Symmetric information  
Asymmetric information  
^{1} Among them, $f_{L1}^{A{\rm{*}}}{\rm{ = }}0$, $f_{L2}^{A{\rm{*}}}{\rm{ = }}\frac{{\left({1  \rho } \right){\beta _L}\left({u{\rm{ + }}v} \right)  \rho \left({{\beta _H}{\rm{ + }}w{\beta _H}  {\beta _L}  w{\beta _L}} \right)}}{{\left({1  \rho } \right){\beta _L}{\rm{ + }}\rho {\beta _H}  \rho {\beta _L}}}$, $x = \frac{{\rho {\beta _L}\left({{\beta _H}{\rm{ + }}w{\beta _H}  {\beta _L}  w{\beta _L}} \right)}}{{1  \rho }}$ 
Circumstances  Strategies 
The information of contractor's transformation capability is symmetric  Make the optimal outsourcing contract according to the type of contractor 
The information of contractor's transformation capability is asymmetric  Make a set of optimal outsourcing contract menu for contractors to choose from 
Circumstances  Strategies 
The information of contractor's transformation capability is symmetric  Make the optimal outsourcing contract according to the type of contractor 
The information of contractor's transformation capability is asymmetric  Make a set of optimal outsourcing contract menu for contractors to choose from 
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