# American Institute of Mathematical Sciences

January  2021, 17(1): 409-426. doi: 10.3934/jimo.2019118

## Incentives for production capacity improvement in construction supplier development

 School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

* Corresponding author: Wei Zeng

Received  February 2019 Revised  April 2019 Published  January 2021 Early access  September 2019

The purpose of this paper is to investigate the supplier development (SD) in construction industry. As the supplier's production capacity cannot meet the construction requirements, the owner wants to take incentives to encourage the supplier to improve its production capacity. A principal-agent model and a Stackelberg game model are proposed to study the impact of owner's incentives including cost sharing and purchase price incentive on the production capacity improvement in SD. Furthermore, we give a sensitivity analysis of the influence of supplier's internal and external parameters, i.e., purchase quantity, cost structure, market price and market demand, etc., on the production capacity improvement. The findings of this study can help the owner to make a better decision on the incentive mechanisms for SD, resulting in both better SD practices and a win-win situation.

Citation: Yanjun He, Wei Zeng, Minghui Yu, Hongtao Zhou, Delie Ming. Incentives for production capacity improvement in construction supplier development. Journal of Industrial and Management Optimization, 2021, 17 (1) : 409-426. doi: 10.3934/jimo.2019118
##### References:
 [1] W. E. Back, D. Grau and G. Mejia-Aguilar, Effectiveness evaluation of contract incentives on project performance, Int. J. Constr. Educ. Res., 9 (2013), 288-306.  doi: 10.1080/15578771.2012.729551. [2] D. Bower, G. Ashby, K. Gerald and W. Smyk, Incentive mechanisms for project success, J. Manag. Eng., 18 (2002), 37-43.  doi: 10.1061/(ASCE)0742-597X(2002)18:1(37). [3] G. P. Cachon, Supply chain coordination with contracts, Handbooks Oper. Res. Manag. Sci., 11 (2003), 227-339.  doi: 10.1016/S0927-0507(03)11006-7. [4] G. P. Cachon and M. A. Lariviere, Supply chain coordination with revenue-sharing contracts: Strengths and limitations, Manage. Sci., 51 (2003), 30-44.  doi: 10.1287/mnsc.1040.0215. [5] R. Chavhan, K. Mahajan and J. Sarang, Supplier developmet: Theories and practices, IOSR J. Mech. Civ. Eng., 3 (2012), 37-51.  doi: 10.9790/1684-0333751. [6] J. Chen, The impact of sharing customer returns information in a supply chain with and without a buyback policy, IEur. J. Oper. Res., 213 (2011), 478-488.  doi: 10.1016/j.ejor.2011.03.027. [7] A. De Toni and G. Nassimbeni, Just-in-time purchasing: An empirical study of operational practices, supplier development and performance, Omega, 28 (2000), 631-651.  doi: 10.1016/S0305-0483(00)00016-5. [8] D. Duffie and J. Pan, An overview of value at risk, The Journal of Derivatives Spring, 4 (1997), 7-49.  doi: 10.3905/jod.1997.407971. [9] J. H. Dyer and N. W. Hatch, Relation-specific capabilities and barriers to knowledge transfers: Creating advantage through network relationships, Strateg. Manag. J., 27 (2006), 701-719.  doi: 10.1002/smj.543. [10] D. Fudenberg and J. Tirole, Game Theory, MIT Press, Cambridge, MA, 1991. [11] P. W. T. Ghijsen, J. Semeijn and S. Ernstson, Supplier satisfaction and commitment: The role of influence strategies and supplier development, J. Purch. Supply Manag., 16 (2010), 17-26.  doi: 10.1016/j.pursup.2009.06.002. [12] M. I. Hohn, Relational supply contracts: Optimal concessions in return policies for continuous quality improvements, Lect. Notes Econ. Math. Syst., 629 (2010), 1-118. [13] X. M. Huang, S.-M. Choi and W.-K.Ching, On improving incentive in a supply chain: Wholesale price contract vs quantity dependent contract, The 40th International Conference on Computers & Indutrial Engineering, (2010). doi: 10.1109/ICCIE.2010.5668333. [14] D. R. Krause and L. M. Ellram, Critical elements of supplier development: The buying-firm perspective, European Journal of Purchasing and Supply Management, 3 (1997), 21-31. [15] D. R. Krause and L. M. Ellram, Success factors in supplier development, Int. J. Phys. Distrib. Logist. Manag., 27 (1997), 39-52.  doi: 10.1108/09600039710162277. [16] D. R. Krause, R. B. Handfield and B. B. Tyler, The relationships between supplier development, commitment, social capital accumulation and performance improvement, Journal of operations management, 25 (2007), 528-545. [17] D. R. Krause, T. V. Scannell and R. J. Calantone, A structural analysis of the effectiveness of buying firms' strategies to improve supplier performance, Decis. Sci., 31 (2000), 33-55.  doi: 10.1111/j.1540-5915.2000.tb00923.x. [18] C. V. S. Kumar and S. Routroy, Modeling supplier development barriers in indian manufacturing industry, Asia Pacific Manag. Rev., 23 (2018), 235-250.  doi: 10.1016/j.apmrv.2017.11.002. [19] J.-J. Laffont and D. Martimort, The Theory of Incentives: The Principal-Agent Model, Princeton and Oxford: Princeton UP[J], 2002. doi: 10.2307/j.ctv7h0rwr. [20] H. L. Lee and M. J. Rosenblatt, A generalized quantity discount pricing model to increase supplier's profits, Manage. Sci., 32 (1986), 1177-1185.  doi: 10.3166/jesa.37.363-390. [21] X. Meng and B. Gallagher, The impact of incentive mechanisms on project performance, International Journal of Project Management, 30 (2012), 352-362. [22] K. J. Mizgier, J. M. Pasia and S. Talluri, Multiobjective capital allocation for supplier development under risk, Int. J. Prod. Res., 55 (2017), 5243-5258.  doi: 10.1080/00207543.2017.1302618. [23] R. M. Monczka and J. P. Morgan, Supply base strategies to maximize supplier performance, Int. J. Phys. Distrib. Logist. Manag., 23 (1996), 42-54. [24] H. Nagati and C. Rebolledo, Supplier development efforts: The suppliers' point of view, Ind. Mark. Manag., 42 (2013), 180-188.  doi: 10.1016/j.indmarman.2012.12.006. [25] R. G. Newman and K. A. Rhee, A case study of NUMMI and its suppliers, Journal of Purchasing & Materials Management, 26 (1990), 15-21. [26] A. Noorizadeh, K. Rashidi and A. Peltokorpi, Categorizing suppliers for development investments in construction: Application of DEA and RFM concept, Constr. Manag. Econ., 36 (2018), 487-506.  doi: 10.1080/01446193.2017.1416151. [27] C. Prahinski and W. C. Benton, Supplier evaluations: Communication strategies to improve supplier performance, Journal of Operations Management, 22 (2004), 39-62. [28] M. Proch, K. Worthmann and J. Schlüchtermann, A negotiation-based algorithm to coordinate supplier development in decentralized supply chains, Eur. J. Oper. Res., 256 (2017), 412-429.  doi: 10.1016/j.ejor.2016.06.029. [29] P. A. Rubin and W. C. Benton, A generalized framework for quantity discount pricing schedules, Decis. Sci., 34 (2003), 173-188.  doi: 10.1111/1540-5915.02437. [30] S. Sarykalin, G. Serraino and S. Uryasev, Value-at-risk vs. conditional value-at-risk in risk management and optimization, State-of-the-Art Decision-Making Tools in the InformationIntensive Age. Informs, (2008), 270–294. [31] H. Shin and T. I. Tunca, Do firms invest in forecasting efficiently? The effect of competition on demand forecast investments and supply chain coordination, Oper. Res., 58 (2010), 1592-1610.  doi: 10.1287/opre.1100.0876. [32] E. Sucky and S. M. Durst, Supplier development: Current status of empirical research, Int. J. Procure. Manag., 6 (2013), 92-127.  doi: 10.1504/IJPM.2013.050612. [33] M. Suprapto, H. L. M. Bakker and H. G. Mooi, How do contract types and incentives matter to project performance?, International Journal of Project Management, 34 (2016), 1071–1087. [34] S. Talluri, R. Narasimhan and W. M. Chung, Manufacturer cooperation in supplier development under risk, European Journal of Operational Research, 207 (2010), 165-173.  doi: 10.1016/j.ejor.2010.03.041. [35] A. A. Tsay, The quantity flexibility contract and supplier-customer incentives, Manage. Sci., 45 (1999), 1289-1462.  doi: 10.1287/mnsc.45.10.1339. [36] S. M. Wagner, Indirect and direct supplier development: Performance implications of individual and combined effects, IEEE Trans. Eng. Manag., 57 (2010), 536-546.  doi: 10.1109/TEM.2009.2013839. [37] S. M. Wagner, Supplier development practices: An exploratory study, Eur. J. Mark., 40 (2006), 554-571.  doi: 10.1108/03090560610657831. [38] Z. K. Weng, Coordinating order quantities between the manufacturer and the buyer: A generalized newsvendor model, Eur. J. Oper. Res., 156 (2004), 148-161.  doi: 10.1016/S0377-2217(03)00003-1. [39] Y. Y. Xu and A. Bisi, Wholesale-price contracts with postponed and fixed retail prices, Oper. Res. Lett., 40 (2012), 250-257.  doi: 10.1016/j.orl.2012.04.001. [40] W. Zeng, H. W. Wang, H. Li, H. T. Zhou, P. Wu and Y. Le, Incentive mechanisms for supplier development in mega construction projects, IEEE Transactions on Engineering Management, 66 (2019), 252-265.  doi: 10.1109/TEM.2018.2808169.

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##### References:
 [1] W. E. Back, D. Grau and G. Mejia-Aguilar, Effectiveness evaluation of contract incentives on project performance, Int. J. Constr. Educ. Res., 9 (2013), 288-306.  doi: 10.1080/15578771.2012.729551. [2] D. Bower, G. Ashby, K. Gerald and W. Smyk, Incentive mechanisms for project success, J. Manag. Eng., 18 (2002), 37-43.  doi: 10.1061/(ASCE)0742-597X(2002)18:1(37). [3] G. P. Cachon, Supply chain coordination with contracts, Handbooks Oper. Res. Manag. Sci., 11 (2003), 227-339.  doi: 10.1016/S0927-0507(03)11006-7. [4] G. P. Cachon and M. A. Lariviere, Supply chain coordination with revenue-sharing contracts: Strengths and limitations, Manage. Sci., 51 (2003), 30-44.  doi: 10.1287/mnsc.1040.0215. [5] R. Chavhan, K. Mahajan and J. Sarang, Supplier developmet: Theories and practices, IOSR J. Mech. Civ. Eng., 3 (2012), 37-51.  doi: 10.9790/1684-0333751. [6] J. Chen, The impact of sharing customer returns information in a supply chain with and without a buyback policy, IEur. J. Oper. Res., 213 (2011), 478-488.  doi: 10.1016/j.ejor.2011.03.027. [7] A. De Toni and G. Nassimbeni, Just-in-time purchasing: An empirical study of operational practices, supplier development and performance, Omega, 28 (2000), 631-651.  doi: 10.1016/S0305-0483(00)00016-5. [8] D. Duffie and J. Pan, An overview of value at risk, The Journal of Derivatives Spring, 4 (1997), 7-49.  doi: 10.3905/jod.1997.407971. [9] J. H. Dyer and N. W. Hatch, Relation-specific capabilities and barriers to knowledge transfers: Creating advantage through network relationships, Strateg. Manag. J., 27 (2006), 701-719.  doi: 10.1002/smj.543. [10] D. Fudenberg and J. Tirole, Game Theory, MIT Press, Cambridge, MA, 1991. [11] P. W. T. Ghijsen, J. Semeijn and S. Ernstson, Supplier satisfaction and commitment: The role of influence strategies and supplier development, J. Purch. Supply Manag., 16 (2010), 17-26.  doi: 10.1016/j.pursup.2009.06.002. [12] M. I. Hohn, Relational supply contracts: Optimal concessions in return policies for continuous quality improvements, Lect. Notes Econ. Math. Syst., 629 (2010), 1-118. [13] X. M. Huang, S.-M. Choi and W.-K.Ching, On improving incentive in a supply chain: Wholesale price contract vs quantity dependent contract, The 40th International Conference on Computers & Indutrial Engineering, (2010). doi: 10.1109/ICCIE.2010.5668333. [14] D. R. Krause and L. M. Ellram, Critical elements of supplier development: The buying-firm perspective, European Journal of Purchasing and Supply Management, 3 (1997), 21-31. [15] D. R. Krause and L. M. Ellram, Success factors in supplier development, Int. J. Phys. Distrib. Logist. Manag., 27 (1997), 39-52.  doi: 10.1108/09600039710162277. [16] D. R. Krause, R. B. Handfield and B. B. Tyler, The relationships between supplier development, commitment, social capital accumulation and performance improvement, Journal of operations management, 25 (2007), 528-545. [17] D. R. Krause, T. V. Scannell and R. J. Calantone, A structural analysis of the effectiveness of buying firms' strategies to improve supplier performance, Decis. Sci., 31 (2000), 33-55.  doi: 10.1111/j.1540-5915.2000.tb00923.x. [18] C. V. S. Kumar and S. Routroy, Modeling supplier development barriers in indian manufacturing industry, Asia Pacific Manag. Rev., 23 (2018), 235-250.  doi: 10.1016/j.apmrv.2017.11.002. [19] J.-J. Laffont and D. Martimort, The Theory of Incentives: The Principal-Agent Model, Princeton and Oxford: Princeton UP[J], 2002. doi: 10.2307/j.ctv7h0rwr. [20] H. L. Lee and M. J. Rosenblatt, A generalized quantity discount pricing model to increase supplier's profits, Manage. Sci., 32 (1986), 1177-1185.  doi: 10.3166/jesa.37.363-390. [21] X. Meng and B. Gallagher, The impact of incentive mechanisms on project performance, International Journal of Project Management, 30 (2012), 352-362. [22] K. J. Mizgier, J. M. Pasia and S. Talluri, Multiobjective capital allocation for supplier development under risk, Int. J. Prod. Res., 55 (2017), 5243-5258.  doi: 10.1080/00207543.2017.1302618. [23] R. M. Monczka and J. P. Morgan, Supply base strategies to maximize supplier performance, Int. J. Phys. Distrib. Logist. Manag., 23 (1996), 42-54. [24] H. Nagati and C. Rebolledo, Supplier development efforts: The suppliers' point of view, Ind. Mark. Manag., 42 (2013), 180-188.  doi: 10.1016/j.indmarman.2012.12.006. [25] R. G. Newman and K. A. Rhee, A case study of NUMMI and its suppliers, Journal of Purchasing & Materials Management, 26 (1990), 15-21. [26] A. Noorizadeh, K. Rashidi and A. Peltokorpi, Categorizing suppliers for development investments in construction: Application of DEA and RFM concept, Constr. Manag. Econ., 36 (2018), 487-506.  doi: 10.1080/01446193.2017.1416151. [27] C. Prahinski and W. C. Benton, Supplier evaluations: Communication strategies to improve supplier performance, Journal of Operations Management, 22 (2004), 39-62. [28] M. Proch, K. Worthmann and J. Schlüchtermann, A negotiation-based algorithm to coordinate supplier development in decentralized supply chains, Eur. J. Oper. Res., 256 (2017), 412-429.  doi: 10.1016/j.ejor.2016.06.029. [29] P. A. Rubin and W. C. Benton, A generalized framework for quantity discount pricing schedules, Decis. Sci., 34 (2003), 173-188.  doi: 10.1111/1540-5915.02437. [30] S. Sarykalin, G. Serraino and S. Uryasev, Value-at-risk vs. conditional value-at-risk in risk management and optimization, State-of-the-Art Decision-Making Tools in the InformationIntensive Age. Informs, (2008), 270–294. [31] H. Shin and T. I. Tunca, Do firms invest in forecasting efficiently? The effect of competition on demand forecast investments and supply chain coordination, Oper. Res., 58 (2010), 1592-1610.  doi: 10.1287/opre.1100.0876. [32] E. Sucky and S. M. Durst, Supplier development: Current status of empirical research, Int. J. Procure. Manag., 6 (2013), 92-127.  doi: 10.1504/IJPM.2013.050612. [33] M. Suprapto, H. L. M. Bakker and H. G. Mooi, How do contract types and incentives matter to project performance?, International Journal of Project Management, 34 (2016), 1071–1087. [34] S. Talluri, R. Narasimhan and W. M. Chung, Manufacturer cooperation in supplier development under risk, European Journal of Operational Research, 207 (2010), 165-173.  doi: 10.1016/j.ejor.2010.03.041. [35] A. A. Tsay, The quantity flexibility contract and supplier-customer incentives, Manage. Sci., 45 (1999), 1289-1462.  doi: 10.1287/mnsc.45.10.1339. [36] S. M. Wagner, Indirect and direct supplier development: Performance implications of individual and combined effects, IEEE Trans. Eng. Manag., 57 (2010), 536-546.  doi: 10.1109/TEM.2009.2013839. [37] S. M. Wagner, Supplier development practices: An exploratory study, Eur. J. Mark., 40 (2006), 554-571.  doi: 10.1108/03090560610657831. [38] Z. K. Weng, Coordinating order quantities between the manufacturer and the buyer: A generalized newsvendor model, Eur. J. Oper. Res., 156 (2004), 148-161.  doi: 10.1016/S0377-2217(03)00003-1. [39] Y. Y. Xu and A. Bisi, Wholesale-price contracts with postponed and fixed retail prices, Oper. Res. Lett., 40 (2012), 250-257.  doi: 10.1016/j.orl.2012.04.001. [40] W. Zeng, H. W. Wang, H. Li, H. T. Zhou, P. Wu and Y. Le, Incentive mechanisms for supplier development in mega construction projects, IEEE Transactions on Engineering Management, 66 (2019), 252-265.  doi: 10.1109/TEM.2018.2808169.
The genetic algorithm flowchart of the principal-agent model
The evolution process of the principal-agent model
The evolution process of the Stackelberg game model
Overview of differences between reactive/strategic and direct/indirect supplier development
 Characteristics Incentive mechanism Reactive Correct of the laggard supplier's deficiency and achieve short-term improvements; Problem-driven or supplier self-select through performance or capability deficiency [15]. Limited, minimal and specific investments or negative feedback to achieve short-term improvement and competitiveness [14]. Proactive Achieve continuous improvement of supply base, long-term competitive advantages; Market-oriented [14]. Significant levels of resource commitment and investment to pursuit continuous improvement and long-term competitiveness [14]. Direct Deep corporation with the supplier and commits financial and/or human capital and plays an active role; Collaborative approach based on frequent manufacturer-supplier exchanges, resulting in bilateral deployment of relationship-specific investments [15], [23], [28]. Support in equipment or capital investments; Advice on organizational procedures and training of technical staff training, furnishing temporary on-site support to enhance further interaction [23], [36]. Indirect Limited, minimal and specific investments; focus on supplier identification, targets (goals) setting, measurement of goal attainment, as well as feedback of goal attainment to suppliers [15], [36]. Evaluating the suppliers' operations, setting performance goals, providing performance feedback, instilling competitive pressure, promising future business based on goal attainment or recognizing the suppliers' progress by designating them as preferred suppliers [15], [36].
 Characteristics Incentive mechanism Reactive Correct of the laggard supplier's deficiency and achieve short-term improvements; Problem-driven or supplier self-select through performance or capability deficiency [15]. Limited, minimal and specific investments or negative feedback to achieve short-term improvement and competitiveness [14]. Proactive Achieve continuous improvement of supply base, long-term competitive advantages; Market-oriented [14]. Significant levels of resource commitment and investment to pursuit continuous improvement and long-term competitiveness [14]. Direct Deep corporation with the supplier and commits financial and/or human capital and plays an active role; Collaborative approach based on frequent manufacturer-supplier exchanges, resulting in bilateral deployment of relationship-specific investments [15], [23], [28]. Support in equipment or capital investments; Advice on organizational procedures and training of technical staff training, furnishing temporary on-site support to enhance further interaction [23], [36]. Indirect Limited, minimal and specific investments; focus on supplier identification, targets (goals) setting, measurement of goal attainment, as well as feedback of goal attainment to suppliers [15], [36]. Evaluating the suppliers' operations, setting performance goals, providing performance feedback, instilling competitive pressure, promising future business based on goal attainment or recognizing the suppliers' progress by designating them as preferred suppliers [15], [36].
Overview of differences between reactive/strategic and direct/indirect supplier development
 Symbol Definition $q_{0}$ The production capacity of the supplier before the SD program $q^{N}$ The production capacity when not participating the SD program $q$ The production capacity after SD program $r$ The production cost of per unit $p$ The market price $k$ The cost per unit of production capacity improvement $Q$ Purchase quantity $h$ Overcapacity cost per unit $\lambda$ Purchase price incentive $\rho$ The discount rate of future market profits $\theta$ Cost sharing ratio $\omega$ Owner's utility parameter for the production capacity improvement $\delta$ The supplier's risk aversion parameter $D$ The demand in future market $\Pi_{s}^{N}$ The supplier's total profits when not participating the SD program $\Pi_{0}$ The supplier's reservation utility of future market $\Pi_{s}$ The supplier's total profits $\Pi_{sc}$ The supplier's profits of current project $\Pi_{sf}$ The supplier's profits of future market $\Pi_{b}$ The owner's profits
 Symbol Definition $q_{0}$ The production capacity of the supplier before the SD program $q^{N}$ The production capacity when not participating the SD program $q$ The production capacity after SD program $r$ The production cost of per unit $p$ The market price $k$ The cost per unit of production capacity improvement $Q$ Purchase quantity $h$ Overcapacity cost per unit $\lambda$ Purchase price incentive $\rho$ The discount rate of future market profits $\theta$ Cost sharing ratio $\omega$ Owner's utility parameter for the production capacity improvement $\delta$ The supplier's risk aversion parameter $D$ The demand in future market $\Pi_{s}^{N}$ The supplier's total profits when not participating the SD program $\Pi_{0}$ The supplier's reservation utility of future market $\Pi_{s}$ The supplier's total profits $\Pi_{sc}$ The supplier's profits of current project $\Pi_{sf}$ The supplier's profits of future market $\Pi_{b}$ The owner's profits
Summary of the sensitivity analysis in the Stackelberg game Model
 Changes in the parameter values Optimal production capacity $q^\ast=q_1$ Optimal production capacity $q^\ast=q_2$ Optimal production capacity $q^\ast=q_3$ 1.Increase in parameters related to the current project 1.1 The owner's utility parameter for the production capacity improvement $\omega$ $-$ $-$ $-$ 1.2 Purchase quantity $Q$ $-$ $-$ $\uparrow$ 2. Increase of supplier's parameters 2.1 Production cost per unit $r$ ↓ ↓ $-$ 2.2 The cost per unit of production capacity improvement $k$ ↓ $-$ $-$ 2.3 Overcapacity cost per unit $h$ $↓$ $↓$ $-$ 2.4 The supplieros risk aversion parameter $\delta$ $-$ $\uparrow$ $-$ 2.5 The supplieros reservation utility of future market $\mathrm{\Pi}_0$ $-$ $↓$ $-$ 3. Increase in market condition parameters 3.1 The market price $p$ $\uparrow$ $\uparrow$ $-$ 3.2 The discount rate of future market profits $\rho$ $\uparrow$ $-$ $-$ 4. Increase of incentive parameters 4.1 Cost sharing ratio $\theta$ $\uparrow$ $-$ $-$ 4.2 Purchase price incentive $\lambda$ $-$ $-$ $-$
 Changes in the parameter values Optimal production capacity $q^\ast=q_1$ Optimal production capacity $q^\ast=q_2$ Optimal production capacity $q^\ast=q_3$ 1.Increase in parameters related to the current project 1.1 The owner's utility parameter for the production capacity improvement $\omega$ $-$ $-$ $-$ 1.2 Purchase quantity $Q$ $-$ $-$ $\uparrow$ 2. Increase of supplier's parameters 2.1 Production cost per unit $r$ ↓ ↓ $-$ 2.2 The cost per unit of production capacity improvement $k$ ↓ $-$ $-$ 2.3 Overcapacity cost per unit $h$ $↓$ $↓$ $-$ 2.4 The supplieros risk aversion parameter $\delta$ $-$ $\uparrow$ $-$ 2.5 The supplieros reservation utility of future market $\mathrm{\Pi}_0$ $-$ $↓$ $-$ 3. Increase in market condition parameters 3.1 The market price $p$ $\uparrow$ $\uparrow$ $-$ 3.2 The discount rate of future market profits $\rho$ $\uparrow$ $-$ $-$ 4. Increase of incentive parameters 4.1 Cost sharing ratio $\theta$ $\uparrow$ $-$ $-$ 4.2 Purchase price incentive $\lambda$ $-$ $-$ $-$
Experiment Parameters
 $q_0$ p r k Q $\rho$ $\omega$ h $\Pi_0$ $\delta$ 30 100 40 20 60 0.9 20 10 300 0.1
 $q_0$ p r k Q $\rho$ $\omega$ h $\Pi_0$ $\delta$ 30 100 40 20 60 0.9 20 10 300 0.1
Parametric Analysis Results
 $\Pi_b$ $\Pi_s$ q $\lambda$ $\theta$ Principal-agent model 3803501.6 3029.1 898.4 30 0.38 Stackelberg game model 1157932.3 35456 1000 0.0011 1
 $\Pi_b$ $\Pi_s$ q $\lambda$ $\theta$ Principal-agent model 3803501.6 3029.1 898.4 30 0.38 Stackelberg game model 1157932.3 35456 1000 0.0011 1
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