||A Two-Step Computation Strategy for Designing Decentralized Supply Chains with Fair Profit Allocation Plans Using Nash Cooperative Bargaining Model
||Department of Chemical Engineering
Fair profit allocation
Nash cooperative bargaining approach
Traditional supply-chain management methods often treated the given system as a whole, without considering the conflicting interests of its participants. Game theory was adopted in a number of prior studies to identify fair prices and throughputs of the intermediates so as to maintain sustainable operations. In particular, the mathematical frameworks of a series of fictitious systems have already been proposed in the literature. The proper designs of distributed processing systems were generated to facilitate implementation of a decentralized optimization strategy. In these supply chains, the supplier-produced intermediates were bought by consumers to manufacture the final products. However, when the total profit of a supply chain is maximized without constraints, the maximum total profit may not be divided and allocated to every actor fairly. This deficiency could lead to various negative impacts, including dissatisfaction of actors, instability of coalition, loss of markets, and reduction in revenue. For this reason, a cooperative game theory has already been applied to generate fair-profit allocation plans among the supplier(s) and consumer(s) so as to establish a long-term working relationship. The present work developed a two-step approach addresses this issue. Finding the maximum total profit of the whole chain is the primary task of the first step, while the Nash cooperative bargaining approach is adopted in the second step so as to distribute the total proﬁt among the actors fairly. Consequently, the corresponding intermediate prices and throughputs can also be estimated as well. Various case studies in fictitious systems and the petroleum supply chain are provided as examples to demonstrate the feasibility of the proposed approach. It can be observed from the optimization results of various case studies in fictitious systems and the petroleum supply chain that the goal to get the fair profit allocation plans can be achieved while still maintaining the maximum total profit of the whole chain.
Table of Contents IV
List of Figures VII
List of Tables IX
Chapter 1 1
1.1 Background 1
1.2 Literature Review 1
1.3 Research Objectives 4
1.4 Thesis Structure 4
Chapter 2 6
2.1 Incentive for More Studies 6
2.2 Existing Approach 7
2.2.1 Model Structure 7
2.2.2 Mathematical Model 8
2.2.3 Optimization Formulation 13
2.2.4 Example 1 14
2.3 Revenue Sharing Scheme (Yue and You, 2014) 17
2.4 Nash Cooperative Bargaining Method 18
2.5 The Proposed Solution Procedure 18
2.5.1 Step 1 18
2.5.2 Step 2 19
2.6 Simple Examples 19
2.6.1 Example 1: 1 Supplier, 1 Consumer and 1 Intermediate Product 19
2.6.2 Example 2: 1 Supplier, 2 Consumers and 2 Intermediate Products 21
2.6.3 Example 3: 1 Supplier, 2 Consumers and 1 Intermediate Product 23
Chapter 3 26
3.1 Model Structure 26
3.2 General Model Formulations 30
3.2.1 Model I – the separation process 30
3.2.2 Model II – the reaction-separation process 31
3.2.3 Model III – the storage process 34
3.2.4 Profit and cost models 34
3.3 Specific Unit Models 36
3.3.1 Atmospheric distillation (S) 36
3.3.2 LPG retailer (C1) 37
3.3.3 Reformer (C2) 38
3.3.4 Naphtha cracker (C3) 39
3.3.5 Kerosene retailer (C4) 40
3.3.6 Hydrotreater (C5) 40
3.3.7 Vacuum distillation (C6) 41
3.4 Extension 42
3.4.1 Gasoline retailer (E1) 44
3.5 Objective Functions 45
3.5.1 Base case 45
3.5.2 Extended case 46
Chapter 4 48
4.1 Base Case 48
4.2 Extended Case 54
4.3 Grouping Structures 67
4.3.1 Structure I 67
4.3.2 Structure II 76
4.3.3 Concluding remark 86
Chapter 5 87
5.1 Conclusions 87
5.2 Future Works 87
Amirtaheri, O., Zandieh, M., Dorri, B., & Motameni, A. R. (2017). A bi-level programming approach for production-distribution supply chain problem. Computers & Industrial Engineering, 110, 527-537.
Brock, H. W. (Ed.). (1979). Game theory, social choice and ethics. Boston: D. Reidel Publishing Co.
Cachon, G. P., & Lariviere, M. A. (2005). Supply chain coordination with revenue-sharing contracts: strengths and limitations. Management science, 51(1), 30-44.
Dana, Jr, J. D., & Spier, K. E. (2001). Revenue sharing and vertical control in the video rental industry. The Journal of Industrial Economics, 49(3), 223-245.
Giannoccaro, I., & Pontrandolfo, P. (2004). Supply chain coordination by revenue sharing contracts. International journal of production economics, 89(2), 131-139.
Gjerdrum, J., Shah, N., & Papageorgiou, L. G. (2001). Transfer prices for multienterprise supply chain optimization. Industrial & Engineering Chemistry Research, 40(7), 1650-1660.
Gjerdrum, J., Shah, N., & Papageorgiou, L. G. (2002). Fair transfer price and inventory holding policies in two-enterprise supply chains. European Journal of Operational Research, 143(3), 582-599.
Hwang, W., Bakshi, N., & DeMiguel, V. (2018). Wholesale price contracts for reliable supply. Production and Operations Management, 27(6), 1021-1037.
Kuo, T. H., & Chang, C. T. (2008). Application of a mathematic programming model for integrated planning and scheduling of petroleum supply networks. Industrial & Engineering Chemistry Research, 47(6), 1935-1954.
Kuo, T. H., & Chang, C. T. (2008). Optimal planning strategy for the supply chains of light aromatic compounds in petrochemical industries. Computers & Chemical Engineering, 32(6), 1147-1166.
Leng, M., & Parlar, M. (2012). Transfer pricing in a multidivisional firm: A cooperative game analysis. Operations Research Letters, 40(5), 364-369.
Levenspiel, O. (1998). Chemical Reaction Engineering Third Edition. New York: Wiley.
Liu, S., & Papageorgiou, L. G. (2018). Fair profit distribution in multi-echelon supply chains via transfer prices. Omega, 80, 77-94.
Liu, S., Fucarino, R., & Papageorgiou, L. G. (2016). Fair Transfer Prices of Global Supply Chains in the Process Industry. In Computational Management Science (pp. 141-149). Springer, Cham.
Liu, Y., Ding, C., Fan, C., & Chen, X. (2014). Pricing decision under dual-channel structure considering fairness and free-riding behavior. Discrete Dynamics in Nature and Society, 2014.
Mokhlesian, M., & Zegordi, S. H. (2014). Application of multidivisional bi-level programming to coordinate pricing and inventory decisions in a multiproduct competitive supply chain. The International Journal of Advanced Manufacturing Technology, 71(9-12), 1975-1989.
Myerson, R. (1991). Game Theory: Analysis of Conflict. Harvard University Press, United States.
Nash Jr, J. F. (1950). The bargaining problem. Econometrica: Journal of the Econometric Society, 155-162.
Okamoto, Y. (2008). Fair cost allocations under conflicts—a game-theoretic point of view—. Discrete Optimization, 5(1), 1-18.
Qin, Z., & Yang, J. (2008). Analysis of a revenue-sharing contract in supply chain management. International Journal of Logistics: Research and Applications, 11(1), 17-29.
Rosenthal, E. C. (2008). A game-theoretic approach to transfer pricing in a vertically integrated supply chain. International Journal of Production Economics, 115(2), 542-552.
Roth, A. E. (2012). Axiomatic models of bargaining (Vol. 170). New York: Springer Science & Business Media.
Teng, Y., Li, X., Wu, P., & Wang, X. (2019). Using cooperative game theory to determine profit distribution in IPD projects. International Journal of Construction Management, 19(1), 32-45.
Torres, A. I., & Stephanopoulos, G. (2016). Design of multi‐actor distributed processing systems: A game‐theoretical approach. AIChE Journal, 62(9), 3369-3391.
Torres, A. I., Bochenski, T., Schmidt, J. E., & Stephanopoulos, G. (2016). Economically optimal multi-actor processing networks: material flows and price assignment of the intermediates using Lagrangian decomposition. In Computer Aided Chemical Engineering (Vol. 38, pp. 1383-1388). Elsevier.
Torres, A. I., Cybulska, I., Fang, C. J., Thomsen, M. H., Schmidt, J. E., & Stephanopoulos, G. (2015). A novel approach for the identification of economic opportunities within the framework of a biorefinery. In Computer Aided Chemical Engineering (Vol. 37, pp. 1175-1180). Elsevier.
Von Neumann, J., & Morgenstern, O. (2007). Theory of games and economic behavior (commemorative edition). Princeton university press, United States.
Wang, F., Zhuo, X., & Niu, B. (2016). Sustainability analysis and buy-back coordination in a fashion supply chain with price competition and demand uncertainty. Sustainability, 9(1), 25.
Yue, D., & You, F. (2014). Fair profit allocation in supply chain optimization with transfer price and revenue sharing: MINLP model and algorithm for cellulosic biofuel supply chains. AIChE Journal, 60(9), 3211-3229.
Zhang, D., Samsatli, N. J., Hawkes, A. D., Brett, D. J., Shah, N., & Papageorgiou, L. G. (2013). Fair electricity transfers price and unit capacity selection for microgrids. Energy Economics, 36, 581-593.