Supply Chain Network Equilibrium with Profit Sharing Contract Responding to Emergencies

1. LSMS & ICSEE 2010 Supply Chain Network Equilibrium with Profit Sharing Contract Responding to Emergencies Ating Yang Lindu Zhao Institute of Systems Engineering, Southeast University Nanjing, China Oct. 23, 2010

2. Outline 1. Introduction 2. Model formulation 3. Numerical example 4. Conclusions

3. 1. Introduction • LSMS&ICSEE2010 2010 International Conference on Life System Modeling and Simulation & 2010 International Conference on Intelligent Computing for Sustainable Energy and Environment • Received over 800 paper submissions from 23 countries and regions • 195 were subsequently selected and recommended for publication by Springer in two volumes of Lecture Notes in Computer Science (LNCS) and one volume of Lecture Notes in Bioinformatics (LNBI) • 60 high-quality papers are recommended for publication in SCI indexed international journals • Conference program • Keynote addresses • Special sessions • Themed workshops • Poster presentations • Achievement

4. 1. Introduction Scenes & Photos

5. Wenchuan earthquake 2008.5.12 Asian financial crisis 1998 Sudan red incident 2005.3 9-11 terrorist attack 2001.9.11 Iraq war 2003.3.20 North Dakota flood 1997.4.18 Haiti earthquake 2010.1.12 Sanlu milk powder incident 2008 1995 2000 2005 2010 London bombings 2005.7.7 China’s snowstorm 2008.1 SARS 2003 Yangtze river flood 1998 Air France crash 2000.7.25 H1N1 2009.4.13 Indonesian tsunami 2004.12.26 1. Introduction • Background Oklahoma City bombing 1995.4.19 Fig. 1 Emergent events in recent years

6. 1. Introduction • Supply chain competition competition • Supply chain network is a network consisted of multiple manufacturers, multiple suppliers, multiple retailers and multiple customers. • Nagurney et al.(2002) first bring forward this concept. • The steady behaviors of decision-makers can be characterized by a group of equilibrium conditions. • But, Chee et al.(2004) indicate that the market could hardly be in equilibrium state, due to the private or imperfect information, decentralized decision-making, convert behaviors and so on. • Cachon(2003) describes various contracts in the newsvendor model, and proves that the buyback contract and profit sharing contract can coordinate a single supply chain. Companies Supply chains

7. 1. Introduction • Emergency environment • Yu et al.(2005) investigate the supply chain coordination problem under demand disruptions by using the quantity discount contract. • Sun and Ma(2008) describe a revenue sharing contract model for a two-stage supply chain that faced stochastic market demands in response to an emergent event. • Teng et al.(2009) establish a supply chain network equilibrium with stochastic demands with a quantity discount contract and prove by the numerical example that the anti-disruption ability of the supply chain network will be improved with the contract. In this paper, we introduce profit sharing contract into the supply chain network equilibrium model and analyze the impacts of emergent events have on this model. Then prove that manufacturers and retailers need to adjust the contracts parameters to achieve a new supply chain network equilibrium state.

8. 2. Model formulation • Assumptions : • Manufacturers must satisfy all of the retailers’ orders; • All information is symmetrical; • Retailers must choose order quantities and manufacturers before the start of a single selling season. Fig. 2 Network structure of supply chain

9. 2. Model formulation • Parameters:

10. 2. Model formulation • Without Emergencies: • Expected sales at retailer j: • Expected left over inventory at retailer j: • Lost sales at the retailer j: • The additional transfer payment from retailer j to manufacturer i :

11. 2. Model formulation • Manufacturers :production cost function of manufacturer i :transaction cost between manufacturer i and retailer j • The profits of manufacturers : • Optimality conditions of manufacturers • Assume that the manufacturers compete in a non-cooperative fashion, and the cost functions for each manufacturer are continuous and convex, then the optimality conditions for all the manufacturers satisfy the following variational inequality:

12. 2. Model formulation • Retailers :handling cost of retailer j The profits of retailers : • Optimality conditions of retailers • Assume the handling cost for each retailer is continuous and convex, then the optimality conditions for all the retailers satisfy the variational inequality:

13. 2. Model formulation • Optimality condition of the supply chain network • The optimal condition of wholesale price charged for the product by manufacturer to retailer is:

14. 2. Model formulation • Under Emergencies: • Expected sales at retailer j: • Expected left over inventory at retailer j: • Lost sales at the retailer j: • Demand distribution function:

15. 2. Model formulation • The optimization problem of manufacturers ：extra production cost when order quantity increases ：extra disposal cost when order quantity declines • The optimization problem of retailers

16. 3. Numerical example • Two-stage prediction–correction algorithm • The algorithm generates two predictors which satisfy two acceptance criteria. • That projection-based algorithm merely requires dynamic regulation of step length, avoiding excessive iterations. • It is a light-weight approach, which can be easily applied in practice. • Comparing to the common Euler algorithm is proved having a better global convergence. Fig. 3 Supply chain network for numerical example

17. 3. Numerical example Fig. 4 The convergence of the simulation

18. 3. Numerical example • Under Emergencies

19. 4. Conclusions • Conclusions: • Propose a SCN equilibrium model under emergencies; • profit sharing contract can coordinate the model; • manufacturers and retailers can adjust the contracts parameters together to achieve a new supply chain network equilibrium state through bargaining when facing emergent events. • Future work: • Other contracts: quantity discount, buy back, option contract etc. • Compare and identify the application situation of different contracts; • Find a optimal range of contract parameters.

20. Thank You! http://log.seu.edu.cn atingyang@163.com 2010-10-23