1. Statics and Dynamics of Complex Network Systems: Supply Chain Analysis and Financial Networks with Intermediation Ke MKIDS Mini-Workshop September 10, 2003 The Virtual Center for Supernetworks

2. Introduction Literature Survey Related Publications Research Motivation

3. Literature Survey Supply Chain Analysis: Nagurney and Dong (2002) Nagurney, Dong, and Zhang (2001) Nagurney, Loo, Dong, and Zhang (2001) Nagurney and Dong (2000) Nagurney, Dong, and Mokhatarian (2000, 2001) Financial Networks with Intermediation: Thore (1969, 1980) Nagurney, Dong, and Hughes (1992) Nagurney and Dong (1995, 1996a, b)

4. Related Publications Nagurney, Ke, Cruz, Hancock, and Southworth (2002) Nagurney and Ke (2001a, b) Nagurney and Ke (2003)

5. Research Motivation We propose a multilevel network to capture distinct flows, in particular, the logistical, informational, and financial flows within the same supply chain network system. The theoretical framework provides an abstraction of decision-making in the case of agents, such as firms, consumers, as well as intermediaries, who operate in a decentralized fashion on both physical and virtual networks, and allows not only for the visualization of business processes as networks but also for the prediction of production volumes and shipments of products, prices, as well as, as appropriate information and financial flows.

6. Research Motivation (Cont.) We develop a framework for the modeling, analysis, and computation of solutions to financial network problems in the presence of intermediation. Advances in telecommunications have had an enormous effect on financial services and the options available for financial transactions. We then will further to include the electronic transaction in the financial network modeling.

7. Dynamics of Supply Chains: a Multilevel Network Prospective

8. Notations m firms with a typical firm denoted by i, n retailers with a typical retailer denoted by j, o demand markets with a typical demand market denoted by k.

9. The Demand Market Price Dynamics

10. The Dynamics of the Commodity Shipments Between the Retailers and the Demand Markets

11. The Dynamics of the Prices at the Retail Outlets

12. The Dynamics of Commodity Shipments Between Firms and Retailers

13. The Projected Dynamical System Let X = the shipment and price variables and F(X) (F ij, F jk, F j, F k ) i=1,…,m; j=1,…,n; k=1,…,o, Where ;

14. Then the dynamic model can be rewritten as the PDS defined by the initial value problem: = Π K (X, -F(X)), X(0)=X 0.

15. The Equilibrium Point

16. Qualitative Properties Monotonicity Lipschitz continuity Existence and uniqueness of a solution to the initial value problem Stability of the system

17. A Discrete Time Algorithm Step 0: Initialization Step 1: Computation Step 2: Convergence verification

18. Step 1: Computation Compute (Q 1 , Q 2 ,, )  by solving the variational inequality:

19. Financial Networks with Intermediation

20. Introduction Financial network with intermediation consists of: –source of funds –intermediaries –consumers of funds the flows on the links: the allocation of the financial instruments Multilevel supply chain network consists of: –manufacturers –retailers –consumer markets the flows on the links: prices of products

21. Introduction (Cont.) direction of financial flows: from top tier, through middle tier, until the bottom tier. objective of the decision-makers of first two tiers –profit maximization –minimization of risks direction of financial flows: –bottom up objective of the decision-makers of first two tiers: –Profit maximization

22. The Behavior of Source Agents

23. The Optimality Conditions for Source Agents

24. The Behavior of Financial Intermediaries

25. The Optimality Conditions for All Intermediaries

26. The Behavior of Consumers at Demand Markets

27. The Optimality Conditions for Demand Markets

28. The Equilibrium Conditions

29. Qualitative Properties Monotonicity Existence of a solution to the VI problem Uniqueness Lipschitz continuity

30. The Algorithm

32. Financial Networks with Electronic Transactions

33. The Network Structure electronic transactions source agents can transact: –with the intermediaries either physically or electronically –with the consumers in an electronic manner. intermediaries transact with the consumers either physically or electronically

34. Notations l: the transaction mode –l=1: a physical transaction –l=2: an electronic transaction via the Internet All other notations and assumptions remain the same as in the previous model.

35. The Behavior of Source Agents

36. The Optimality Conditions for Source Agents

37. The Behavior of Financial Intermediaries

38. The Optimality Conditions for All Intermediaries

39. The Behavior of Consumers at Demand Markets

40. The Optimality Conditions for Demand Markets

41. The Equilibrium Conditions

42. Qualitative Properties Monotonicity Existence of a solution to the VI problem Uniqueness Lipschitz continuity

43. The Algorithm Step 0: Initialization Step 1: Computation Step 2: Convergence verification

44. Step1: Computation

45. Numerical Examples

46. Numerical Examples (Cont.)

49. Summary The dynamic supply chain network model and a series of financial equilibrium models are developed here. Sufficient progress has already been obtained as evidenced from our publications. We extend the work in general financial equilibrium modeling, analysis, and computation in a network framework to include financial intermediaries, the underlying dynamics associated with the financial flows and prices, and the inclusion of electronic transactions. It, thus, will incorporate the dimension, lacking in financial flow of funds accounts, of the explicit dynamic behavior of the various financial agents as well as the price dynamics.

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