Dynamics of Global Supply Chain and Electric Power Networks: Models, Pricing Analysis, and Computations

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1 Dynamics of Global Supply Chain and Electric Power Networks: Models, Pricing Analysis, and Computations A Presented by Department of Finance and Operations Management Isenberg School of Management University of Massachusetts Amherst 28 August 2006

2 Acknowledgments This research was supported in part by NSF Grant No.:IIS AT&T Industrial Ecology Fellowship This support is gratefully acknowledged

3 Outline 1 2 3

4 Motivation Outline Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example Challenging intellectual questions Importance of supply chain decision-making Increasing globalization E-commerce

5 Global Supply Chain Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example Network equilibrium Several classes of decision-makers Optimization problem for every decision-maker is unique

6 Global Supply Chain Network Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example Country 1 Manufacturers Country L Manufacturers 11 I1 1L IL 1 H 1 H 1 H 1 H 1 H 1 H 1 H Currencies 1 j J Retailers 111 khl KHL Demand Market/Currency/Country combination

7 Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example Optimizing Behavior of Manufacturer i in country l Maximize Profit Maximize JX HX j=1 h=1 (ρ il 1jh e h )q il jh JX HX j=1 h=1 c il jh(q il jh) f il (Q 1 )

8 Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example The Optimality Conditions of All Manufacturers Variational Inequality Formulation Determine Q 1 R+ IJHL satisfying " IX LX JX HX f il (Q 1 ) qjh il i=1 l=1 j=1 h=1 jh(q il + cil jh ) qjh il Q 1 R IJHL + # h i ρ il 1jh e h qjh il qjh il 0

9 Characteristics of the Model Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example E-commerce Risk Time

10 Supernetwork Structure Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example Country 1 Manufacturers Country L Manufacturers 11 I1 1L IL 1 H 1 H 1 H 1 H 1 H 1 H 1 H Currencies 11 jˆl JL Distributors 111 kh l KHL Retailers

11 Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example Multicriteria Decision-Making Behavior of Manufacturer i in country l Maximize Profit Maximize JX HX j=1 h=1 LX ˆl=1 (ρ il 1 e h )q il + f il (Q 1, Q 2 ) JX HX j=1 h=1 KX HX k=1 h=1 LX ˆl=1 c il (qil LX l=1 (ρ il 1kh l e h )q il kh l ) KX HX k=1 h=1 LX l=1 c il kh l (qil kh l ) Minimize Risk Minimize r il (Q 1, Q 2 )

12 Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example Dynamics of Product Transactions between Manufacturer i in country l and Distributor j in country ˆl q il = 8 >< >: φ il " γ jˆl f il (Q 1,Q 2 ) q il α il r il (Q 1,Q 2 ) q il max ( 0, φ il " α il r il (Q 1,Q 2 ) q il cil (qil ) q il β jˆl r jˆl (Q 1,Q 3 ) q il γ jˆl f il (Q 1,Q 2 ) q il β jˆl r jˆl (Q 1,Q 3 ) q il # c jˆl (Q1,Q 3 ) q il, if q il > 0 cil (qil ) q il #) c jˆl (Q1,Q 3 ) q il, if q il = 0

13 Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example Dynamics of the Price at Demand Market kh l Assumption The rate of change of the price is proportional to the difference between the expected demand and the total amount transacted with the retailer. ρ 3kh l = 8 >< >: φ kh l max P I P d kh l Ll=1 i=1 q ( il 0, φ kh l kh l d kh l P I i=1 P Ll=1 q il kh l P J P Ḽ qjˆl j=1, if ρ l=1 kh l 3kh l > 0 ) P J j=1 P Ḽ l=1 qjˆl kh l, if ρ 3kh l = 0

14 Projected Dynamical System (PDS) Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example Ẋ = Π K (X, F(X)), X(0) = X 0

15 Stationary Points Outline Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example Theorem Since the feasible set is a convex polyhedron, the set of stationary points of the described PDS coincides with the set of solutions to the appropriately constructed VI problem: determine X K, such that F(X ), X X 0, X K

16 Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example The Euler Method (Dupuis and Nagurney (1993)) Step 0: Initialization Set X 0 K. Let T denote an iteration counter. Let T = 1 and set the sequence {α T } so that T =1 α T =, α T > 0, α T 0, as T. Step 1: Computation Compute X T K by solving the variational inequality subproblem: X T + α T F (X T 1 ) X T 1, X X T 0, X K. Step 2: Convergence Verification If X T X T 1 ɛ, with ɛ > 0, a pre-specified tolerance, then stop; otherwise, set T := T + 1, and go to Step 1.

17 Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example Numerical Example: Network Structure Country 1 Manufacturers Country 2 Manufacturers Distributors Retailers

18 Numerical Example: Data Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example Production cost functions f 11 (q) = 2.5(q 11 ) 2 + q 11 q q 11, f 21 (q) = 2.5(q 21 ) 2 + q 11 q q 21, f 12 (q) = 2.5(q 12 ) 2 + q 12 q q 12, f 22 (q) = 2.5(q 12 ) 2 + q 12 q q 22. Transaction cost functions c il =.5(q il ) q il c il =.5(q il kh l kh l )2 + 5q il,, kh l i, l, j, h,ˆl i, l, k, h, l

19 Numerical Example: Data Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example Handling cost functions c jˆl =.5( P 2 i=1 c kh l =.5( P 2 j=1 Demand P 2 l=1 qil )2, P 2ˆl=1 q jˆl kh l )2, Uniformly distributed in Risk function j,ˆl k, h, l h i 0, 100 k, h, l ρ 3kh l r 11 = ( X kh l q 11 kh l 2) 2

20 Numerical Example: Results Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example Example 1 Example 2 Example 3 Electronic Transactions q kh l q kh l q kh l q kh l Physical Transactions q q q q q jˆl kh l Prices γ jˆl ρ 3kh l

21 Dynamic Trajectory: Flow Global Supply Chain Network Model under Risk and Uncertainty Euler Method Numerical Example Experiment 1 Experiment 2 Experiment 3 Experiment Amount of flow Iteration

22 Electric Power Market Electric Power Supply Chain Network Dynamics under Risk and Uncertainty Global Electric Power Supply Chain Model Size Structure Complexity

23 Electric Power Supply Chain Network Electric Power Supply Chain Network Dynamics under Risk and Uncertainty Global Electric Power Supply Chain Model 1 g G Power Generators 1 s S Power Suppliers 1 T 1 T 1 T 1 T 1 T 1 T Transmission Service Providers 1 k K Demand Markets

24 Electric Power Supply Chain Network Dynamics under Risk and Uncertainty Global Electric Power Supply Chain Model Decision-Making Behavior of Power Generator g Maximize Profit Maximize SX ρ 1gsq gs f g(q 1 ) SX s=1 s=1 c gs(q gs)

25 Additional Motivation Electric Power Supply Chain Network Dynamics under Risk and Uncertainty Global Electric Power Supply Chain Model Weather conditions Demands for various goods and services Prices variability introduces risk Supply and/or demand sensitivity

26 Electric Power Supply Chain Network Electric Power Supply Chain Network Dynamics under Risk and Uncertainty Global Electric Power Supply Chain Model 1 g G Power Generators 1 s S Power Suppliers 1 T 1 T 1 T 1 T 1 T 1 T Transmission Service Providers 1 k K Demand Markets

27 Electric Power Supply Chain Network Dynamics under Risk and Uncertainty Global Electric Power Supply Chain Model Multicriteria Decision-Making Behavior of Power Generator g Maximize Profit Maximize SX ρ 1gs q gs f g(q 1 ) SX s=1 s=1 c gs(q gs) Minimize Risk Minimize r g(q 1 )

28 Electric Power Supply Chain Network Dynamics under Risk and Uncertainty Global Electric Power Supply Chain Model Dynamics of the Price at Demand Market k Assumption The rate of change of the price is proportional to the difference between the expected demand and the total amount transacted with the demand market. ρ 3k = 8 < : φ k hd P S P k (ρ 3k ) T i s=1 t=1 qt sk max{0, φ k hd k (ρ 3k ) P S s=1 P T t=1 qt sk, i if ρ 3k > 0 }, if ρ 3k = 0

29 Dynamic Trajectory: Price Electric Power Supply Chain Network Dynamics under Risk and Uncertainty Global Electric Power Supply Chain Model Experiment 1 Experiment 2 Experiment 3 Experiment Experiment 1 Experiment 2 Experiment 3 Experiment Price 150 Price Iteration Iteration

30 Theoretical Results Electric Power Supply Chain Network Dynamics under Risk and Uncertainty Global Electric Power Supply Chain Model Theorem If the feasible set is R N + and φ (φ 1,..., φ N ) T is a vector of positive terms. Then: where: VI(F, K) VI(F, K) F (F 1,..., F N )T and F (φ 1 F 1,..., φ NF N )T

31 More Motivation Outline Electric Power Supply Chain Network Dynamics under Risk and Uncertainty Global Electric Power Supply Chain Model Explicit modeling of fuel suppliers Spatially distributed generation plants owned by one company Self-supply generation Inelastic demand

32 Electric Power Supply Chain Network Dynamics under Risk and Uncertainty Global Electric Power Supply Chain Model Global Electric Power Supply Chain Network 11 1I H1 HI Fuel Supplier/Fuel Type Combinations A1 AI Alternative Uses 11 1n 1N G1 Gn GN 11 gm GM Power Generator/ Power Plant Combinations 1 S Power Suppliers 1 T 1 T 1 T 1 T Transmission Service Providers 1 K Demand Markets

33 Electric Power Supply Chain Network Dynamics under Risk and Uncertainty Global Electric Power Supply Chain Model Decision-Making Behavior of Power Generator g Maximize Profit Maximize 2 NX 4 X S n=1 X ρ K X 1gns qgns + ρ H 1gnk q gnk s=1 k=1 h=1 2 MX 4 X S + m=1 IX i=1 ρ gn 0hi s=1 ρ 1gms qgms + K X k=1 ρ 1gmk q gmk fgm(qgm) S X s=1 SX q gn f hi gn(q gn) c gns(q gns) c gnk (q gnk ) s=1 k=1 c gms(q gms) KX k=1 KX c gmk (q gmk ) subject to: SX s=1 q gns + KX k=1 q gnk = HX IX h=1 i=1 α gn hi q gn, n hi

34 Summary Outline Electric Power Supply Chain Network Dynamics under Risk and Uncertainty Global Electric Power Supply Chain Model Global Supply Chain user-optimization risk statics & dynamics e-commerce multiple currencies Electric Power Network user-optimization risk statics & dynamics self-supply fuel suppliers

35 Contribution Outline Electric Power Supply Chain Network Dynamics under Risk and Uncertainty Global Electric Power Supply Chain Model Mathematical and Computer Modelling (2003) Transportation Research: Part E (2005) Advances in Computational Economics, Finance and Management Science. Computational Management Science, Springer (2005) Transportation Economics: Towards better Performing Transport Systems, Routledge (2006)

36 Theoretical Development Transform the model to a transportation network equilibrium model as was done in the recent work by Nagurney, Liu, Cojocaru, and Daniele (2005) Reformulate the model as an evolutionary variational inequality

37 Empirical Testing Data from New England ISO 300+ power generators 800+ power generating units 7 owners of transmission lines 2500 locations (6.5 million consumers)

38 Thank You! Questions? Comments?

Modeling of Electric Power Supply Chain Networks with Fuel Suppliers via Variational Inequalities

Modeling of Electric Power Supply Chain Networks with Fuel Suppliers via Variational Inequalities Anna Nagurney Zugang Liu Faculty of Economics and Business, The University of Sydney Radcliffe Institute