Supply Chain Supernetworks With Random Demands

Transcription

1 Supply Chain Supernetworks With Random Demands June Dong Ding Zhang School of Business State University of New York at Oswego Anna Nagurney Isenberg School of Management University of Massachusetts at Amherst 同济大学

2

3 Sources: plants vendors ports Regional Warehouses: stocking points Field Warehouses: stocking points Customers, demand centers sinks Supply Production/ purchase costs Inventory & warehousing costs Transportation costs Inventory & warehousing costs Transportation costs

4 Supply Chain Management Definition: Supply Chain Management is primarily concerned with the efficient integration of suppliers, factories, warehouses and stores so that merchandise is produced and distributed in the right quantities, to the right locations and at the right time, and so as to minimize total system cost subject to satisfying service requirements.

5 What do we see? Coordination within a supply chain among manufacturer, distributor, and retailer as well as Competition among manufacturers distributors retailers

6 The Dynamics of the Supply Chain Order Size Distributor Orders Retailer Orders Customer Demand Production Plan Time Source: Tom Mc Guffry, Electronic Commerce and Value Chain Management, 1998

7 What Management Gets... Order Size Customer Demand Production Plan Source: Tom Mc Guffry, Electronic Commerce and Value Chain Management, 1998 Time

8 What Management Wants Volumes Production Plan Customer Demand Time Source: Tom Mc Guffry, Electronic Commerce and Value Chain Management, 1998

9 What is a Supernetwork? A Supernetwork is a network, consisting of nodes, links, and flows, that is over and above existing networks.

10 Applications of Supernetworks Telecommuting/Commuting Decision-Making Teleshopping/Shopping Decision- Making Supply Chain Networks with Electronic Commerce Financial Networks with Electronic Transactions.

11 A Multitiered Supply Chain Supernetwork Example

12 Dong, Zhang, Nagurney, A Supply Chain Network Equilibrium Model with Random Demands, European Journal of Operations Research, Assume general random demands facing retailers Study Noncooperative behaviors Formulate the optimality conditions as VIP Give conditions of the distribution functions for the existence and uniqueness of the solution Algorithms

13 The Supernetwork Supply Chain Model with Random Demands Captures multi-tiers manufacturers distributors retailers demand markets competition at the same tier Coordination among different tiers Determines production quantities shipments prices expected demands Includes physical transactions electronic transactions

14 Supernetwork Structure

15 Behavior of the Manufacturers Profit maximization problem for manufacturer i q i * 1ij : production output q : shipment from i to j ij q : shipment from i to j via e-link ρ ik ρ * 1ik : price charged by manufacturer i to distributor : price charged by manufacturer i to retailer k j

16 The Optimality Condition for Manufacturers

17 Behavior of the Distributors Profit maximization problem for distributor j q : shipment from i to j ij q : shipment from j to j γ jk * j : price charged by distributor j

18 Optimality Conditions for the Distributors

19 k ik jk i= 1 j= 1 3k dˆ ( ρ k k m s = q + q ρ : demand price at retailer k 3k 3k n The Retailers ) : random demand at retailer ( x, ρ ) : density function P ( x, ρ ) : probability function of dˆ ( ρ ) k 3k k 3k x P ( x, ρ ) = P ( dˆ x) = ( x, ρ ) dx k 3k k k k 3k 0 min{ s, ˆ k dk}: the actual sale of k cannot exceed this amount k

20

21 λ λ + k k : unit penalty of having excess supply at retailer k : unit penalty of having excess demand at retailer k The expected total penalty of retailer k is given by

22 Behavior of the Retailers Profit maximization problem for retailer k Applying the definitions of,, + - k k

23 Optimality Conditions for the Retailers

24 The Stochastic Market Equilibrium For any retailer k Conditions where a.e. means that the corresponding equality or inequality holds almost everywhere.

25 Supply Chain Network Equilibrium Definition: with Random Demands The equilibrium state of the supply chain with random demands is one where the product flows between the tiers of the decision-makers coincide and the product shipments and prices satisfy the sum of the optimality conditions (5), (9), and (20), and the conditions (22).

26 Variational Inequality Formulation

27 Qualitative Properties Under certain conditions we proved the existence of the solution and the uniqueness of the solution to the VIP.

28

29

30

31

32 Algorithm

33

34 Numerical Examples

35

36 Example 1 λ b * ij * ik * jk * 2 j * 3k = λ = 1, k = 1, 2 + k k k = 100, k = 1,2. q =.3697, i = 1, 2; j = 1, 2. q =.3487, i = 1, 2; k = 1, 2. q =.3697, j = 1, 2; k = 1, 2. ρ ρ d = , j = 1,2. = , k = 1, 2. ( ρ ) = d ( ρ ) = * * Example 2 λ b * ij * ik * jk * 2 j * 3k = λ = 1, k = 1, 2 + k k k = 1000, k = 1,2. q =.6974, i = 1, 2; j = 1, 2. q = , i = 1,2; k = 1,2. q =.6973, j = 1,2; k = 1,2. ρ ρ d = , j = 1,2. = , k = 1,2. ( ρ ) = d ( ρ ) = * *

37 Questions? More information about Supernetworks can be found at Contact me at