1. Integrated Supply Chain Analysis and Decision Support (I98-S01)

2. RESEARCH TEAM INVESTIGATORS: G. Berkstresser S. Fang R. King T. Little H. Nuttle J. Wilson Textiles and Apparel Mgmt. Industrial Engineering Textiles and Apparel Mgmt. Industrial Engineering

3. STUDENTS: S-H. Chen Y. Liao A. Medaglia Ph.D. Operations Research Ph.D. Industrial Engineering Ph.D. Operations Research RESEARCH TEAM

4. Background Supply chains involve the activity and interaction of many entities. Successful operation requires coordination of decision making among the entities. Decisions must be made in settings involving vagueness and uncertainty. Performance evaluation is complicated by the presence of conflicting objectives. These issues become more serious as the number of operations and number of players in the chain increase.

5. Performance measures, such as service level and cost, and system parameters, such as inventory levels, plant capacities, and leadtimes, are understood in a general sort of way. Precise relationships between system parameters and performance measures are really not known and, in fact, will change from one time to another depending on uncertain factors such as customer demand and manufacturing yields. Background (cont.)

6. Fuzzy mathematics permits one to directly model imprecise relationships using linguistic variables. While fuzzy logic permits one to do approximate reasoning to obtain useful results. Background (cont.)

7. Objectives Attack Critical Soft Goods Supply Chain integration and decision support problems using Fuzzy Mathematics and Neural Network technologies: Develop the capability to model soft goods supply chain design and decision making problems using this framework. Develop mathematical models for specific scenarios involving both numerical and linguistic data. Design and evaluate approaches for solving the models. Prototype a decision support system.

8. Multi-Customer Due-Date Bargainer

9. Combines the Order Management, Resource Management, Due-Date Bargaining and Schedule Management Function into one package. Multi-Customer Due-Date Bargainer is a new tool for due-date negotiation between a manufacturer and customers Multi-Customer Due-Date Bargainer (MCDDB) MCDDB

10. Step I:Input order data. Step II:Calculate the Manufacturer’s prefer Due-Date (no overtime). Step III: Calculate the Fuzzy Promised Due-Date balancing overtime use and delayed delivery. Steps of MCDDB Step IV:Execute bargaining process with dissatisfied customers.

11. Source: MCDDB (Beta Version)

15. Membership Functions 1 0 x 1 0 x Fuzzy Customer Due-Date 1 Fuzzy Available Resource

16. Source: MCDDB (Beta Version)

19. Master Production Schedule

20. Source: MCDDB (Beta Version) Resource Utilization

21. Supply Chain Modeling and Optimization Using Soft Computing Based Simulation

22. Introduction Supply chains involve the activity and interaction of many entities. Decision makers typically have imprecise goals. –e.g. “High service level” Some system parameters may also be imprecise. –e.g. “Production capacity” Discrete event simulation can help design and analyze supply chains. Many configurations and courses of action need to be investigated. Even experts have to spend a considerable amount of time searching for good alternatives. Soft computing guided simulation speeds up the process.

23. Scheme Supply Chain Configuration Simulation Activate Fuzzy Rules/Logic Goals met? Stop Input - Performance Data Fuzzy System / Relationship Identification Knowledge Extraction Soft Computing Guided Simulation Yes No SCBS (Alpha Version)

24. Knits Wovens Distribution Center 1 Retailer 1 Retailer 2 Distribution Center 2 Source: SCBS (Alpha Version)

25. Knits Wovens Distribution Center 1 Retailer 1 Retailer 2 Distribution Center 2

26. Linguistic Terms Factory –Production rate (low, medium, high) –Finished inventory (small, medium, large) –Utilization (low, medium, high) Distribution Center –Inventory level (small, medium, large) Demand Point / Retailer –Demand rate (low, medium, high) –Service level (low, medium, high) Changes in inventory limits –Large drop, Small drop, No change, Small increase, Large increase Changes in production rates –Large reduction, Small reduction, No reduction, Small increase, Large increase

27. Knits Wovens Distribution Center 1 Retailer 1 Retailer 2 Distribution Center 2 Source: SCBS (Alpha Version)

28. Rule base to guide supply chain reconfiguration Example rule 1: If Inventory level in the Distribution Center 1 is High and Inventory level in the Factory (Wovens) is Medium then Change in production rate in the Factory (Wovens) is Small Reduction. Example rule 2: If Service level in Retailer 1 is Low and Inventory level in the Distribution Center 1 is Low then Change in production rate in the Factory (Knits) is Large Increase.

29. Goals The degree of fulfillment of the goals can be evaluated. e.g. Goal 1:High Service Level in Retailer 1. Goal 2:Low Inventory Level in Retailer 2. Goal 3:Medium Inventory Level in Factory (Knits). Each goal is met to a certain degree. A complicated a multi-criteria objective can be specified using AND, OR, NOT operators, –e.g. High S.L. in Retailer 1 and Low Inventory Level in Retailer 2 and not Low Throughput in Retailer 1 and Low Finished Inventory in Factory (Knits).

30. System / Relationship Identification

31. Supply Chain Configuration Simulation Activate Fuzzy Rules/Logic Goals met? Stop Input - Performance Data Fuzzy System / Relationship Identification Knowledge Extraction Soft Computing Guided Simulation Yes No In the previous scheme Source: SCBS (Alpha Version)

32. Methodologies for System Identification Conventional Mathematics Fuzzy Systems Neural Networks

33. Flow Chart Baseline design Fine tuning Steepest descent method to solve the nonlinear optimization problem for the parameters of the membership functions in the IF parts Recursive least-squares estimation method to solve the linear least- squares estimation problem for the parameters of the first order polynomial functions in the Then parts Subtractive clustering =>number of clusters =>number of rules FCM clustering algorithm =>input space partition =>membership functions in the IF parts

34. Neural Networks Idea –to approximate the relationship between input and output data pairs. Steps: –train the neural network with existing data. –predict performance using trained neural network.

35. Network Architecture Inputs Input Layer Hidden Layer Output Layer Outputs x1x1 x2x2 xnxn w 11 w 21 w jn v 11 v 21 v mj y1y1 y2y2 ymym

36. Test Case Truck-Backup Problem DOCK 4060 y=100 10 0 x=100 10

37. Results Comparison

38. Decision Surface Modeling

39. Decision Surface Modeling (Retail Model & Sourcing Simulator) Objective is to provide an interactive system that captures the essential features of the retail model in multidimensional, mathematical relationships between performance measures, e.g., service level, and key parameters, e.g., reorder leadtimes. Provide retailer with a rapid, easy-to-use, visual tool to help understand and predict the impact on system performance of “what-if” scenarios such as: –What are the consequences of reducing initial season inventory? –What are the consequences of poor forecast? –What are the cost/benefits of reducing reorder lead times?

40. Source: Sourcing Simulator (Version 2.0)

41. Neural Network Architecture A neural network consists of several layers of computational units called neurons and a set of data-connections which join neurons in one layer to those in another. The network takes inputs and produces outputs through the work of trained neurons. Neurons usually calculate their outputs as a sigmoid, or signal activation function of their inputs, Using some known results, i.e., input-output pairs for the system being modeled, a weight is assigned to each connection to determine how an activation that travels along it influences the receiving neuron. The process of repeatedly exposing the network to known results for proper weight assignment is called “training”.

42. Learning Curve Source: Sourcing Simulator (Version 2.0)

43. Offshore vs QR Sourcing Service Level Performance Source: Sourcing Simulator (Version 2.0)

44. Early Peak vs Late Peak Demand Gross Margin Performance 4] Source: Sourcing Simulator (Version 2.0)

45. Service Level -- Adjusted Gross Margin Tradeoff Service Level Adjusted Gross Margin Source: Sourcing Simulator (Version 2.0)

46. Confidence Intervals for Estimated Decision Surfaces A new approach based on jackknifing promises to yield reliable, realistic confidence and prediction bands on the estimated response surface. With k replications (runs) of n training patterns (design points), we combine k+1 response surface estimates to obtain both point and confidence interval estimates of the average response E[Y(x)] at each selected combination x = [x 1, x 2,..., x m ] of the m decision variables. On the jth replication of all training patterns, common random numbers are used to sharpen the estimation of the ANN weights; but as usual, different replications are mutually independent.

47. New Jackknife Procedure Let Y(x) denote an ANN estimate of the average simulation response at design point x when all k replications of the simulation are included in the training data. Let Y -j (x) denote the ANN estimate of the average simulation response when the jth replication of each training pattern is deleted.

48. New Jackknife Procedure The jth pseudovalue is Z j =kY(x) – (k–1)Y -j (x); and from the sample mean Z and the sample standard deviation S Z of the pseudovalues, we compute the 100(1–  )% confidence interval for the expected response at design point x: Z  t 1-  /2; k-1 S Z /  k.

50. Confidence Intervals for Estimated Decision Surfaces A new approach based on jackknifing promises to yield reliable, realistic confidence and prediction bands on the estimated response surface. With k replications (runs) of n training patterns (design points), we combine k+1 response surface estimates to obtain both point and confidence interval estimates of the average response E[Y(x)] at each selected combination x = [x 1, x 2,..., x m ] of the m decision variables. On the jth replication of all training patterns, common random numbers are used to sharpen the estimation of the ANN weights; but as usual, different replications are mutually independent.

54. Fuzzy Inventory Replenishment System

55. Centennial Apparel If demand is “strong” and inventory level is “low” then purchase amount is “large”. Fuzzy Inventory Replenishment System Centennial Apparel

56. Replenishment Policy Crisp (Q,R) System Q = purchase amount R = re-order point Fuzzy (Q,R) Control System Fuzzy Variables Membership Functions Fuzzy Rules Approximate Reasoning Method Defuzzification Method Policy : whenever inventory is below R, purchase Q Policy : apply fuzzy rules to specify purchase quantity

57. Fuzzy (Q,R) Inventory System Linguistic Variables Inventory: Low, Medium, High Demand : Low, Medium, High Purchase : Low, Medium, High

58. Source: Fuzzy (Q,R) (Beta Version) Fuzzy (Q,R) Inventory System Membership Functions Trapezoid Numbers

59. Source: Fuzzy (Q,R) (Beta Version) Fuzzy Rules Fuzzy (Q,R) Inventory System

60. Source: Fuzzy (Q,R) (Beta Version) Case Study

61. Source: Fuzzy (Q,R) (Beta Version) Case Study Statistics from 50 Runs

62. Source: Fuzzy (Q,R) (Beta Version) Case Study Modify Fuzzy Rules

63. Source: Fuzzy (Q,R) (Beta Version) Case Study Performance Improved

64. More to come... http://www.ie.ncsu.edu/fangroup/