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

Integrated Supply ChainAnalysis and Decision Support

(I98-S01)

RESEARCH TEAMRESEARCH TEAM

INVESTIGATORS:G. BerkstresserS. FangR. KingT. LittleH. NuttleJ. Wilson

Textiles and Apparel Mgmt.Industrial EngineeringIndustrial EngineeringTextiles and Apparel Mgmt.Industrial EngineeringIndustrial Engineering

STUDENTS:S-H. ChenY. LiaoA. Medaglia

Ph.D. Operations ResearchPh.D. Industrial EngineeringPh.D. Operations Research

RESEARCH TEAMRESEARCH TEAM

BackgroundBackground

• 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.

• 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.)Background (cont.)

• 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.)Background (cont.)

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.

Multi-Customer Due-Date Bargainer

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)

• 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.

Source: MCDDB (Beta Version)

Genetic Algorithm• Permutation Representation : [3 6 8 1 9 4 5 2 7]• Genetic Operators: Order Crossover (OX) Reciprocal Exchange Mutation

• Roulette Wheel Selection.• Fitness Function: Total Weighted Easrliness/Tardiness

1 32 4 5 6 7 8 9

7 39 4 5 6 1 2 8

5 47 9 1 3 6 2 8

selected substring

parent 1

parent 2

offspring

1 32 4 5 6 7 8 9

1 62 4 5 3 7 8 9

select two positions at rendom

swap the re lative orders

Membership Functions

)(μ x

Fuzzy Customer Due-Date

Fuzzy Available Resource

Master Production Schedule

Resource Utilization

Supply Chain Modeling and Optimization Using

Soft Computing Based Simulation

Supply Chain Modeling and Optimization Using

Soft Computing Based Simulation

IntroductionIntroduction

• 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.

SchemeScheme

Supply Chain Configuration

Simulation

Activate Fuzzy Rules/Logic

Goals met?

Input - PerformanceData

Fuzzy System / Relationship

Identification

KnowledgeExtraction

Soft ComputingGuided Simulation

SCBS (Alpha Version)

Wovens

Distribution Center 1

Retailer 1

Retailer 2

Source: SCBS (Alpha Version)

Wovens

Retailer 1

Retailer 2

Linguistic TermsLinguistic 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

Wovens

Retailer 1

Retailer 2

Rule base to guide supply chain reconfiguration

• Example rule 1:

Inventory level in the Distribution Center 1 is High

Inventory level in the Factory (Wovens) is Medium

Change in production rate in the Factory (Wovens) is Small Reduction.• Example rule 2:

Service level in Retailer 1 is Low

Inventory level in the Distribution Center 1 is Low

Change in production rate in the Factory (Knits) is Large Increase.

GoalsGoals

• 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).

System / Relationship Identification

Supply Chain Configuration

Simulation

Activate Fuzzy Rules/Logic

Goals met?

Input - PerformanceData

Fuzzy System / Relationship

Identification

KnowledgeExtraction

Soft ComputingGuided Simulation

In the previous schemeIn the previous scheme

Methodologies for System Identification

• Conventional Mathematics

• Fuzzy Systems

• Neural Networks

Flow ChartBaseline design

Fine tuning

Steepest descent methodto solve the nonlinear optimization problem forthe 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

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.

Network Architecture

InputsInputLayer

HiddenLayer

OutputLayer Outputs

•••

Test Case

Truck-Backup ProblemDOCK

40 60y=100

0 x=100

Results ComparisonPrediction Results

0 50 100 150 200 250 300 350 400 450 500

Training data

NeuralNet Clustering

Decision Surface ModelingDecision Surface Modeling

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?

Service Level vs Lead Time and InitialInventory

ServiceLevel

Lead Time(from 1 to 3)and Initial Inventory (from 35 to 65)

6562.960.7

58.656.4

54.352.1

5047.9

45.743.6

41.439.3

37.135

91.692.3

1.41.7

1.92.1

2.32.6

Source: Sourcing Simulator (Version 2.0)

Neural Network ArchitectureNeural 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,

f x xe( )

• 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”.

Learning CurveLearning Curve

Epoch vs Mean Square Error (MSE)

1 501 1001 1501 2001 2501 3001 3501 4001 4501

251 751 1251 1751 2251 2751 3251 3751 4251 4751

Offshore

Service Level(SL)%

Volume Error Percent

-30 -20 -10 0 10 20 30

Service Level(SL)%

Volume Error Percent

-30 -20 -10 0 10 20 30

Offshore vs QR Sourcing Service Level Performance

Early Peak vs Late Peak Demand Gross Margin Performance

Early Peak Demand

GrossMargin

Initial Stocking Percent of Plan [ 35 to 65 ] and Reorder Lead Time [ 1 to

Late Peak Demand

GrossMargin

Initial Stocking Percent of Plan [ 35 to 65 ] and Reorder Lead Time [ 1 to

Service Level -- Adjusted Gross MarginTradeoff

Service LevelService Level Adjusted Gross MarginAdjusted Gross Margin

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 = [x1, x2, ..., xm] 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.

New Jackknife ProcedureNew 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.

New Jackknife ProcedureNew Jackknife Procedure

• The jth pseudovalue is

Zj=kY(x) – (k–1)Y-j(x);

and from the sample mean Z and the sample standard

deviation SZ of the pseudovalues, we compute the

100(1–)% confidence interval for the expected

response at design point x:

Z t1-/2; k-1 SZ /k.

ANN Predictions vs Simulation Confidence IntervalsFor Normal Data

1.00E+05

2.00E+05

3.00E+05

4.00E+05

1 2 3 4 5 6 7 8 9 10

Testing Pattern

Jackknife LimitJackknife LimitSimulation Limit

Simulation Limit

Fuzzy Inventory Replenishment System

CentennialApparel

If demand is “strong” and inventory level is “low” then purchase amount is “large”.

Fuzzy Inventory Replenishment SystemFuzzy Inventory Replenishment System

CentennialApparel

Replenishment PolicyReplenishment Policy

• Crisp (Q,R) SystemQ = purchase amountR = re-order point

• Fuzzy (Q,R) Control SystemFuzzy VariablesMembership FunctionsFuzzy RulesApproximate Reasoning MethodDefuzzification Method

Policy : whenever inventory is below R, purchase Q

Policy : apply fuzzy rules to specify purchase quantity

Fuzzy (Q,R) Inventory SystemFuzzy (Q,R) Inventory System

Linguistic VariablesInventory: Low, Medium, High

Demand : Low, Medium, High

Purchase : Low, Medium, High

Source: Fuzzy (Q,R) (Beta Version)

Membership FunctionsTrapezoid Numbers

Fuzzy Rules

Case StudyCase Study

Statistics from 50 Runs

Modify Fuzzy Rules

Performance Improved

More to come...

http://www.ie.ncsu.edu/fangroup/

More to come...

http://www.ie.ncsu.edu/fangroup/

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

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