Integrated Supply Chain Analysis and Decision Support (I98-S01)
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Transcript of 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
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)
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)
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
Source: MCDDB (Beta Version)
Membership Functions
1
0x
id
)(μ x
* id
1
0x
)(μ x
Fuzzy Customer Due-Date
11 r1
Fuzzy Available Resource
Source: MCDDB (Beta Version)
Source: MCDDB (Beta Version)
Source: MCDDB (Beta Version)
Source: MCDDB (Beta Version)
Master Production Schedule
Source: MCDDB (Beta Version)
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?
Stop
Input - PerformanceData
Fuzzy System / Relationship
Identification
KnowledgeExtraction
Soft ComputingGuided Simulation
Yes
No
SCBS (Alpha Version)
Knits
Wovens
Distribution Center 1
Retailer 1
Retailer 2
Distribution Center 2
Source: SCBS (Alpha Version)
Knits
Wovens
Distribution Center 1
Retailer 1
Retailer 2
Distribution Center 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
Knits
Wovens
Distribution Center 1
Retailer 1
Retailer 2
Distribution Center 2
Source: SCBS (Alpha Version)
Rule base to guide supply chain reconfiguration
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.
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
System / Relationship Identification
Supply Chain Configuration
Simulation
Activate Fuzzy Rules/Logic
Goals met?
Stop
Input - PerformanceData
Fuzzy System / Relationship
Identification
KnowledgeExtraction
Soft ComputingGuided Simulation
Yes
No
In the previous schemeIn the previous scheme
Source: SCBS (Alpha Version)
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
x1
x2
xn
w11
w21
wjn
v11
v21
vmj
y1
y2
ym
•••
•••
•••
Test Case
Truck-Backup ProblemDOCK
40 60y=100
10
10
0 x=100
1010
Results ComparisonPrediction Results
50
100
150
200
250
300
350
400
450
0 50 100 150 200 250 300 350 400 450 500
Training data
Te
sti
ng
Da
ta
NeuralNet Clustering
Decision Surface ModelingDecision Surface Modeling
Decision Surface Modeling(Retail Model & Sourcing Simulator)
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
93.1
93.9
94.6
95.4
96.2
97.0
97.7
11.2
1.41.7
1.92.1
2.32.6
2.83
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( )
1
1
• 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)
Epoch
0.001
0.004
0.007
0.009
0.012
0.015
0.018
0.021
0.023
0.026
0.029
1 501 1001 1501 2001 2501 3001 3501 4001 4501
251 751 1251 1751 2251 2751 3251 3751 4251 4751
Source: Sourcing Simulator (Version 2.0)
Offshore
Service Level(SL)%
Volume Error Percent
50
60
70
80
90
100
-30 -20 -10 0 10 20 30
QR
Service Level(SL)%
Volume Error Percent
50
60
70
80
90
100
-30 -20 -10 0 10 20 30
Offshore vs QR Sourcing Service Level Performance
Offshore vs QR Sourcing Service Level Performance
Source: Sourcing Simulator (Version 2.0)
Early Peak vs Late Peak Demand Gross Margin 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
4
3
2
1
59000
59750
60500
61250
62000
62750
63500
64250
65000
35
45
55
65
Late Peak Demand
GrossMargin
Initial Stocking Percent of Plan [ 35 to 65 ] and Reorder Lead Time [ 1 to
4
3
2
1
59000
59750
60500
61250
62000
62750
63500
64250
65000
35
45
55
65
4] 4]
Source: Sourcing Simulator (Version 2.0)
Service Level -- Adjusted Gross MarginTradeoff
Service Level -- Adjusted Gross MarginTradeoff
Service LevelService Level Adjusted Gross MarginAdjusted Gross Margin
Source: Sourcing Simulator (Version 2.0)
Confidence Intervals for Estimated Decision Surfaces
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
Ave
rag
e In
ven
tory
Lev
el (
Po
un
ds)
Jackknife LimitJackknife LimitSimulation Limit
Simulation Limit
Fuzzy Inventory Replenishment System
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)
Fuzzy (Q,R) Inventory SystemFuzzy (Q,R) Inventory System
Membership FunctionsTrapezoid Numbers
Source: Fuzzy (Q,R) (Beta Version)
Fuzzy Rules
Fuzzy (Q,R) Inventory SystemFuzzy (Q,R) Inventory System
Source: Fuzzy (Q,R) (Beta Version)
Case StudyCase Study
Source: Fuzzy (Q,R) (Beta Version)
Case StudyCase Study
Statistics from 50 Runs
Source: Fuzzy (Q,R) (Beta Version)
Case StudyCase Study
Modify Fuzzy Rules
Source: Fuzzy (Q,R) (Beta Version)
Case StudyCase Study
Performance Improved
More to come...
http://www.ie.ncsu.edu/fangroup/
More to come...
http://www.ie.ncsu.edu/fangroup/