Simulation-based Simulation-based

Optimization for Supply Optimization for Supply

Chain DesignChain Design

INRIA TeamINRIA Team

April 7, 2004 April 7, 2004 Torino-ItalyTorino-Italy

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Keys issues in supply chain Keys issues in supply chain designdesign

Uncertainties and risks Demand fluctuation Supply disruption Transportation instability

Interrelation between decisions at different levels

Strategic decisions Operational decisions

Multiobjective Costs vs. Customer service level

Characteristics of the case studies Demand seasonality, unstable transportation

lead-time Supplier selection, inventory control Cost, lead-time, demand fill-rate

Characteristics of the case studies Demand seasonality, unstable transportation

lead-time Supplier selection, inventory control Cost, lead-time, demand fill-rate

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A case study from textile industryA case study from textile industry(actual situation)(actual situation)

Company outsources its production to outside contractors and focuses only on product design, marketing and distribution issues,

One part of the global supply chain of the company, which distributes a single type of product “classic boot” around Europe, is considered,

According to the inventory control policy, the DC places replenishment orders periodically,

A unique supplier in Far East is employed for stock replenishment,

There is only one transportation link that connects the DC and the supplier,

After a period of supply lead-time, required boots are collected into containers and transported by boat from Far East to a European harbor and then to the DC by trucks

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A case study from textile industryA case study from textile industry(evaluated scenario)(evaluated scenario)

Cheapest

Actual

Fastest

Normal

Company motivations 1. Current order-to-delivery lead-time (period from the moment when the DC places an order to the moment when the DC receives required products) is relatively long:

“long distance (Far East-Europe)+boat as the principle carrier”

2. High variability demands for “classic boot” + frequently stock-out

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ProblemProblem

Optimal supply portfolio Possibly multi-supplier Combinations of various

transportation modes Traditional approaches

Analytical Hierarchic Process (AHP) Elimination Mathematical programming

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Why simulation-optimization?Why simulation-optimization?

Strategic + operational decisions Supply chain network design Order assignment ratio Inventory control parameters

Dynamic in nature Demand seasonality Unstable transportation time

Multiple criteria Total costs Backlog ratio

OriginaOriginal l

work !work !

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The proposed methodologyThe proposed methodology

Objective: To design supply chain networks that are efficient in real-life conditions

Objective: To design supply chain networks that are efficient in real-life conditions

Performances estimations

Solution EvaluatorSolution EvaluatorSolution EvaluatorSolution Evaluator

OptimizerOptimizerOptimizerOptimizer

Supply chain configurations

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Key requirementsKey requirements

Optimizer Combinatorial optimization Capable to learn from previous

evaluations Suitable for multiobjective optimization

Optimizer Combinatorial optimization Capable to learn from previous

evaluations Suitable for multiobjective optimization

Evaluator Faithful and efficient evaluation Capable to catch stochastic facts Flexible for different SC structures

Evaluator Faithful and efficient evaluation Capable to catch stochastic facts Flexible for different SC structures

Genetic Genetic AlgorithmAlgorithmGenetic Genetic

AlgorithmAlgorithm

Rule-based Simulation

Rule-based Simulation

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What is Genetic Algorithm? What is Genetic Algorithm?

A search algorithm Large and non-linear search

space Based on the mechanics of

natural selection and evolution Generation by generation Selection Crossover Mutation

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Characteristics of GACharacteristics of GA

Probabilistic in nature

Search from one population to another

Use only objective function information to guide the search direction

Need a sufficient number of simulation runs, time-consuming

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An exampleAn example

Chromosome

Gene

Phenotype Integer value Network configuration Schedule …

Replenishment level: 1*27+0*26+1*25+0*24+0*23+0*22+1*21+1*20

= 163

Network configuration:Supplier1 Supplier7Supplier3 Supplier8

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Simulation-based optimizationSimulation-based optimization

Step1: Generate an initial population of chromosomes 1 chromosome = 1 network configuration

Step1: Generate an initial population of chromosomes 1 chromosome = 1 network configuration

00 1111 00 Plane + truck

Boat +truck

Boat + plane + truck

Boat +truck

Plane + truck

Boat + plane + truck

Truck Truck

Delivery

Supplier 2Far East

DistributionCenter

Supplier 1Far East

Supplier 3Europe Supplier 4

Europe

EuropeanMarket

00 1100 00

00 0011 00

00 1100 11

11 0000 00

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Simulation-based optimizationSimulation-based optimization

Step1: Generate an initial population of chromosomes 1 chromosome = 1 network configuration and 1 set of parameters

Step1: Generate an initial population of chromosomes 1 chromosome = 1 network configuration and 1 set of parametersStep2: Evaluate all chromosomes by simulation Fitness = f (KPI1, KPI2, …)Step2: Evaluate all chromosomes by simulation Fitness = f (KPI1, KPI2, …)

Plane + truck

Boat +truck

Boat + plane + truck

Boat +truck

Plane + truck

Boat + plane + truck

Truck Truck

Delivery

Supplier 2Far East

DistributionCenter

Supplier 1Far East

Supplier 3Europe Supplier 4

Europe

EuropeanMarket

Purchasing cost Transportation cost Inventory cost

Unmet demand

Purchasing cost Transportation cost Inventory cost

Unmet demand

KPI

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Simulation-based optimizationSimulation-based optimization

Step1: Generate an initial population of chromosomes 1 chromosome = 1 network configuration

Step1: Generate an initial population of chromosomes 1 chromosome = 1 network configurationStep2: Evaluate all chromosomes by simulation Fitness = f (KPI1, KPI2, …)Step2: Evaluate all chromosomes by simulation Fitness = f (KPI1, KPI2, …)

Step3: Selection of chromosomes for crossoverStep3: Selection of chromosomes for crossover

Step4: Produce offspring by crossover and mutationStep4: Produce offspring by crossover and mutationStep5: Repair of offspring for feasibilityStep5: Repair of offspring for feasibility

Return to Step2Return to Step2

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Application on the case studyApplication on the case study

Supplier

FOB Price* Duties* Supply leadtime* Minimum order size* Engagement cost

Distribution Center

Storage capacity Over-capacity cost Holding cost Ordering cost

Customer

Demand quantity* Demand interval* Behavior type Expected leadtime Service priority

Transportation Link

Transportation leadtime* Carrier capacity Unit shipment cost* Batch shipment cost*

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GA specifications in SGA caseGA specifications in SGA case

Population size = 12 Generation number = 500 pCrossover = 0.9 pMutation = 0.01 Fitness = Purchasing costs + Transportation costs

+ Inventory costs + ß*Backlogged ß (€/pair) : punishment factor

Binary variablesfor supplier selection decisions

Integer variablesfor assignment weights

A integer variablefor replenishment level

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Principal assumptionsPrincipal assumptions

Simulation horizon = 3 years Customer behavior

Non-patient customer Weekly demand: N( 783, 100 )

Inventory control policy Periodic replenishment Replenish period = 7 days

Proportional order assignment

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Single-objective GA (SGA)Single-objective GA (SGA) Minimize the total costs Total costs = Cpurch. + Ctrans. + Cinventory + Clost sales Best-so-far solution:

1- Unique supplier from Far East: Supplier B

2- Two transportation links :

Boat + truck (73.7%) and Plane + truck (26.3%)

3- Replenishment level: 10800

4- Total costs: 1.48 e+006 €

1,30E+06

1,50E+06

1,70E+06

1,90E+06

2,10E+06

0 25 50 75 100 125 150Generation

Tot

al C

osts

€

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GA specifications in MOGA caseGA specifications in MOGA case

Population size = 100 Generation number = 2000 pCrossover = 0.9 pMutation = 0.1

Binary variablesfor supplier selection

Integer variablesfor transportationallocation weights Integer variables

for reorder point

Integer variablesfor order quantity

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Principal assumptions in MOGAPrincipal assumptions in MOGA

Simulation horizon = 4 years Simulation replications = 10 times Customer behavior

Non-patient customer Weekly demand: N( 783, 100 )

Inventory control policy (R, Q) Replenish period = 7 days

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Multi-objective GA (MOGA)Multi-objective GA (MOGA)

Modifications regarding to SGA Pareto optimality; Fitness assignment; Solution filter

Two objectives Minimize the total cost Maximize the demand fill-rate

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Innovations of the proposed Innovations of the proposed approachapproach

Capable to optimize both supply chain configurations operational decisions

Uncertainties and risks covered

Multi-objective decision-making