Simulation-based Optimization
for Supply Chain Design
INRIA Team
April 7, 2004
Torino-Italy
Keys issues in supply chain design
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Uncertainties and risks
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Interrelation between decisions at different levels
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Strategic decisions
Operational decisions
Multiobjective
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Demand fluctuation
Supply disruption
Transportation instability
Costs vs. Customer service level
Characteristics of the case studies
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Demand seasonality, unstable transportation lead-time
Supplier selection, inventory control
Cost, lead-time, demand fill-rate
2
A case study from textile industry
(actual situation)
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Company outsources its production to outside contractors and
focuses only on product design, marketing and distribution issues,
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One part of the global supply chain of the company, which
distributes a single type of product “classic boot” around Europe, is
considered,
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According to the inventory control policy,
the DC places replenishment orders periodically,
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A unique supplier in Far East is employed
for stock replenishment,
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There is only one transportation link
that connects the DC and the supplier,
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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
3
A case study from textile industry
(evaluated scenario)
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
Actual
Cheapest
Normal
Fastest
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Problem
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Optimal supply portfolio
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Possibly multi-supplier
Combinations of various transportation
modes
Traditional approaches
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Analytical Hierarchic Process (AHP)
Elimination
Mathematical programming
5
Why simulation-optimization?
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Strategic + operational decisions
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Dynamic in nature
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Supply chain network design
Order assignment ratio
Inventory control parameters
Demand seasonality
Unstable transportation time
Original
work !
Multiple criteria
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Total costs
Backlog ratio
6
The proposed methodology
Objective: To design supply chain networks
that are efficient in real-life conditions
Optimizer
Supply chain
configurations
Performances
estimations
Solution Evaluator
7
Key requirements
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Optimizer
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Combinatorial optimization
Capable to learn from previous evaluations
Suitable for multiobjective optimization
Evaluator
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Faithful and efficient evaluation
Capable to catch stochastic facts
Flexible for different SC structures
Genetic
Algorithm
Rule-based
Simulation
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What is Genetic Algorithm?
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A search algorithm
Large and non-linear search space
Based on the mechanics of natural
selection and evolution
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Generation by generation
Selection
Crossover
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Mutation
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Characteristics of GA
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Probabilistic in nature
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Search from one population to another
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Use only objective function information
to guide the search direction
Need a sufficient number of simulation
runs, time-consuming
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An example
Chromosome
Phenotype
 Integer value
 Network configuration
 Schedule
…
Gene
Replenishment level: 1*27+0*26+1*25+0*24+0*23+0*22+1*21+1*20 = 163
Network configuration:
Supplier1 Supplier3 Supplier7 Supplier8
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Simulation-based optimization
Step1: Generate an initial population of chromosomes
1 chromosome = 1 network configuration
Boat +truck
0 1 1 0
0 0 1 0
0 1 0 0
0 0 1 1
Plane + truck
Supplier 1
Far East
Boat + plane + truck
Boat +truck
Plane + truck
Supplier 2 Boat + plane + truck
Far East
Truck Truck
Delivery
Distribution
Center
European
Market
Supplier 3
Europe Supplier 4
Europe
1 0 0 0
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Simulation-based optimization
Step1: Generate an initial population of chromosomes
1 chromosome = 1 network configuration and 1 set of parameters
Step2: Evaluate all chromosomes by simulation
Fitness = f (KPI1, KPI2, …)
Boat +truck
Plane + truck
Supplier 1
Far East
Boat + plane + truck
Boat +truck
Plane + truck
Supplier 2 Boat + plane + truck
Far East
Truck Truck
Supplier 3
Europe Supplier 4
Europe
Delivery
KPI
Distribution
Center
European
Market
 Purchasing cost
 Transportation cost
 Inventory cost
 Unmet demand
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Simulation-based optimization
Step1: Generate an initial population of chromosomes
1 chromosome = 1 network configuration
Step2: Evaluate all chromosomes by simulation
Fitness = f (KPI1, KPI2, …)
Step3: Selection of chromosomes for crossover
Step4: Produce offspring by crossover and mutation
Step5: Repair of offspring for feasibility
Return to Step2
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Application on the case study
Customer
Demand quantity*
Demand interval*
Behavior type
Expected leadtime
Service priority
Distribution Center
Supplier
FOB Price*
Storage capacity
Duties*
Over-capacity cost
Supply leadtime*
Holding cost
Minimum order size*
Ordering cost
Engagement cost
Transportation Link
Transportation leadtime*
Carrier capacity
Unit shipment cost*
Batch shipment cost*
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GA specifications in SGA case
Binary variables
for supplier selection decisions
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Integer variables
for assignment weights
A integer variable
for replenishment level
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
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Principal assumptions
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Simulation horizon = 3 years
Customer behavior
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Inventory control policy
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Non-patient customer
Weekly demand: N( 783, 100 )
Periodic replenishment
Replenish period = 7 days
Proportional order assignment
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Single-objective GA (SGA)
Minimize the total costs
Total costs = Cpurch. + Ctrans. + Cinventory + Clost sales
Best-so-far solution:
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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 €
7,9% Transportation
Total Costs €
2,10E+06
1,6%
1,90E+06
Inventory
9,6% Lost sales
1,70E+06
1,50E+06
1,30E+06
0
25
50
75 100
Generation
125
150
Purchasing
80,9%
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GA specifications in MOGA case
Binary variables
for supplier selection
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Integer variables
Integer variables
for transportation
for order quantity
allocation weights Integer variables
for reorder point
Population size = 100
Generation number = 2000
pCrossover = 0.9
pMutation = 0.1
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Principal assumptions in MOGA
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Simulation horizon = 4 years
Simulation replications = 10 times
Customer behavior
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Non-patient customer
Weekly demand: N( 783, 100 )
Inventory control policy
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(R, Q)
Replenish period = 7 days
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Multi-objective GA (MOGA)
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Modifications regarding to SGA
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Pareto optimality; Fitness assignment; Solution filter
Two objectives
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Minimize the total cost
Maximize the demand fill-rate
Demand Fill-Rate
100%
95%
90%
85%
80%
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9 10 11 12 13 14 15 16 17 18
Unit Cost (€)
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Innovations of the proposed approach
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Capable to optimize both
 supply chain configurations
 operational decisions
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Uncertainties and risks covered
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Multi-objective decision-making
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