1. Simulation-based Optimization for Supply Chain Design INRIA Team April 7, 2004 Torino-Italy

2. 2 Keys issues in supply chain design 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

3. 3 A case study from textile industry (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

4. 4 A case study from textile industry (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

5. 5 Problem Optimal supply portfolio Possibly multi-supplier Combinations of various transportation modes Traditional approaches Analytical Hierarchic Process (AHP) Elimination Mathematical programming

6. 6 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 Original work !

7. 7 The proposed methodology Objective: To design supply chain networks that are efficient in real-life conditions Performances estimations Solution Evaluator OptimizerOptimizer Supply chain configurations

8. 8 Key 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 Algorithm Rule-based Simulation

9. 9 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

10. 10 Characteristics 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

11. 11 An example Chromosome Gene Phenotype Integer value Network configuration Schedule … Replenishment level : 1*2 7 +0*2 6 +1*2 5 +0*2 4 +0*2 3 +0*2 2 +1*2 1 +1*2 0 = 163 Network configuration :

12. 12 Simulation-based optimization Step1: Generate an initial population of chromosomes 1 chromosome = 1 network configuration0110 010 0 001 0 010 1 100 0

13. 13 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, …) Purchasing cost Transportation cost Inventory cost Unmet demand KPI

14. 14 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

15. 15 Application on the case study

16. 16 GA 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

17. 17 Principal 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

18. 18 Single-objective GA (SGA) Minimize the total costs Total costs = C purch. + C trans. + C inventory + C lost 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

19. 19 GA specifications in MOGA case Population size = 100 Generation number = 2000 pCrossover = 0.9 pMutation = 0.1

20. 20 Principal 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

21. 21 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

22. 22 Innovations of the proposed approach Capable to optimize both supply chain configurations operational decisions Uncertainties and risks covered Multi-objective decision-making