Simulation-based Optimization for Supply Chain Design

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

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

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. 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

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

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

8. Genetic Algorithm Rule-based Simulation Key requirements • 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

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. 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. Network configuration: 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

12. 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 Simulation-based optimization Step1: Generate an initial population of chromosomes 1 chromosome = 1 network configuration

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

14. Step3: Selection of chromosomes for crossover Step4: Produce offspring by crossover and mutation Step5: Repair of offspring for feasibility Return to Step2 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, …)

15. Application on the case study

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. 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. 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 €

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

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