1. 1 Simulation Modeling and Analysis Session 13 Simulation Optimization

2. 2 Outline Introduction Evolutionary Algorithms Single Variable Optimization An inventory control problem

3. 3 Introduction Optimization is the science of determining “best” solutions to mathematically defined problems, which are often models of physical reality. Simulation is a methodology to transform inputs (decision variables) into outputs (performance measures).

4. 4 Simulation Optimization Simulation Optimization is a methodology to discover the values of decision variables required to minimize or maximize specific measures of performance. Typically, from a starting set of inputs simulation computes outputs. These are used in turn by an optimization algorithm to produce an improved set of inputs.

5. 5 How to find optima? 1.- Identify all possible decision variables affecting the output of the system. 2.- Using all possible values of each decision variable identify all possible solutions (I.e. the response surface). 3.- Evaluate all solutions accurately 4.- Compare each solution fairly 5.- Select the best answer

6. 6 Optimization of well posed problems Well posed problems –Have unique solutions. –Small changes in inputs produce correspondingly small changes in output. Numerical methods such as Newton- Raphson and Linear Programming are available to optimize well posed problems.

7. 7 Optimization of stochastic simulation model problems Stochastic simulation models –Not well posed –Complex response surfaces Heuristic techniques are available to optimize stochastic simulation problems.

8. 8 Evolutionary Algorithms EA conduct search of response surface using a population of solutions. Information about the response surface is then provided from many points at once.

9. 9 Steps in Evolutionary Algorithms 1.- Generate a population of solutions by randomly distributing throughout solution space. 2.- Accurately compute the response of each solution. 3.- Select the best solutions and apply genetic operators to produce new offspring solutions. 4.- Return to step 2 until a single solution emerges.

10. 10 Single Variable Optimization The Transformed Ackley function –Local optima Many maxima and minima –Global optima Two maxima (x = +9.54 and x = -9.54) One minimum (x = 0)

11. 11 Ackley function Randomly select 10 values of x (initial offspring size = 10) from -10 < x < -8 Challenge: to evolve from the original offspring to the minimum without stopping at the local minima. Result: Global minimum is determined after 8 generations.

12. 12 Inventory Control Problem What is the minimum amount of inventory required to support production in a JIT environment where parts are pulled through the system using kanban cards? Number of kanban cards influences WIP. Trigger values = number of kanban cards that must accumulate before a workstation begins production

13. 13 Two-Stage Pull Production Two-Stage Pull Production System –Customer demand pulls subassemblies from Stage One WIP to Assembly Lines. –Kanban card sent to Stage One Process. When trigger value is reached parts are pulled from Stage Two WIP to process. –Following processing, subassemblies and kanban cards are sent to Stage One WIP.

14. 14 Two-Stage Pull Production - contd –Stage Two Line processes raw materials into component parts to be pulled by Stage One. –As components are pulled from Stage Two WIP a kanban card is sent to the kanban post for Stage Two Line. When trigger value is reached production orders are issued to Stage Two Line. –As orders are completed at Stage Two Line, orders and kanban cards are sent to Stage Two WIP.

15. 15 Two-Stage Pull Production - contd Goal: Minimize inventory at the State One WIP location. Maximize throughput while minimizing the number of kanban cards in the system. Performance measure to be minimized f(a) = C1 (A + M) - C2 (TK1) - C3 (TK2) Solution Vector (I = 11 part types) a = (K1i,K2i,TK2i)

16. 16 Two-Stage Pull Production - contd Model: –Constant interarrival times for customer orders. –Number of defective subassemblies found at the assembly lines is stochastic. –Production times for Stage One Process and Stage Two Line are constant. –Set up time, time between failures and time to repair have triangular distributions. –Runs: 10 day warm up and 20 day steady state.

17. 17 Two-Stage Pull Production - contd Four independent runs of the models are performed each time a solution is evaluated. Performance score is the average of the four runs. SimRunner finds 110 kanban cards and f = 37.945 after 150 generations.