Simulation Ir. Risnandi MM

1. Simulation Ir. Risnandi MM POM-ris-YAI

2. What is Simulation Advantage and Disadvantage Monte Carlo Simulation Simulation of a Queuing Problem Simulation and Inventory Analyses POM-ris-YAI

3. Ris What is simulation What is Simulation ? There are many kind of simulations, and also this module stresses Monte Carlo simulations, you should be aware of physical simulations such as a wind tunnel model, flight simulator etc. Simulation is the attempt to duplicate the features, appearance, and characteristic of the real system The idea behind simulation is threefold: 1. To imitate a real world situation mathematically 2. Then to study its properties and operating characteristics, and 3. Finally to draw conclusions and make action decisions based of the simulations POM-ris-YAI

4. Ris What is simulation Most of the large companies in the world use simulation models, such as in Table F.1 Table F.1 Some applications of simulation Ambulance location and dispatching Bus scheduling Assembly line balancing Design of library operations Parking lot and harbor design Taxi, truck, and railroad dispatching Distribution system design Production facility scheduling Scheduling aircraft Plant layout Labor-hiring decisions Capital investments Personnel scheduling Production scheduling Traffic-light timing Sales forecasting Voting pattern prediction Inventory planning and control POM-ris-YAI

5. Ris The process of simulation • Define the problem. • Introduce the important variables associated with the problem. • Construct a numerical model. • Set up possible courses of action for tasting. • Run the experiment. • Consider the results (possible modifying the model or changing data inputs). • Decide what course of action to take. POM-ris-YAI

6. Ris The process of simulation Define the problem Introduce variables Construct model Specify values of variables Conduct simulation Examine results Select best course POM-ris-YAI

7. Ris The main advantages of simulation are as follows • Simulation is relatively straightforward and flexible • It can be used to analyzed large and complex real-world situations that cannot be solved by conventional operations management models. • Real world complications can be included that most OM models cannot permit. • Time compression is possible. • Simulation allows “what-if” type of questions. • Simulations do not interfere with real world system • Simulation can study the interactive effects of individual components or variables in order to determine which one is important. POM-ris-YAI

8. Ris The main disadvantages of simulation are as follows • Good simulation models can be very expensive. • It is a trial-and-error approach that may produce different solutions in repeated runs. • The simulation model does not produce answer without adequate, realistic input. • Each simulation model is unique. POM-ris-YAI

9. Ris Monte Carlo Simulation Monte Carlo method is a simulation technique that uses random elements when chance exists in their behavior The technique break down into five simple steps: 1. Establish probability distributions 2. Building a cumulative probability distribution for each variable. 3. Setting random-number intervals 4. Generating random numbers. 5. Simulating the experiment. POM-ris-YAI

10. Ris Example F.1 Simulation tire demand at a store To establish a probability distribution for tire, we assume that historical demand is a good indicator of future outcomes. Table F.2 Demand for Barry’s Auto Tire POM-ris-YAI

11. Example F.1 Simulation tire demand at a store Table F.3 The Assignment of Random-Number interval for Barry’s Auto Tire POM-ris-YAI

12. Example F.1 Simulation tire demand at a store Table F.3 The Assignment of Random-Number interval for Barry’s Auto Tire Total 10 days demand: 39 Average daily demand: 39/10 = 0.30 From table F3 Expected demand = sum {(probability of i units) (demand of i units)} = 0.05x0 + 0.1x1 + 0.2x2 + 0.3x3 + 0.2x4 + 0.15x5 = 2.95 If the simulation was repeated hundreds or thousands time, the average simulated demand would be nearly the same as the expected demand POM-ris-YAI

13. Ris Example F.2 Simulation of queuing problem Table F.5 Overnight Barge Arrivals Rates and Random-number Intervals POM-ris-YAI

14. Ris Example F.2 Simulation of queuing problem Table F.6 Unloading Rates and Random-number Intervals POM-ris-YAI

15. Ris Example F.2 Simulation of queuing problem Table F.7 Queuing Simulation of Port of New Orleans Barge Unloading POM-ris-YAI

16. Ris Example F.2 Simulation of queuing problem The POM managers will likely be interested in at least three useful and important pieces of information: Average number of barges delayed to the next day : = 20 delays / 15 days = 1.33 barges delayed per day Average number of nightly arrivals = 41 arrivals / 15 day = 2.73 arrivals per night Average number of barges unloaded each day = 39 unloadings / 15 days = 2.63 unloadings per day POM-ris-YAI

17. Example F.3 An Inventory simulation with 2 variables Table F.8 Probabilistic and Random-number Intervals for Daily Ace Drill Demand POM-ris-YAI

18. Example F.3 An Inventory simulation with 2 variables Table F.9 Probabilistic and Random-number Intervals for Reorder Lead Time POM-ris-YAI

19. Example F.3 An Inventory simulation with 2 variables Table F.10 Simkin Hardware’s First Inventory Simulation. Order Quantity = 10 units, Reorder Point = 5 units POM-ris-YAI

20. Ris Example F.3 An Inventory simulation with 2 variables • Table F.10 was filled in by proceeding 1 day (or line) at a time, working from left to right. It is a four steps process: • Begin each simulated day by checking to see whether any ordered inventory has just arrived. • Generate a daily demand from the demand probability distribution by selecting a random number • Compute: Ending inventory = beginning inventory minus demand. If on hand inventory is in-sufficient to meet the days demand, satisfy as much demand as possible and note the number of lost sales • Determine whether the day’s ending inventory has reached the reorder point (5 units). If it has, and there are not outstanding order, place an orders. Lead time for a new order is simulated by choosing a random number and using the distribution Table F.9 POM-ris-YAI

21. Ris Example F.3 An Inventory simulation with 2 variables Summary Average daily ending inventory : 41 total units / 10 days = 4.1 unit per day Average lost sales: 2 sales lost / 10 days = 0.2 unit per day Average number of order placed: 3 orders / 10 days = 0.3 order per day POM-ris-YAI

22. Ris Example F.3 An Inventory simulation with 2 variables Summary Cost for placing order: $ 10 Holding cost per drill: $ 0.5 Cost of each lost sales: $ 8 Daily order cost: (cost of placing 1 order) x (number of orders placed per day) = $ 10 per order x 0.3 order per day = $ 3 Daily holding cost: (cost of holding 1 unit for 1 day) x (aver ending inventory) = $ 0.5 per unit per day x 4.1 units per day = $ 2.05 Daily stockout cost: (cost per lost sale) x (aver number of lost sales per day) = $ 8 per lost sale x 0.2 lost sales per day = $1.6 Total inventory cost: daily order cost + daily holding cost + daily stockout cost = $ 6.65 POM-ris-YAI