Modelling with simulation
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1. Simulation involves mathematically modeling real-world systems to study their properties and make decisions. Monte Carlo simulation specifically models systems with probabilistic elements using random sampling. 2. The document discusses simulation applications, the simulation process, advantages and disadvantages of simulation, the five steps of Monte Carlo simulation, and using simulation to analyze inventory problems by modeling variable demand and lead times. 3. As an example, the document describes Simkin Hardware store simulating an inventory policy of ordering 10 drills with a reorder point of 5 units to minimize total costs.
Modelling with simulation
- 1. Bonifacio H. Hufana Modelling Simulation Learning Objectives • List the advantages and disadvantages of modelling with simulation • Perform the five steps in a Monte Carlo simulation • Simulate an Inventory Problem • Use excel spread sheets to create simulation Simulation • The attempt to duplicate the features, appearance and characteristics of a real system, usually via a computerized model. • Most of the large companies in the world use simulation models. • The simulation model will then be used to estimate the effects of various action. Table 1 Some Application of Simulation • Ambulance Location and Dispatching • Assembly-line Balancing • Parking lot and Harbor Design • Distribution System Design • Scheduling Aircraft • Labor Hiring Desicions • Personnel Scheduling • Traffic Light Timing • Voting Pattern Prediction • Bus Scheduling • Design Library Operations • Taxi, truck and railroad dispatching
- 2. • Production facility scheduling • Plant layout • Capital investments • Production Sceduling • Sales forecasting • Inventory planning and control Simulation The idea behind simulation is threefold: 1. To imitate a real-world situation mathematically; 2. Then to study its properties and operating characteristics; 3. Finally, to draw conclusion and make action decisions based on the results of the simulation. Figure 1: The Process of Simulation Simulation Advantages • It can be used to analyze large and complex real-world situations that cannot be solved by conventional operation management models. • Real-world complications can be included that most OM models cannot permit.
- 3. • “Time compression” is possible. • Simulation allows “what-if?” • Simulations do not interfere with real-world systems. Disadvantages • Good simulation models can take a long time to develop. • Simulation is a repetitive approach that may produce different solutions in repeated runs. • Managers must generate all the conditions and constraints for solution that they want to examine. • Each simulation model is unique. Monte Carlo Simulation • A simulation technique that uses random elements when chance exist in their behavior. • The basis of Monte Carlo simulation is experimentation on chance (or probabilistic) elements by means of random sampling. • The technique breaks down into five steps: 1. Setting up a probability distribution for important variables. Example of variables which are probabilistic in nature are the following: • One common way to establish a probability distribution for a given variable is to examine historical outcomes.
- 4. • We can find the probability or relative frequency for each possible outcome of a variable by dividing the frequency of observation by the total number of observations. 2. Building a Cumulative Probability Distribution for Each Variable. 3. Establishing an interval of ramdom numbers for Each Variable. 4. Generating Random Numbers. • These numbers may be generated for simulation problems in two ways. • If the problem is large and the process under study involves many simulation trials, computer programs are available to generate the needed random numbers. • On the other hand, if the simulation is being done by hand, the number may be selected from a table of random digits. 5. Simulating the Experiment. • We may simulate outcomes of an experiment by simply selecting random numbers from Table 4. It is interesting to note that the average demand of 3.9 tires in this 10 day simulation. It differs substantially from the expected daily demand, which may calculate from the data in Table 3. = (.05)(0) + (.10)(1)+ (.20)(2)+(.30)(3)+(.20)(4) = 0 + .1 + .4 + .9 + .8 + .75 = 2.95 tires However, if this simulation was repeated hundreds or thousands of times, the average simulated demand would be nearly same as expected demand. Simulation and Inventory Analysis • In real-world inventory situations, demand and lead time are variables, so accurate analysis becomes extremely difficult to handle by any means than simulation.
- 5. • Sample Problem: • Simkin’s Hardware Store, in Reno, sells Ace model electric drill. Daily demand for this particular product is relatively low but subject to some variability. Lead times tend to be variable as well. Mark Simkin wants to develop a simulation test an inventory policy ordering 10 drills, with a reorder point of 5. In other words, every time the on-hand inventory level at the end of the day is 5 or less, Simkin will call his supplier that evening and place an order for 10 more drills. Simkin notes that if the lead time is 1 day, the order will not arrive the next morning but rather at the beginning of the following workday. Stockouts become lost sales, not backorders. • • *APPROACH: Simkin wants to follow the 5 steps of Monte Carlo simulation process. • He wants to make a series of simulation runs, trying out various order quantities and reorder points, to minimize his total inventory cost for the item. • Solution: Over the past 300 days, Simkin has observed the sales shown in column 2 of Table 5. He converts this historical frequency into a probability distribution for the variable daily demand(column 3). A cumulative probability distribution is formed in column 4 of Table 5. Finally, simkin establishes an interval of random numbers to represent each possible daily demand(column 5). • Simkin Hardware’s First Inventory Simulation. Wherein Order Quantity: 10 Units; Reorder Point: 5 Units •