Introduction to simulation model What is model Model

Introduction to simulation model

What is model? • Model are simulation that try to include the essentials while omitting unimportant details.

Relationship between input and output parameters and model

Classification of problem solving

What is simulation? • Simulation is the process of designing a mathematical or logical model of a real system and then conducting computer based experiments with the model to describe, explain, and predict the behavior of the real system (Stewart & Ronald, 1990).

When should we simulate? • • • The system is complex Uncertainty exists in the variables Real experiments are impossible or costly The processes are repetitive Stakeholders can’t agree on policy

When should not we simulate? • 1. The problem can be solved using common sense • 2. Simulation should not be used if the problem can be solved analytically • 3. Simulation should not be used if it is easier to perform direct experiments • 4. If the costs exceed the savings • 5. Simulation should not be performed if the resources (data, personnel )or time are not available.

Types of simulation • In dynamic simulation models, events occur sequentially over time. Specialized software is required. • In static simulation models time is not explicit and the analysis can be done in Excel spreadsheets.

Monte carlo simulation • The Monte Carlo method is used for static simulation. • The computer creates the values of the stochastic random variables. • The distribution and its parameters are specified. • Samples are repeatedly drawn from each distribution. • Each sample yields one possible outcome for each stochastic variable. • For each output variable, look at percentiles as well as the mean. • For each input variable, look at a histogram to verify that we are sampling from the desired distribution.

Phases of simulation project • Phase I (design) – identify the problem, set objectives, design the model, collect data. • Phase II (execution) – empirical modeling, specify the variables, validate the model, execute the simulation, prepare reports. • Phase III (communication) – explain the findings to decision makers.

Risk assessment • Risk assessment means thinking about a range of outcomes and their probabilities. • Variation is inevitable. • Knowing the 95% range of possible values for the decision variable as well as the “most likely” value m, is the point of risk assessment. • Risk assessment is useful when the model is complex

Distribution • Four probability distributions are used more with static simulation because they correspond to real life and can be easily simulated in Excel.

Distribution

Distribution

Distribution

Distribution

Other Ways to Get Random Data Tools > Data Analysis > Random Number Generation

Example 1: (machine reliability and maintenance) A large milling machine has three different bearings that fail in service. The probabil ity distribution of the life of each bearing is identical. When a bearing fails, the mill stops, a repairperson is called, and a new bearing is installed. The delay time of the repairper son's arriving at the milling machine is also a random variable. Downtime for the mill is estimated at $10 per minute, and the direct on‑site cost of the repairperson is $24 per hour. It takes 20 minutes to change one bearing, 30 minutes to change two bearings, and 40 minutes to change all three. Each bearing costs $30. A proposal has been made to re place all three bearings whenever a bearing fails instead of replacing them individually. Is this proposal worthwhile? Assuming historical data on bearing life has been collected and rounded to the nearest 100 hours, but that the detailed data have been discarded. In addition, the delay time has been estimated judgmentally as either 5, 10, or 15 minutes based on conversations with workers (distribution shown in Table 3. 1). The form of the data forces us to make some assumptions about the simulation model. For example, because bear ing lives are rounded to increments of 100 hours, there will be instances when the model will generate multiple bearing failures at the same time. This is unlikely to occur in prac tice, so we can reasonably assume that no more than one bearing will be replaced at any breakdown time. The baring life distribution shows in Table 3. 2.

Dynamic simulation • In a dynamic simulation, stochastic variables may be discrete (measured only at regular time intervals) or continuous (changing smoothly over time). • Discrete event simulation assesses the system state by a clock at distinct points in time. • A snapshot of the system state at any given moment is observed.

Dynamic simulation • The emphasis in discrete event simulation is on measurements such as Arrival rates Service rates Length of queues Waiting time Capacity utilization System throughput

• Examples for discrete event simulation with Arena see extra sheet.