Simulation Department of Industrial Engineering Anadolu University Onur Kaya END 201, Ext: 6439 onur_kaya@anadolu.edu.tr

Some questions What comes to your mind when you hear the word “simulation”?

What is simulation? Wikipedia says: “Simulation is the imitation of the operation of a real-world process or system over time. The act of simulating something first requires that a model be developed; this model represents the key characteristics or behaviors/functions of the selected physical or abstract system or process. The model represents the system itself, whereas the simulation represents the operation of the system over time.”

Some questions What comes to your mind when you hear the word “simulation”? Have you seen simulations in your life before?

Examples Computer games? Flight simulators? ...

Some questions What comes to your mind when you hear the word “simulation”? Have you seen simulations in your life before? Why do you think we need simulation in IE?

How would you calculate how much you are going to wait in a queue? Any assumptions? Are they valid? How can we check their validity?

How would you calculate how much you are going to wait in queues if you visit Disneyland?

A queueing network? How to analyze them analytically? Assumptions?

More questions on If you are a visitor: How would you calculate how much you are going to wait in queues? … If you are a manager of Disneyland: How would you calculate the effect of having one more attraction point on the queue lengths of all other points? If you are a manager of Disneyland: How would you decide on the effects of the entrance prices?

Other complicated systems? Hospitals Factories Inventory systems Project Management Logistics, supply chain and distribution systems Transportation models and traffic Biological and cellulary systems Risk analysis in finance, insurance, options pricing, portfolio analysis etc. Call centers Large scale systems such as internet backbone, wireless networks etc. ….. http://wintersim.org

The Nature of Simulation Most real-world systems are too complex to allow realistic models to be evaluated analytically. These models are usually studied by means of simulation. First, see whether you can solve the problem analytically; if you cannot, then use simulation. Simulation is the technique that imitates the operations of a complex real-world system where a computer is generally used to evaluate a model numerically, and data are gathered in order to estimate the desired true characteristics of the model.

The Nature of Simulation Statistical analysis often uses data that is gathered in the past. Simulation is based on statistical analysis of data that is generated on the future observations of a system by imitating its operations. Simulation is one of the most widely used techniques in operations research, management science and industrial engineering.

Advantages Simulation is often the only type of investigation for complex real-world systems with stochastic elements that cannot be analytically evaluated. It allows one to estimate the performance of a system under a projected set of operating conditions. Alternative proposed system designs or alternative operating policies can be compared via simulation. There is better control over experimental conditions in simulation than there is in experimenting with the system itself. Simulation allows one to study the system with a long time frame due to time compression.

Disadvantages Each run of a simulation run provides an estimate and not the exact value of model characteristics. An analytical model and its solution, if available, is always preferable. Simulation models are often expensive and time-consuming to develop. The large volume of numbers produced or the persuasive impact of a realistic animation often creates a tendency to place more confidence in the results than it is justified.

Which is more likely? Getting a sum of 7 or 8 when two dice are rolled? Getting a 1 or 2 when a single die is rolled? We can easily find the probability of each event and compare. But let’s try to simulate: We need two dice! Since we don’t have a die we need to simulate the dice on a computer.

A static simulation Simulating the roll of two dice. Let U be a continuous random variable in the interval (0,1). Then 6U is a continuous random variable in the interval (0,6). Define FLOOR(x) as the largest integer that is less than or equal to x. Then FLOOR(6U)+1 is a discrete random variable that has the same probability mass function as the number in the roll of a single die! Estimate the expected value of the sum of the numbers that show up when two dice are rolled by simulation. Estimate the probability of getting a sum of 7.

Which is more likely? To estimate probabilities we need to roll the dice several times. To estimate the probability exactly we need to roll the die infinitely many times but this is impractical even for a computer. We’ll roll a finite number of times and then perform a statistical analysis.

Why are most simulation examples much more complicated? The input model is more complicated and requires estimation itself i.e. number of patients arriving to an emergency room in a certain time interval The process is much more complicated Patients are seen by a nurse and directed to a room (if available) The best doctor available has to be directed (she may be busy consulting other patients) The doctor’s exam may take a random amount of time. The next step depends on the exam… We need to emulate the dynamics and then replicate several times for statistical analysis.

Examples Designing and analyzing manufacturing systems Determining hardware and software requirements for communications networks Determining hardware and software requirements for computer systems Designing and operating transportation systems like airports, freeways, ports and subways Evaluating designs and operations of service systems like hospitals, call centers, post offices Reengineering of business processes Determining ordering policies for inventory systems Analyzing financial or economic systems

The systems approach