Lecture 2

1. Lecture 2 Model Classification and Steps in a Simulation Study

2. Definition of Simulation • Simulation is the imitation of an operation of a real-world process or system over time. • Simulation is a method of understanding, representing and solving complex interdependent system. • Simulation is the process of designing a model of a real system and conducting experiments with this model for the purpose either of understanding the behavior of the system or of evaluating various strategies (with the limits imposed by a criterion or a set of criteria) for the operation of the system.

3. Definition of Simulation(cont’) • Simulation in general is to pretend that one deals with a real thing while really working with an imitation. • A flight simulator on a PC is computer model of some aspects of the flight: it shows on the screen the controls and what the “pilot” (the youngster who operates it) is supposed to see from the “cockpit” (his armchair).

4. When to use Model • To fly a simulator is safer and cheaper than the real airplane. • For precisely this reason, models are used in industry, commerce and military: it is very costly, dangerous and often impossible to make experiments with real systems. • Provided that models are adequate descriptions of reality (they are valid), experimenting with them can save money, suffering and even time.

5. When to use Simulations • Systems which change with time such as a gas station where cars come and go (called dynamic systems) and involve randomness (nobody can guess at exactly which time and next cars should arrive at the station) are good candidates for simulation. • Modeling complex dynamic systems theoretically need too many simplifications and the emerging models may not be therefore valid. • Simulation does not require that many simplifying assumptions, making it the only tool even in absence of randomness.

6. How to simulate? • Suppose we are interested in a gas station. We may describe the behaviour of this system graphically by plotting the number of cars in the station; the state of the system. • Every time a car arrives the graph increases by one unit while a departing car causes the graph to drop one unit. • This graph (called sample path), could be obtained from observation of a real station, but could also be artificially constructed. • Such artificial construction and the analysis of the resulting sample path consists of the simulation.

7. Types of Models • Models can be classified as being mathematical or physical. • A mathematical model uses symbolic notation and mathematical equations to represent a system. • A simulation model is particular type of mathematical model of a system.

8. Type of Simulation • Simulation models may be further classified as being: • Static model or Dynamic model • Deterministic model or Stochastic model • Discrete model or Continuous model

9. Static vs Dynamic • Static models and dynamic models are classification by the dependency on time • A static simulation model, sometimes called a Monte Carlo simulation, represents a system at a particular point in time. • For example, Mark Six, inventory level • Dynamic simulation models represent systems in which state of the variables change over time. The simulation of a bank from 9:00am to 4:00pm is an example of a dynamic simulation. • For example, service time, waiting time.

10. Deterministic vsStochastic • Classification by the nature of the variables • Simulation models that contain no random variables are classified as deterministic. • For example, deterministic arrivals would occur at a dentist’s office if all arrived at the scheduled appointment time. • A stochastic simulation model has one or more random variables as input. • Random inputs lead to random outputs. • For example, random arrival, random product demand, random incoming calls.

11. Deterministic vsStochastic (cont’) • Since the outputs are random, they can be considered only as estimates of the true characteristics of a model. • For example, the simulation of a bank would usually involve random interarrival times and random service times.

12. Discrete vs Continuous • Discrete and continuous models are defined in an analogous manner, classification by system nature. • A discrete model is one in which the state variable(s) change only at a discrete set of points in time. • The bank is an example of a discrete system, since the state variable, the number of customers in the bank, changes only when a customer arrives or when the service provided a customer is complete. • Other examples, busy/idle counter, occupied/free machine.

13. Discrete vs Continuous(cont’) • A continuous model is one in which the state variable(s) change continuously over time. • An example is the head of water behind a dam. During and for some time after a rain storm, water flows into the lake behind the dam. • Water is drawn from the dam for flood control and to make electricity. • Evaporation also decreases the water level. • But, continuous system can be approximated by a discrete-event system, depending on the expected preciseness and the objective of the study.

14. Applications - Service Applications • Staffing • A bank manager might determine that three tellers on duty results in a tolerable wait for service during most of the day, but that her customers’ “time in queue” is too long during the busy lunch hour and in the late afternoon. • She could then assess the impacts of adding additional part-time help during the peak hours.

15. Applications - Service Applications (cont’) • Procedure Improvement • Many organizations have learned that internal consumers are customers. • In an effort to improve the responsiveness of their administrative and support functions many of these companies are using simulation to model revised procedures designed to streamline processing of paperwork, telephone calls and other daily transactions.

16. Advantages ofSimulation • New policies, operating procedures, decision rules, information flows, organizational procedures, and so on can be explored without disrupting ongoing operations of the real system. • New hardware designs, physical layouts, transportation systems, and so on, can be tested without committing resources for their acquisition. • Hypotheses about how or why certain phenomena occur can be tested for feasibility. • Time can be compressed or expanded allowing for a speedup or slowdown of the phenomena under investigation.

17. Advantages ofSimulation (cont’) • Insight can be obtained about the interaction of variables. • Insight can be obtained about the importance of variables to the performance of the system. • Bottleneck analysis can be performed indicating where work-in-process, information, materials, and so on are being excessively delayed. • A simulation study can help in understanding how the system operates rather than how individuals think the system operates. • “What-if” questions can be answered.

18. Disadvantages ofSimulation • Model building requires special training. • Simulation results may be difficult to interpret. • Simulation modeling and analysis can be time consuming and expensive. Skimping on resources for modeling and analysis may result in a simulation model or analysis that is not sufficient for the task. • Simulation is used in some cases when an analytical solution is possible, or even preferable. This might be particularly true in the simulation of some waiting lines where closed-form queueing models are available.

19. Defense of Simulation • Vendors of simulation software have been actively developing packages that contain all or part of models that need only input data for their operation. • Many simulation software vendors have developed output analysis capabilities within their packages for performing very thorough analysis. • Simulation can be performed faster today than yesterday, and even faster tomorrow. This is attributable to the advances in hardware that permit rapid running of scenarios.

20. Defense of Simulation (cont’) • Closed-form models are not able to analyze most of the complex systems that are encountered in practice.

21. Steps in aSimulation Study Problem formulation Experimental design Setting of objectives and overall project plan Production runs and analysis Model Conceptualization Data Collection More runs? Model translation Documentation and reporting Verified? No Yes Implementation Validated? No No Yes

22. Steps in aSimulation Study (cont’) • Problem formulation • If the statement is provided by the policy makers, or those that have the problem, the analyst must ensure that the problem being described is clearly understood. If a problem statement is being developed by the analyst, it is important that the policy makers understand and agree with the formulation. • Setting of objectives and overall project plan • The objectives indicate the questions to be answered by simulation. The overall project plan should include a statement of the alternative systems to be considered, and a method for evaluating the effectiveness of these alternatives.

23. Steps in aSimulation Study(cont’) • Model conceptualization • This is another important and difficult subject. The basic steps are to consider all the related factors first, then evaluate each one (keep or ignore) and reach the final model. • Data collection • The more data you have  the more complete information you have  the more precise model you can build  the better solution you would get. • Model translation • Program the model into a computer language. Simulation languages are powerful and flexible. In most cases, some computer software packages are involved. The model development time is greatly reduce. Furthermore, software packages have added features that enhance their flexibility.

24. Steps in aSimulation Study(cont’) • Verified? • Verification pertains to the computer program prepared for the simulation model. Is the computer program performing properly? If the input parameters and logical structure or the model are correctly represented in the computer, verification has been complete. • Validated? • Validation is the determination that a model is an accurate representation of the real system. Validation is usually achieved through the calibration of the model, an iterative process of comparing the model to actual system behaviour and using the discrepancies between the two, and the insights gained, to improve the model.

25. Steps in aSimulation Study(cont’) • Experimental design • The alternatives that are to be simulated must be determined. For each system design that is simulated, decisions need to be made concerning the length of the initialization period, the length of simulation runs, and the number of replications to be made of each run. • Production runs and analysis • Production runs, and their subsequent analysis, are used to estimate measures of performance for the system designs that are being simulated. • More runs? • The analyst determines of additional runs are needed and what design those additional experiments should follow.

26. Steps in aSimulation Study(cont’) • Documentation and reporting • Program documentation: • If the program is going to be used again by the same or different analysts, it may be necessary to understand how the program operates. • The model users can change parameters at will in an effort to determine the relationships between input parameters and output measures of performance, or to determine the input parameters that “optimize” some output measure of performance. • Progress report: • It provides the important written history of a simulation project.

27. Steps in aSimulation Study(cont’) • Implementation • The success of the implementation phase depends on how well the previous eleven steps have been performed.