## What is Simulation ?

Meaning and Definition of Simulation :

A simulated model may be defined as one which depicts the working of a large scale system of man, machines, materials and information operating over a period of time in a simulated environment of the real world conditions.
Simulation is a numerical solution method that seeks optimal alternatives (strategies) through a trial and error process. The simulation approach can be used too study almost any problem that involves uncertainty, i.e., one or more decision variables can be represented a probability distribution, like decision making under risk.

According to Shannon :
"Simulation is the process of designing a model of a real system and conducting experiments with this model for the purpose of understanding the behavior (with the limits imposed by a criterion or set of criteria) for the operation of the system".

According to Levin & Kirk Patrick :
"Simulation is an appropriate substitute for mathematical evaluation of a model in many situations. Although it too involves assumptions, they are manageable. The use of simulation enables us to provide insights into certain management problem where mathematical evaluation of a model is not possible."

#### Contents :

1. Meaning and Definition of Simulation.
2. Scope of Simulation Techniques.
3. Phases of Simulation.
4. Application of Simulation.
5. Types of Simulation.
6. Models of Simulation.
7. Benefits of Simulation.
8. Limitations of Simulation.
9. Monte Carlo Simulation Procedure.
10. Random Digits and Methods of Generating Probability Distribution : Example.

### Scope of Simulation Techniques :

Scope of Simulation in different area is as follows :

1) Healthcare (Clinical) Simulators :
Medical health simulators are developed and deployed to teach healing and diagnostic procedures. It is also used to teach medical concepts and decision making to personnel who are involved in the professions.

2) Computer Simulators :
Simulators have been proposed as an ideal tool for assessment of students for clinical skills. Programmed patients and simulated clinical situations, including mock disaster drills, have been used extensively for education and evaluation. These "lifelike" simulations are expensive, and lack reproducibility. A fully functional "3Pi" simulator would be the most specific tool available for teaching and measurement of clinical skills. Such a simulator meets the goals of an objective and standardised examination for clinical competence. This system is superior to examinations that use "standard patients because it permits the quantitative measurement or competence, as well as reproducing the same objective findings.

3) Military Simulations :
Military simulations are e models in which theories of warfare can be tested and advanced without the need for actual hostilities. It is also known as war games. They exist in different forms with various degree of realism.

4) Finance Simulations :
In financing computer simulation are often used for scenario planning.

5) Flight Simulators :
A flight simulator is used for the training of the pilots on the ground. A pilot gets permission by this technique to crash his simulated "aircraft" without being hurt. Pilots are trained with the use of flight simulators to operate aircraft in extremely dangerous situations, such as landing with no engines, or complete electrical or hydraulic failures. High-fidelity visual systems and hydraulic motion systems are included in most advanced simulators. The simulator is normally cheaper to operate than a real trainer aircraft.

6) Engineering, Technology or Process Simulation :
Simulation is an important feature in engineering systems or any system that involves many processes, For example, in electrical engineering, delay lines may be used to simulate propagation delay and phase shift caused by an actual transmission line. Similarly, dummy loads may be used to simulate impedance without simulating propagation, and is used in situations where propagation is unwanted. A simulator may imitate only a few of the operations and functions of the unit it simulates.

### Phases of Simulation :

Step 1: Identify the Problem :
If an inventory system is being simulated, then the problem may concern the determination of the size of order (number of units to be ordered) when inventory level falls up to recorder level (point).

Step 2 : i) Identify the Decision Variables
ii) Decide the Performance Criterion (Objective) & Decision Rules
For example, demand (consumption rate), lead time and safety stock are identified as decision variables in inventory problem. These variables shall be liable to measure the performance of the system in terms of total inventory cost under the decision rule - when to order.

Step 3 : Construct a Numerical Model :
Construct a model which is possible to be analysed on the computer. Sometimes the model is written in a specific simulation language which is suitable for the given problem under analysis.

Step 4 : Validate the Model :
It is ensuring that the model should be representing the system truly which is analysed and the result will be reliable.

Step 5 : Design the Experiments :
Design the experiments with the, help of simulation model by listing particular values of variables to be tested (i.e. list of courses of action for testing) at each trial (run).

Step 6 : Run Simulation Model :
For obtaining the results in the form of operating characteristics run the model on the computer.

Step 7 : Examine the Results in Terms of Problem Solution :
Results are examined as well as their reliability and correctness. Best course of action is selected after completing the simulation process otherwise desired changes are done in model decision variables parameters or design, and return to step 3.

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### Applications of Simulation :

The range of applications of computer simulation method is very wide, since simulation represents an approach rather than an application of a special technique like linear programming. Some of the business applications are as follows :

1) Queuing Problems :
If the distribution of inter arrival times and service times are known then the queuing theory provides the techniques which are used to determine the measures of effectiveness such as queue length, average waiting time, etc. The problem of establishing a balance between the costs can be determined when these costs are assigned to waiting time of customers and idle time of the service facility.
Sometimes it is not possible to solve various queuing problems with the use of analytical methods. In this case simulation is the only possible method to solve these types of problems. For solving complex simulation problem Monte Carlo simulation is the important technique. GPSS program is basically structured for queuing simulation model.

2) Job Shop Scheduling :
Deterministic times for different operations of a given order are involved in the development of a number of job shop simulation programmes. In spite of the absence of probabilistic elements in such a model, the high degree of interaction between orders due to their different processing times for similar operations and to different order operation sequences, makes it difficult to predict the waiting time for a particular order at any given work center. Orders must be scheduled at different work centers with an allowance for waiting time. Simulation is the best suitable technique to make reasonable and accurate estimate of such allowances which are required for efficient scheduling of orders. With the use of simulation technique it is possible to forecast the manpower and machine workloads.

3) Inventory Problems :
In various inventory problem especially storage problem cannot solved analytically because the distribution followed by demand or. supply is very complex. The solution can be obtained by using simulation technique. With the use of past data it is possible to determine the probability distribution of the input and output functions and the inventory system run artificially by generating the future observations on the assumption of the same distributions. Trial and error method is used to find the decision for the optimisation problems.
With the help of random numbers the artificial sample for the future can be generated. The demand during lead time to provide adequate service to customers is the basis of the selection of reorder point in inventory control. Simulation technique can be used to investigate the effect of different inventory policies if the lead time and the demand of inventory per unit of time are random variables.
For wider applicability as well as those for specialised use a lot of work has been done to develop inventory simulation models. In various inventory problem queuing characteristics can be seen. For example, a problem concerned with the optimal inventory of rental cars can be viewed as a queuing problem where the servers are cars.

4) Network Management :
A number of network simulation models have also been developed. For example, simulation of probabilistic activity times in PERT networks. The critical path and the project duration can be evaluated with a randomly selected activity times for each activity. The probability distribution of project completion time and the probability that each of given activity on the critical path can be determined by repeating the process.

5) Financial Management :
Financial studies involving risky investment and profit planning.

6) Marketing Management :
Marketing decisions faces uncertainties in various stages such as in new product introduction. Simulation methods are very important for solving marketing problems which have probabilistic outcomes. Generation off random numbers is used to predict the outcomes and results are analysed in terms of the specific decisions the management must make. Simulation is applicable in marketing in various ways such as new product planning.

### Types of Simulation :

There are several types of simulation. A few of them are listed below :

1) Deterministic and Probabilistic Simulation :
If a process is very complex or consist of multiple stages with complicated (but known) procedural interactions between them then deterministic simulation is used. The performance measures of this type of system would be extremely detailed and time consuming. The process which is formulated as a simulation with fixed procedures (algorithms) provides the determination of output and performance measure in a straightforward manner. A probabilistic simulation follows a certain probability distribution because one or more independent variables (e.g., the arrival rate of customers at a service-window) is probabilistic.

2) Time Dependent and Time Independent Simulation :
In time independent simulation it is not necessary to know the exact time of happening the event. For example, in an inventory control situation, one may know that the demand of the inventory is five units per day, but it is not necessary to know that the in which time the items was demanded. In time dependent simulation it is required to know the exact time when the event is likely to occur. For example, in a queuing situation the precise time of arrival should be known.

3) Visual Interactive Simulation :
Computer graphic displays are used by the visual interactive simulation to present the consequences of change in the value of input variation in the model. When the simulation is running then the decisions are implemented interactively. Dynamic systems that evolve over time in terms of animation can be shown by these simulations. The progress of the simulation is watched by the decision-maker in an animated form on a graphics terminal and can change the simulation as it progress.

Several participants are involved in a business game simulation model and they are required to play a role in a game that simulates a realistic competitive situation. Individuals or teams compete to achieve their goals, such as profit maximisation, in competition or cooperation, with the other individuals or teams. The few advantages of business games are :
• The knowledge and experience gained by the participants are more memorable then passive instruction and they learn faster.
• To face the special circumstances complexities, inter-functional dependencies, unexpected events, and other such factors can be introduced into the game.
• The time compression - allowing many years of experience in only minutes or hours - lets the participants try out actions that they would not be willing to risk in an actual situation and see the result in the future.
• Provide insight into the behavior of an organisation. The dynamics of team decision-making style highlight the roles assumed by individuals on the teams, the effect of personality types and managerial styles, the emergence of team conflict and cooperation, and so on.

5) Corporate and Financial Simulations :
Corporate planning, especially the financial aspects uses the corporate and financial simulation. The models incorporate production, finance, marketing, and possibly other functions, into one model which can be deterministic or probabilistic when risk analysis is desired.

### Simulation Models :

Simulation models are mainly of two types :

1) Continuous Models :
Continuous models are used for the system whose behavior changes continuously with time. Difference differential equations are used by this model to describe the interactions among the different elements of the system. A typical example deals with the study of world population dynamics.

2) Discrete Models :
Discrete models are used for the study of waiting lines, with the objective of determining average waiting time and the length of the queue. When a customer enter or leaves the system then these measures would be changed. At all other instants, nothing from the standpoint of collecting statistics occurs in the system. The instants at which changes take place occur at discrete points in time, giving rise to the name discrete event simulation.

Broadly simulation models can be classified into following four categories :

i) Deterministic Models :
In these models, input and output variables should not be random variables and exact functional relationship is used to describe the models.

ii) Stochastic Models :
In these models, probability functions are used to describe at least one of the variables or functional relationship.

iii) Static Models :
Representation of a system at a particular time or representation of a system in which time does not play any role is known as static simulation model. Monte Carlo Models is an example of static simulation.

iv) Dynamic Models :
A system which changes over the time is represented by a dynamic simulation model such as conveyor system in a factory.

### Benefits of Simulation :

1. In various cases, mathematical programming and experimentation with the actual system are unable to solve various complex important managerial decision problems and if it is possible then it will be costly. In simulation solution is obtained by experimentation with a model of the system with affecting the real system.
2. With the help of simulation management can predict the occurrence of difficulties and bottlenecks due to the introduction of new machines, equipment or process. Thus, simulation eliminates the requirement of costly trial and error method of trying out the new concept on real methods and equipment.
3. Operating personnel and non-technical managers can easily understand the simulation technique because it is relatively free from mathematics. This helps in getting the propose plans accepted and implemented.
4. Simulation models are comparatively flexible and can be changed according to the changing environments of the real situation.
5. Computer simulation can increase the performance of a system over several years and large calculations are done in few minutes of computer running time.
6. In comparison to mathematical model Simulation technique is easier to use and it is superior technique to the mathematical analysis.
7. In the operations of complex plans, simulation is used for training the operating and managerial staff. It is very important technique to train the people before putting into their hands in the real system. Simulated exercises have been developed to teach the trainee for gaining sufficient exercise and experience.

### Limitations of Simulation :

1. Simulation does not produce optimum results. When the model deals with uncertainties, the results of simulation are only reliable approximations subject to statistical errors.
2. Quantification of the variables is another difficulty. In a number of situations it is not possible to quantify all the variables that affect the behavior of the system.
3. In very large and complex problems, the large number of variables and the inter-relationships between them make the problem very unwieldy and hard to program. The number of variables may be too large and may exceed the capacity of the available computer.
4. Simulation is, by no means a cheap method of analysis. In a number of situations, simulation is comparatively costlier and time consuming.

Monte Carlo Simulation :

The Monte Carlo simulation technique is based on the technique that the given system under analysis is replaced by a system described by some known probability distribution and then random samples are drawn from probability distributing by means of random numbers. An empirical probability distribution can be constructed if it is not possible to explain a system in terms of standard probability distribution such as Normal, Poisson, Exponential, Gamma, etc.

### Monte Carlo Simulation Procedure :

The Monte Carlo simulation technique consists of the following steps :

Step 1 : Clearly Define the Problem :
• Identify the objectives of the problem.
• Identify the main factors which have the greatest effect on the objectives of the problem.

Step 2 : Construct an Appropriate Model
• Specify the variables and parameters of the model.
• Formulate the appropriate decision rules, i.e., state the conditions under which the experiment is to be performed.
• Identify the type of distribution that will be used - models used either theoretical distributions or empirical distributions to state the patterns the occurrence associated with the variables.
• Specify the manner in which time will change.
• Define the relationship between the variables and parameters.

Step 3 : Prepare the Model for Experimentation :
• Define the starting conditions for the simulation.
• Specify the number of runs of simulation to be made.

Step 4 : Using Steps 1 to 3, Experiment with the Model :
• Fine a coding system that will correlate the factors defined in Step 1 with the random numbers to be generated for the simulation.
• Select a random number generator and create the random numbers to be used in the simulation.
• Associate the generated random numbers with the factors identified in Step 1 and coded in Step 4 (a).

Step 5 : Summarize and Examine the Results Obtained in Step 4.

Step 6 : Evaluate the Results of the Simulation :
Select the best course of action.

#### Random Digits and Methods of Generating Probability Distribution :

In Monte Carlo Simulation a sequence of random numbers are required to generate which is an integral part o the simulation model. The selection of random observations (samples) from the probability distribution is facilitated by these sequences of random numbers. In a sequence of integer number, a random number is a number between 0 to 9 whose probability of occurrence is same as that of any other number in the sequence. In a simulation model, any decision variable can be represented as a random variable and it is assumed that it must be follow some theoretical probability distribution such as normal, Poisson, exponential etc., or an empirical distribution. Simple arithmetic computation and computer generator is used to generate random numbers which is based on some known probability distributions.

Example :

MINITRANS is concerned with its local mini-bus maintenance facilities. Particular interest has been expressed regarding the time that buses are being withheld from service. Since their principal activity is providing maintenance service for the mini-buses based at the local bus terminal, management naturally wants to maintain a good record, not only for reliability of service but also for the rate at which service is performed.
A study of the maintenance service facilities offered by MINITRANS revealed that the reliability factor was excellent. But service, no information was provided regarding the service rate, a second study was initiated to gather data regarding the number of buses requiring service and the rate at which buses are being serviced. The results of this study, gathered over a 40-day period, are presented in Table (service requests) and Table (units completing service) :

Table : Requests for Service

 Number of Buses Requesting Service Frequency of request for service Probability 0 2 0.05 1 4 0.10 2 2.4 9.60 3 4 0.10 4 2 0.05 5 4 0.10

Table : Completed Service

 Number of Buses Completing Service Frequency of request for service Probability 0 4 0.10 1 8 0.20 2 2.0 9.50 3 4 0.10 4 2 0.05 5 2 0.05

At the current time, MINITRANS has one maintenance team that does the required work. All incoming mini-buses are serviced on a first-come, first-served basis, and work is done on a 24-hours schedule.
Using the given data, simulate the arrival service pattern at the company's maintenance facility. (In the simulation, assume that the service group is equivalent to a single service facility). From this simulation determine the means number of units that must be held over to the following day awaiting service.

Solution :

Step 1 : Define the Problem
The company's objective is to determine, through simulation, the rate at which service is being performed and the mean daily number of un-serviced units. Thus data must be generated for two variables: a simulated daily number of units arriving for service and a simulated daily number of units completing service.

Step 2 : Construct an Appropriate Model

i) Identify the Variables and the Parameters :
As noted in Step 1, the variables are the daily number of units which arrive for service and the units which complete service. There are no parameters to be considered.

ii) Formulate an Appropriate Decision Rule :
The simulation should conform to the rule now observed in practice, that is, buses are serviced on a first-come, first-served basis. By implication, units that are not completed in one day are held over until the next day and incoming units simply join the queue.

iii) Identify the type of Distribution that will be used :
Tables provide empirical probability distributions on which the simulation can be based. (If we were given theoretical distributions, as Poisson arrivals and exponential service times, it would have been necessary to calculate the appropriate probabilities under these as sump Lions).

iv) Specify the Manner in which time will be Changed :
For this problem, time is to be measured in fixed increments of one day each.

v) Define the Relationships between Variable and Parameters :
The basic relationship for this problem is one in which the number of buses held over equals the total number of buses waiting to be serviced minus the number of buses actually serviced. That is,
Number held over from previous day + new arrivals = total buses to be serviced.
Total buses to be serviced - number of buses actually serviced = number of buses held over.

Step 3: Prepare the Model for Simulation

i) Specify the Initial Values of the Parameters and the Variables :
At the start of the simulation process, assume that the maintenance facility is empty. When bus arrives for service, work on it will begin immediately

ii) Specify the Number of Simulation Runs to be Made :
According to the problem, a ten-day period is to be simulated: thus there will be ten runs.

Step 4 : Using the Data of Steps 1 - 3 Experiment with the Model

i) Define a coding system that will correlate the factors identified in Step 1 to the random numbers that will be generated :
The coding system for the arrival distribution is shown in Table, the coding system for the service distribution is shown in table.

Table : Coded Arrival Pattern

 Number of Buses Requesting Service Probability Random Number Interval 0 0.05 00-04 1 0.10 05-14 2 0.60 15-74 3 0.10 75-84 4 0.05 85-89 5 0.10 90-99

ii) Select a Random Number Generator :
Choose the tables of random number and take first ten numbers. We let the first two digits relate to the arrival of bus for service and let the last two digits relate to completing service, we get table.

Table : Coded Service Pattern

 Number of Buses Serviced Probability Random Number Interval 0 0.10 00-09 1 0.20 10-29 2 0.50 30-79 3 0.10 80-89 4 0.05 90-94 5 0.05 95-99

iii) Generate random numbers to be used in the simulation in the simulation. see column 2 of table.

Table : Generate Random Numbers

 Day Random Number Generated Arrival Random Number of Service Completions 1 341069 34 69 2 543075 54 75 3 423280 42 80 4 551418 55 18 5 792165 79 65 6 063130 06 30 7 350156 35 56 8 707270 70 70 9 272184 27 84 10 863034 86 34

iv) Correlate the generated random numbers with the factors identified in step 1 and coded in step 4(a).
Correlating The generated random numbers with the data of table yield in simulated arrival service value shown in table column 2 and 4.

v) Summarised results in an appropriate table.

Table : Generated Arrival and Service Completion

 Day Random Number Generated Number Of Arrival Random Number Generated Number Of Service Completions 1 34 2 69 2 2 54 2 75 2 3 42 2 80 3 4 55 2 18 1 5 79 3 65 2 6 06 1 30 2 7 35 2 56 2 8 70 2 70 2 9 27 2 84 3 10 86 4 34 2

Table : Ten-Day Simulation

 Day Number Held over from Previous Year Total Number Number Services Number Of Buses Held over Arrival Awaited Service 1 0 2 2 2 0 2 0 2 2 2 0 3 0 2 2 3 0 4 0 2 2 1 1 5 1 3 4 2 2 6 2 1 3 2 1 7 1 2 3 2 1 8 1 2 3 2 1 9 1 2 3 3 0 10 0 4 4 2 2 Total 6 22 28 21 8 Average 0.6 2.2 2.8 2.1 0.8

Step 5 : Evaluate the result on the basis of the ten day simulation. MINITRANS has an average service rate of 2.1 buses per day. With a simulated arrival rate that average 2.2 buses per day, the backlog average 0-8 buses, bus per day.

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