What is Simulation
A simulation model is a mathematical model that calculates
the impact of uncertain inputs and decisions we make on
outcomes that we care about, such as profit and
loss, investment returns, etc.
A simulation model will include:
inputs that are uncertain numbers/ uncertain
Intermediate calculations as required
Model outputs that depend on the inputs -- These are
Simulation is imitation of some real thing, or a process.
act of simulating something generally involves
representation of certain
key characteristics or
of a selected physical or abstract system.
Simulation involves the use of models to represent real life
the process of designing a model of a real
system and conducting experiments with this model for the
purpose of understanding the behavior for the operation of
Simulation techniques can be used to assist management
decision-making, where analytical methods are either not
available or inappropriate.
Typical business problems where simulation could be used to
aid management decision-making are
Advantages of Simulation
It is useful for sensitivity analysis of complex systems.
It is suitable to analyze large and complex real life problems
that cannot be solved by the usual quantitative methods.
It is the remaining tool when all other techniques become
intractable or fail.
It can be used as a pre-service test to try out new policies and
decision rules for operating a system.
Disadvantages of Simulation
Sometimes simulation models are expensive and take a long
time to develop.
Each application of simulation is ad hoc to a great extent.
The simulation model does not produce answers by itself.
It is the trial and error approach that produces different
solutions in repeated runs .It does not generate optimal
solutions to the problems.
Types of Simulation
Time dependent and time independent simulation :
In time dependent simulation know the precise time when the event is likely
to occur, but incase of time independent simulation it is not important to
know the time when the event is occur.
Corporate and financial simulations :
The corporate and financial simulation is used in corporate
planning, especially the financial aspects. The models integrate
production, finance, marketing, and other functions.
Visual interactive simulation :
It uses computer graphic displays to present the consequences of change in
the value of input variations in the model.
Steps of Simulation Process
Identify the problem :
The simulation process is used to solve a problem only when the
assumptions required for analytical models are not satisfied.
Identify the decision variables and decide the performance:
The inventory control situation, the demand, lead time and safety stock
are identified as decision variables and measure the performance.
Construct a simulation model :
For developing a simulation model, an intimate understanding of the
relationships among the elements of the system being required.
Testing and validating the model :
Any simulation model must represent the system under study. This requires
comparing a model with actual system validation process.
Designing of the experiment :
It refers to controlling the conditions of the study, such as the variables to
include. In this situations where observations are taken but the conditions of the
study are not controlled.
Run the simulation model :
The computer to get the results in the form of operating characteristics.
Evaluating the result :
The simulation process is complete, then select the best course of
action, otherwise make desired changes in model decisions variables.
Simulation and Queuing problems.
A major application of simulation has been in the analysis
of waiting line, or queuing systems.
Since the time spent by people and things waiting in line
is a valuable resource, the reduction of waiting time is an
important aspect of operations management.
Waiting time has also become more important because of
the increased emphasis on quality. Customers equate
quality service with quick service and providing quick
service has become an important aspect of quality service
For queuing systems, it is usually not possible to develop
analytical formulas, and simulation is often the only means of
Simulation can hence be used to investigate problems that are
common in any situation involving customers, items or orders
arriving at a given point, and being processed in a specified
Customers arrive in a bank and form a single queue, which feeds
a number of service desks. The arrival rate of the customers will
determine the number of service desks to have open at any
specific point in time
Components of queuing systems
A queue system can be divided into four components
Arrivals: Concerned with how items (people, cars etc) arrive in
Queue or waiting line: Concerned with what happens between the
arrival of an item requiring service and the time when service is
Service: Concerned with the time taken to serve a customer.
Outlet or departure: The exit from the system.
A queuing problem involves striking a balance between the
cost of making reductions in service time and the benefits
gained from such a reduction
Structures of queuing system
There are a number of structures of queuing systems in
We will study only one i.e. single queue – single service point.
Single queue – single service point
Queue discipline is first come – first served.
Arrivals* are random and for simulation this randomness must
be taken into account.
Service times** are random and for simulation this randomness
must be taken into account
*Inter-arrival time: Is the time between the arrival of successive customers in a
**Service time: Is the length of time taken to serve customers
Monte Carlo simulation
The principle behind the Monte Carlo technique is representative
of the given system under analysis by a system
Setting up a probability distribution to be analysed.
Building a cumulative probability distribution for a
Generate random numbers . Assign an appropriate set
of random numbers to represents value or
range(interval) of values each random variable.