UNIT 3 SIMULATION
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purpose of designing the system or modifying behaviour. In other words, simulation is a tool that builds a model of a real operation that is to be investigated, and then feeds the system with externally generated data. We generally distinguish between deterministic and stochastic simulation. The difference is that the data that are fed into the system are either deterministic or stochastic. This chapter will deal only with stochastic simulation, which is sometimes also referred to as Monte Carlo simulation in reference to the Monte Carlo Casinos and the (hopefully) random outcome of their games of chance.
According to Gupta and Hira (2012), simulation is an imitation of reality. “They further stated that simulation is the representation of reality through the use of models or other device which will react in the same manner as reality under given set of conditions. Simulation has also been defined the use of a system model that has the designed characteristics of reality in order to produce the essence of actual operation. According to Donald G. Malcom, a simulated model may be defined as one which depicts the working of a large scale system of men, machine, materials, and information operating over a period of time in a simulated environment of the actual real world condition.
3.2 Advantages of Simulation Technique
When the simulation technique is compared with the mathematical programming and slandered probability analysis, offers a number of advantages over these techniques. Some of the advantages are:
1. Simulation offers solution by allowing experimentation with models of a system without interfering with the real system.
Simulation is therefore a bypass for complex mathematical analysis.
2. Through simulation, management can foresee the difficulties and bottlenecks which may come up due to the introduction of new machines, equipment or process. It therefore eliminates the need for costly trial and error method of trying out the new concept on real methods and equipment.
3. Simulation is relatively free from mathematics, and thus, can be easily understood by the operating personnel and non-technical managers. This helps in getting the proposed plan accepted and implemented.
3.3 Application of Simulation
Simulation is quite versatile and commonly applied technique for solving decision problems. It has been applied successfully to a wide range of problems of science and technology as given below:
1. In the field of basic sciences, it has been used to evaluate the area under a curve, to estimate the value of , in matrix inversion and study of particle diffusion.
2. In industrial problems including shop floor management, design of computer systems, design of queuing systems, inventory control, communication networks, chemical processes, nuclear reactors, and scheduling of production processes.
3. In business and economic problems, including customer behaviour, price determination, economic forecasting, portfolio selection, and capital budgeting.
4. In social problems, including population growth, effect of environment on health and group behaviour.
3.4 Limitations of Simulation Technique
Despite the many advantages of simulation, it might suffer from some deficiencies in large and complex problems. Some of these limitations are given as follows:
i. Simulation does not produce optimum results when the model deals with uncertainties, the results of simulation only reliable approximations subject to statistical errors.
ii. Quantification of variables is difficult in a number of situations;
it is not possible to quantify all the variables that affect the behaviour of the system.
iii. In very large and complex problems, the large number of variables and the interrelationship between them make the problem very unwieldy and hard to program.
iv. Simulation is by no means, a cheap method of analysis.
v. Simulation has too much tendency to rely on simulation models.
This results in application of the technique to some simple problems which can more appropriately be handled by other techniques of mathematical programming.
3.5 Monte Carlo Simulation
The Monte Carlo method of simulation was developed by two mathematicians Jon Von Neumann and Stainslaw Ulam, during World War II, to study how far neurone would travel through different materials. The technique provides an approximate but quite workable solution to the problem. With the remarkable success of this technique on the neutron problem, it soon became popular and found many applications in business and industry, and at present, forms a very important tool of operation researcher’s tool kit.
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The technique employs random number and is used to solve problems that involve probability and where physical experimentation is impracticable, and formulation of mathematical model is impossible. It is a method of simulation by sampling technique. The following are steps involved in carrying out Monte Carlo simulation.
1. Select the measure of effectiveness (objective function) of the problem. It is either to be minimised or maximised.
2. Identify the variables that affect the measure of effectiveness significantly. For example, a number of service facilities in a queuing problem or demand, lead time and safety stock in inventory problem.
3. Determine the cumulative probability distribution of each variable selected in step 2. Plot these distributions with the values of the variables along the x-axis and cumulative probability values along the y-axis.
4. Get a set of random numbers.
Example:
Customers arrive at a service facility to get required service. The interval and service times are constant and are 1.8minutes and minutes respectively. Simulate the system for 14minutes. Determine the average waiting time of a customer and the idle time of the service facility.
Solution
The arrival times of customers at the service station within 14 minutes will be:
Customer : 1 2 3 4 5 6 7 8
Arrival time : 0 1.8 3.6 5.4 7.2 9.0 10.8 12.6 (minutes)
The time at which the service station begins and ends within time period of 14 minutes is shown below. Waiting time of customers and idle time of service facility are also calculated
Customer Service Waiting time Idle time of Begins ends of customer service facility
1 0 4 0 0
2 4 8 4-1.8 = 2.2 0
3 8 12 8-3.6 = 4.4 0
4 12 16 12-5.4 = 6.6 0
The waiting time of the first four customers is calculated above. For the remaining, it is calculated below.
Customer : 5 6 7 8
Waiting time (min) : 14 – 7.2 = 6.8 5.0 3.2 1.4 Therefore, average waiting time of a customer
= 0 + 2.2 + 4.4 + 6.6 + 6.8 + 5 + 3.2 + 1.4 =29.6 = 3.7 minutes 8 8
Idle time of facility = nil.
4.0 CONCLUSION
This unit will assist you to deal with a complex problem solving situation.
You can apply it in investment appraisal, inventory control and evaluating queuing system.
There are soft-wares that will assist you to generate iterations of simulated numbers.
You need to purchase some of them.
5.0 SUMMARY
This unit provides for us an overview of simulation. It takes us through various conceptualisations on the definition of simulation. Simulation has been defined as the representation of reality through the use of models or other device which will react in the same manner as reality under given set of conditions. A good example of simulation is a children amusement or a cyclical park where children enjoy themselves in a simulated environment like Amusement Parks, Disney Land, Planetarium shows where boats, train rides, etc. are done to simulate actual experience. It is quite versatile and commonly applied technique for solving decision problems such as basic sciences, in industrial problems including shop floor management, in business and economic problems etc.
6.0 TUTOR-MARKED ASSIGNMENT
1. What do you understand by the term simulation?
2. Explain six advantages of simulation.
3. Identify and explain five areas of application of simulation.
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4. Give five limitations of simulation.
7.0 REFERENCES/FURTHER READING
Adebayo, O.A. et al. (2006). Operations Research in Decision and Production Management.
Gupta, P.K. & Hira, D.S. (2012). Operations Research. New – Delhi: S.
Chand & Company.
Jawahar, S. (2006). Overview of System Analysis & Design- Lesson Note No. 1. Ashok Educational Foundation.
Eiselt, H.A. & Sandblom, C. (2012). Operations Research: A Model Based Approach. (2nd ed.). New York: Springer Heidelberg.
UNIT 4 SYSTEMS ANALYSIS