Professor S K Dubey,VSM Amity School of Business OPERATIONS RESEARCH Professor S K Dubey,VSM Amity School of Business

Simulation

Contents Introduction Reasons for using simulation. Steps in simulation process. Advantages, Disadvantages & Limitations of Simulation. Mont-Carlo simulation process Role of Computers in Simulation. Summary. 11/15/2018

Case1 A bombing mission is sent to bomb a military target, which is rectangular in shape and has dimensions 75 meter by 150 meter. The bombers will drop 10 bombs altogether, all aimed at the geometric centre of the target. It is assumed that the bombing run is made parallel to the longest dimension of the target. The deviation of the impact point from the aiming point is normal with mean zero & SD 50 meter in each dimensions. The deviations are independent random variable. Estimate the expected No. of bombs to be used. 11/15/2018

Case2 A bakery keeps stock of a popular brand of cake. Previous experience shows the daily demand pattern is as given below:- Daily Demand 0 10 20 30 40 50 Probability .01 .20 .15 .50 .12 .02 Simulate the daily demand pattern 11/15/2018

Introduction Simulation is a quantitative procedure which describes a process by developing a mathematical model of that process and then conducting a series of organized experiments to forecast the behavior of the process. 11/15/2018

Reasons for using Simulation Simulation may be the only method available. ( Space flight programme) It may not be possible to develop a mathematical solution. Actual observation may be too expensive. There may not be sufficient time to allow the system to operate extensively. Actual operation & observations may be too expensive. 11/15/2018

Steps of Simulation Process Step 1:- Identify the problem. Step2:- Identify the decision variables. Step3:- Decide the performance criterion. Step4:- Construct a numerical model. Step5:- Validate the model. Step6:- Design the experiment. Step7:- Run the simulation model. Step8:- Examine the results. 11/15/2018

Advantages of Simulation Approach is suitable to analyze large & complex real life problems which can’t be solved by use of quantitative methods. It allows the decision maker to study the interactive system variables & the effect of changes in these variables on the system. Simulation experiments are done on the model, not on the system itself. Simulation can be used as a pre service test to try out new policies & decision rules for operating a system before running the risk of experimentation in the real system. 11/15/2018

Disadvantages of Simulation Sometimes simulation models are expensive & take a long time to develop. Ex: A corporate planning model. The simulation model does not produce answers by itself. The user has to provide all the constraints for the solutions which he wants to examine. It is trial & error approach. 11/15/2018

Limitations of Simulation Simulation is not precise. It does not yield an answer but merely provides a set of the system’s responses to different operating conditions. Managers have still to generate the solutions. A good simulation model may be very expensive. It takes years to develop a suitable corporate model. All situations can't be evaluated using simulation. 11/15/2018

Monte Carlo Simulation The Monte-Carlo technique uses random number. It is generally used to solve problems requiring decision-making under uncertainty & where mathematical formulation is impossible. 11/15/2018

Principle behind Monte Carlo Simulation technique The principle behind the Monte Carlo simulation technique is to represent the given system by some known probability distribution. Then draw random samples from the probability distribution by means of random numbers. In case the system can’t be described by a known probability distribution function such as Normal, Poisson, Exponential etc, then an empirical probability distribution can be constructed. 11/15/2018

Monte Carlo Simulation Step1:- Set up probability distribution for variables to be analyzed. Step2:- Build a cumulative probability distribution for each random variable. Step3:- Generate random numbers. Step4:- Assign an appropriate set of random numbers value for each random variables. Step5:- Conduct the simulation experiment by means of random sampling. Step6:- Repeat Step5 until the required number of simulation runs has been generated. Step7:- Design & implement a course of action and maintain control. 11/15/2018

Example (Case1) A bombing mission is sent to bomb a military target, which is rectangular in shape and has dimensions 75 meter by 150 meter. The bombers will drop 10 bombs altogether, all aimed at the geometric centre of the target. It is assumed that the bombing run is made parallel to the longest dimension of the target. The deviation of the impact point from the aiming point is normal with mean zero & SD 50 meter in each dimensions. The deviations are independent random variable. Estimate the expected No. of bombs to be used 11/15/2018

Discussion on Case1 (Target Parameters) Impact Point Flight Line Y -----X---- 75 meters Aiming Point (0,0) 150 meters 11/15/2018

Discussion on Case1 Y : Line Error u : Range error deviate = (X-0)/50 X : Range Error Y : Line Error u : Range error deviate = (X-0)/50 -1.5/2 < u < 1.5/2 v : Line error deviate = (Y-0)/50 - 0.75/2 < v < 0.75/2 11/15/2018

Random Normal Table in Units of Standard Deviates (Z) 0.8 1.95 -2.92 0.34 -0.67 -0.7 -0.54 1.87 1.72 0.88 0.61 0.36 0.42 0.63 -0.9 -1.07 1.15 0.05 -0.48 -1.48 -0.24 0.47 -0.19 0.56 0.16 -0.49 0.24 1.46 1.28 -1.18 -0.32 -0.69 1.57 1.53 0.06 -0.66 2.22 -0.21 1.41 -0.08 0.14 -0.68 0.02 1.67 1.17 -1.75 0.54 2.47 -0.55 -1.13 0.46 1.16 -0.25 1.76 2.62 -0.61 -0.27 11/15/2018

Simulation Trial1 Bomb u v Result 1 0.8 -0.54 Hit 2 0.42 -0.48 3 0.16 1.95 Miss 4 1.87 0.63 5 -1.48 -0.49 6 -2.92 1.72 7 -90 -0.24 8 0.24 0.34 9 0.88 -1.07 10 0.47 1.46   5 Hits 11/15/2018

Simulation Trial 2 Bomb u v Result 1 -0.67 0.61 Hit 2 1.15 -0.19 3 0.9 -0.7 4 0.36 0.05 5 0.56 1.28 6 -1.18 -0.66 Miss 7 0.68 1.76 8 2.47 -0.32 9 2.22 0.02 10 -0.55 2.62   5 Hits 11/15/2018

Simulation Trial 3 Bomb u v Result 1 -0.69 -0.21 Hit 2 1.67 -1.13 Miss -0.61 1.57 4 1.41 1.17 5 0.46 -0.27 6 1.53 -0.08 7 -1.75 1.16 8 0.16 0.06 9 0.14 0.54 10 -0.25   4 Hits 11/15/2018

Role of Computers in Simulation It is difficult to perform simulations without computer. Computer aided simulation also does the sensitivity of the model. Simulation Languages :- GPSS (General Purpose Sys Simulation), SIMSCRIPT, Fortran, C, PASCAL, PL/1, LISP 11/15/2018

Procedure of Computer Simulation Define the problem- nature, scope & importance. Build mathematical model. Write computer program of the model. Process the program on the computer. Evaluate the results of the computer simulation. Recommend a course of management action on the problem. 11/15/2018

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