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# Simulation (qa ii)

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### Simulation (qa ii)

1. 1. SIMULATION MODELINGA Presentation onK.K. Parekh Institute of Management Studies(Amreli)Prepared by :-Mehul Rasadiya
2. 2. INTRODUCTION It is a technique(Quantitative) for carrying outexperiments for analyzing the behavior and evaluatingthe performance of a proposed system under assumedcondition of reality. An experiment or relatively simplified experimental modelof a system is used to examine the components orproperties of system, their behavior I relation to eachother and in relation to the entire system at a point oftime and over period of time, under different assumecondition. The alternative courses, inputs, components, propertiesand variables of the system are experimentallymanipulated in several way to find out their interactionsand impact on the system’s operation and behavior.
3. 3. SIMULATION DEFINATION• Simulation is the imitation of theoperation of a real world system overtime.• Simulation involves the generation of anartificial history of the system and thedrawing of inferences from it.
4. 4. REASON FOR USING SIMULATION Many practical problem where mathematicalsimplification is not feasible. There is no sufficient time to allow the system to operateextensively. Simulation model can be used to conduct experimentswithout disrupting real system. Enable a manager to provide insights into certainproblem where the actual environment is difficult toobserve. The non technical manager can comprehend simulationmore easily than a complex mathematical model.
5. 5. The Process of Simulation
6. 6. ADVANTAGES1. Flexibility2. Can handle large and complex systems3. Can answer “what-if” questions4. Does not interfere with the real system5. Allows study of interaction amongvariables6. “Time compression” is possible7. Handles complications that othermethods can’t
7. 7. DISADVANTAGES1. Can be expensive and time consuming2. Does not generate optimal solutions3. Managers must choose solutions theywant to try (“what-if” scenarios)4. Each model is unique
8. 8. APPLICATION OF SIMULATION Manufacturing and other process Scheduling production processes Design of system(marketing, information,inventory, weapon, manpower employment,traffic light-timing, etc.) Facilities(hospitals, harbors, railways, libraries,schools, design of parking lots, communicationsystem, etc) Resource development programmers( waterresources, human resources, petro-chemical,energy resources, and so on)
9. 9. Deterministic ModelAll data are assumedto be known withcertaintyProbabilistic ModelSome data are describedby probability distribution.System SimulationAn experiment used todescribe sequences of eventsthat occur over time.(inventory, queuing,manufacturing process)Simulation ModelsMonte Carlo SimulationA sampling experiment whosepurpose is to estimate thedistribution of an outcome variablethat depends on severalprobabilistic input variables. (profitprojection, stock portfolio).
10. 10. Steps Involved in Simulation(Monte Carlo Technique) Find the cumulative Probability Assign random numbers Interval corresponding to theProbability. From the random number tables, choose a set ofrequired random numbers from any part of the table.This can be done by following any fixed pattern likerow wise, column wise, diagonal wise. Choice of random numbers whether single digit,double digit, triple digit etc. depends upon the numberof places to which Probability is known. Eg- If theprob. have been calculated to two decimal places,which add up to 1.00, we need 100 numbers of 2 digitto represent each point of probability. Thus we takerandom no.s 00-99 to represent them.
11. 11. CASE STUDYA company manufactures 30 units/day. The sale of these itemsdepends upon demand which has the following distribution. The production cost and sales price of each unit are Rs. 40 and Rs.50, respectively. Any unsold product is to be disposed off at loss ofRs. 15. There is a penalty of Rs. 5 per unit if the demand is not met. Using the following random numbers, estimate the total profit/loss forthe company for the next ten days. 10, 99, 65, 99, 01, 79, 11, 16, 20 If the company decides to produce 29 units per day, what is theadvantage or disadvantage of the company?Sales (Unit) Probability27 0.1028 0.1529 0.2030 0.3531 0.1532 0.05
12. 12. Sales (unit) Probability CumulativeprobabilityRandom No.Interval27 0.10 0.1028 0.1529 0.2030 0.3531 0.1532 0.05
13. 13. Sales (unit) Probability CumulativeprobabilityRandom No.Interval27 0.10 0.1028 0.15 0.2529 0.20 0.4530 0.35 0.8031 0.15 0.9532 0.05 1.00
14. 14. Sales (unit) Probability CumulativeprobabilityRandom No.Interval27 0.10 0.10 00-0928 0.15 0.25 10-2429 0.20 0.45 25-4430 0.35 0.80 45-7931 0.15 0.95 80-9432 0.05 1.00 95-99As the first step, random numbers 00-99 are allocated to variouspossible sales values in production to the probabilities associatedwith them.
15. 15.  Now we simulate the demand for the next 10 days usingthe given random numbers.From the given following information, we haveProfit per unit sold = Rs. 50 – Rs. 40= Rs. 10Loss per unit unsold = Rs. 15Penalty for using demand = Rs. 5 per unit Using these inputs, the profit/loss for the 10 days iscalculated, first when production is 30 units per day andthen when it is 29 units. It is evident that the total profit/loss for the 10 days is Rs.2695 when 30 units are produced. Also, if the companydecides to produce 29 units per day, the total profit worksout to be the same.
16. 16. Days RandomNumbersEstimatedSales(units)Profit/Loss per day with production30 units 29 units1 10 282 993 654 995 956 017 798 19 1610 20
17. 17. Days RandomNumbersEstimatedSales(units)Profit/Loss per day with production30 units 29 units1 10 282 99 323 65 304 99 325 95 326 01 277 79 308 1 289 16 2810 20 28
18. 18. Days RandomNumbersEstimated Sales(units)Profit/Loss per day with production30 units 29 units1 10 28 28*10-2*15 = Rs. 2502 99 323 65 304 99 325 95 326 01 277 79 308 1 289 16 2810 20 28
19. 19. Days RandomNumbersEstimated Sales(units)Profit/Loss per day with production30 units1 10 28 28*10-2*15 = Rs. 2502 99 32 30*10-2*5 = Rs. 2903 65 30 30*10 = Rs. 3004 99 32 30*10-2*5 = Rs. 2905 95 32 30*10-2*5 = Rs. 2906 01 27 27*10-3*15 = Rs. 2257 79 30 30*10 = Rs. 3008 1 28 28*10-2*15 = Rs. 2509 16 28 28*10-2*15 = Rs. 25010 20 28 28*10-2*15 = Rs. 250Total Profit = Rs. 2695
20. 20. Days RandomNumbersEstimated Sales(units)Profit/Loss per day with production30 units 29 units1 10 28 28*10-2*15 = Rs. 250 28*10-1*15 = Rs. 2652 99 32 30*10-2*5 = Rs. 2903 65 30 30*10 = Rs. 3004 99 32 30*10-2*5 = Rs. 2905 95 32 30*10-2*15 = Rs. 2906 01 27 27*10-3*15 = Rs. 2257 79 30 30*10 = Rs. 3008 1 28 28*10-2*15 = Rs. 2509 16 28 28*10-2*15 = Rs. 25010 20 28 28*10-2*15 = Rs. 250Total Profit = Rs. 2695
21. 21. Days RandomNumbersEstimated Sales(units)Profit/Loss per day with production30 units 29 units1 10 28 28*10-2*15 = Rs. 250 28*10-1*15 = Rs. 2652 99 32 30*10-2*5 = Rs. 290 29*10-3*5 = Rs. 2753 65 30 30*10 = Rs. 300 29*10-1*5 = Rs. 2854 99 32 30*10-2*5 = Rs. 290 29*10-3*5 = Rs. 2755 95 32 30*10-2*15 = Rs. 290 29*10-3*5 = Rs. 2656 01 27 27*10-3*15 = Rs. 225 27*10-2*15 = Rs. 2407 79 30 30*10 = Rs. 300 29*10-1*5 = Rs. 2858 1 28 28*10-2*15 = Rs. 250 28*10-1*15 = Rs. 2659 16 28 28*10-2*15 = Rs. 250 28*10-1*15 = Rs. 26510 20 28 28*10-2*15 = Rs. 250 28*10-1*15 = Rs. 265Total Profit = Rs. 2695 = Rs. 2695
22. 22. When company decides to produce 29 units perday, so that time no change in profit or loss.Compare to 30 units per day.When companyproduce 30 unitsWhen companyproduce 29 unitsTotal Profit =Rs. 2695Total Profit =Rs. 2695
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