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# Simulation

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Simulation is a technique for analyzing profit through various methods.

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### Simulation

1. 1. Simulation Sudarshan Kumar Patel Vinay Uppinal
2. 2. Flow Of Presentation:  Introduction  Models  Applications  Risk Analysis  What-if Analysis  Simulation Method  Inventory Simulation  Wait Lines  Advantages and Disadvantages  References
3. 3. Introduction: Simulation:  Simulation is one of the most widely used quantitative approaches to decision making.  It is the method for learning about real system by experimenting with a model that represents the system. This model containsa) Mathematical expressions b) Logical relationships These two describes how to compute the value of the outputs given the values of inputs.
4. 4. Types of inputs Any simulation model has two inputs. i. Controllable inputs ii. Probabilistic inputs Probabilistic inputs Controllable inputs Model Output  Controllable inputs are those inputs which are controlled by decision maker such as total quantity of goods produced by a firm, unit selling cost of that product  Probabilistic inputs are those inputs which are not controlled by decision maker such as direct labour cost, demand..etc.
5. 5. Applications of Simulation: 1. New product development:  Determine the probability that a new product will be profitable.  Probabilistic inputs such as demand, parts cost and labour cost.  Controllable input whether to introduce the product. 2. Traffic flow:  Determine the effect of installing a left turn signal on the flow of traffic through a busy intersection.  Probabilistic inputs such as no. of vehicle arrivals and the fraction that want to make a left turn.  Controllable inputs such as length of time the left turn signal is on. 3. Waiting lines:  Determine the waiting times for customer at a bank’s ATM.  Probabilistic inputs such as customer arrivals and service times.  Controllable inputs such as the no. of ATM machines installed.
6. 6. Risk Analysis: Risk analysis is a process of predicting the outcome of a decision in the face of uncertainty. Calculating Risk Analysis without simulation: Portacom Project:  Target product- portable printer  Preliminary marketing and financial analysis provided the following selling price, first year administrative cost and first year advertising cost.  Parameters: Selling price = \$249/unit Administrative cost = \$400,000 Advertising cost = \$600,000 Here the cost of direct labour, the cost of parts and first year demand for portable printer are not known with certainty and are considered probabilistic inputs. Suppose labour cost = \$45/unit Cost of parts/unit = \$90 First year demand = \$15,000units
7. 7. What if Analysis: One approach to risk analysis is called what-if analysis. This analysis involves generating values for the probabilistic inputs and computing the resulting values for the output(profit). Profit = (\$249 - direct labour cost/unit - parts cost/unit)* (Demand)- \$1000000 Letting , C1=direct labour cost/unit. C2= parts cost/unit. X = First year demand. Profit = (249 – c1-c2)x – 1,000,000. These values constitute the base-case scenario. profit = (249 – 45 – 90)* (15000) – 1,000,000 = 710,000 Thus the base-case scenario leads to an anticipated profit of \$710 Worst case scenario In this case direct labour cost = \$47(the highest value) Parts cost = \$100(highest value) Demand = 15000(lowest value) profit = -847000 So the worst-case scenario leads to projected loss of \$847000
8. 8. Best-case scenario In this case direct labour cost = \$43(the lowest value) Parts cost = \$80(lowest value) Demand = 28500(highest value) profit = \$2591000 So the best-case scenario leads to projected profit of \$2591000 Direct Labour cost Introduce product Parts cost First Year Demand (249 – c1-c2)x - 1000000 Profit Disadvantage: Does not indicate the likelihood of the various profit or loss values.
9. 9. Simulation Method: Using simulation to perform risk analysis for the portacom problem is like playing out many what-if scenarios by randomly generating values for the probabilistic inputs. The advantage of simulation is that it allows us to access the probability of a profit and the probability of a loss. Direct Labour Cost: Suppose direct labour cost will range from \$43 to \$47/unit with probability Direct labour cost / probability unit \$43 0.1 \$44 0.2 \$45 0.4 \$46 0.2 \$47 0.1
10. 10. Parts Cost = \$80 to \$100 First year Demand- the mean or expected value of first year demand is 15000 units the std deviation of 4500 units describes the variability in the first year demand SD = 4500 Mean = 15000 This process of generating probabilistic inputs and computing the value of output is called Simulation.
11. 11. Flowchart for the Portacom Simulation: Model Parameters Selling price/unit = \$249 Administrative Cost=\$400000 Advertising Cost = \$600000 Generating Direct Labour cost, C1 Generate Parts cost, C2 Next Trial Generate First-year Demand, X Computer Profit Profit = (249-C1-C2)x - 1000000
12. 12. Random number intervals for generating values of Direct labour cost/unit: Direct labour cost/unit Probability Intervals of Random no.s \$43 0.1 0.0 but less than 0.1 \$44 0.2 0.1 but less than 0.3 \$45 0.4 0.3 but less than 0.7 \$46 0.2 0.7 but less than 0.9 \$47 0.1 0.9 but less than 1.0 From the above table we calculated randomly 10 values for the direct labour cost/unit
13. 13. Trial Random Number Direct Labour cost (\$) 1 0.9101 47 2 0.2841 44 3 0.6531 45 4 0.0367 43 5 0.3451 45 6 0.2757 44 7 0.6859 45 8 0.6246 45 9 0.4936 45 10 0.8077 46 Calculating the parts cost: Parts cost = a+r(b-a) Where r = random between 0 and 1 a = smallest value for parts cost b = largest value for parts cost Parts cost = 80 + r20
14. 14. Random Generation of 10 values for the parts cost/ unit Trial Random number Parts cost 1 0.2680 85.36 2 0.5842 91.68 3 0.6675 93.35 4 0.9280 98.56 5 0.4180 88.36 6 0.7342 94.68 7 0.4325 88.65 8 0.1186 82.37 9 0.6944 93.89 10 0.7869 95.74
15. 15. How to Calculate Demand: Using excel the following formula can be placed into a cell to obtain a value for a probabilistic input i.e., normally distributed = NORMINV(RAND(),Mean,SD) Random Generation of 10 values for first year Demand: Trial Random no. Demand 1 0.7005 17366 2 0.3204 12900 3 0.8968 20686 4 0.1804 10888 5 0.4346 14259 6 0.9605 22904 7 0.5646 15732 8 0.7334 17804 9 0.0216 5902 10 0.3218 12918
16. 16. Portacom Simulation results for 10 trials: Trial Direct labour cost/unit (\$) Parts cost/unit (\$) Units sold Profit (\$) 1 47 85.36 17366 1025570 2 44 91.68 12900 461828 3 45 93.35 20686 1288906 4 43 98.56 10888 169807 5 45 88.36 14259 648911 6 44 94.68 22904 1526679 7 45 88.65 15732 814686 8 45 82.37 17804 1165501 9 45 93.89 5902 -350131 10 46 95.74 12918 385585 Total 449 912.64 151359 7137432 Average 44.90 91.26 15136 713743
17. 17. Inventory Simulation: In inventory simulation we describe how simulation can be used to establish an inventory policy for a product that has uncertain demand. Sharma Electrical supply company: Fan cost = \$75 Selling price = \$125 Gross profit by sharma = \$125 - \$75 = \$50 Demand Mean = 100unit Std Dev = 20units Sharma receives monthly delivery and replenishes its inventory to level of Q at the beginning of which month (replenishment level) If monthly demand < replenishment level then inventory holding cost = \$15/unit If monthly demand > replenishment level then inventory shortage cost = \$30/unit Controllable input = Q Probabilistic input = Demand Output = net profit and service level
18. 18. Case 1: D<= Q Gross profit = \$50D Holding cost = \$15(Q –D) Net Profit = Gross profit – Holding cost = \$50D - \$15(Q – D) Case 2: D>Q Gross profit = \$50Q Shortage cost = \$30(D – Q) Net profit = Gross profit – Shortage cost = \$50Q - \$30 (D – Q) Month Demand Sales Gross Holding Profit (\$) cost (\$) Shotage cost(\$) Net profit (\$) 1 79 79 3950 315 0 3635 2 111 100 5000 0 330 4670 3 93 93 4650 105 0 4545 4 100 100 5000 0 0 5000 5 118 100 5000 0 540 4460 Total 501 472 23600 420 870 22310 Average 100 94 4720 84 174 4462
19. 19. Waiting line Simulation: The Simulation models discussed thus far have been based on independent trials in which the results in one trial do not affect what happens in subsequent trials. Customer Arrival Time: Probabilistic input arrival time of customer who use the ATM Customer Service Time: Probabilistic input the time a customer spends using the ATM machines.
20. 20. Advantages and Disadvantages: Main advantages of simulation include:  Study the behavior of a system without building it.  Results are accurate in general, compared to analytical model.  Help to find un-expected phenomenon, behavior of the system.  Easy to perform ``What-If'' analysis. Main disadvantages of simulation include:  Expensive to build a simulation model.  Expensive to conduct simulation.  Sometimes it is difficult to interpret the simulation results.
21. 21. References:  Quantitative Methods For Business - Anderson – Sweeny – Williams  Wikipedia  Youtube.