1. Simulation OPIM 310-Lecture #4 Instructor: Jose Cruz

2. Outline  What Is Simulation?  Advantages and Disadvantages of Simulation  Monte Carlo Simulation  Simulation and Profit Analysis  The use of Excel spreadsheets in simulation

3. What is Simulation?  An attempt to duplicate the features, appearance, and characteristics of a real system 1.To imitate a real-world situation mathematically 2.To study its properties and operating characteristics 3.To draw conclusions and make action decisions based on the results of the simulation

4. Simulation Applications Bus scheduling Design of library operations Taxi, truck, and railroad dispatching Production facility scheduling Plant layout Capital investments Production scheduling Sales forecasting Inventory planning and control Ambulance location and dispatching Assembly-line balancing Parking lot and harbor design Distribution system design Scheduling aircraft Labor-hiring decisions Personnel scheduling Traffic-light timing Voting pattern prediction

5. Select best course Examine results Conduct simulation Specify values of variables Construct model Introduce variables The Process of Simulation Define problem

6. Advantages of Simulation 1.Relatively straightforward and flexible 2.Can be used to analyze large and complex real-world situations that cannot be solved by conventional models 3.Real-world complications can be included that most OM models cannot permit 4.“Time compression” is possible

7. Advantages of Simulation 5.Allows “what-if” types of questions 6.Does not interfere with real-world systems 7.Can study the interactive effects of individual components or variables in order to determine which ones are important

8. Disadvantages of Simulation 1.Can be very expensive and may take months to develop 2.It is a trial-and-error approach that may produce different solutions in repeated runs 3.Managers must generate all of the conditions and constraints for solutions they want to examine 4.Each simulation model is unique

9. Monte Carlo Simulation Select numbers randomly from a probability distribution Use these values to observe how a model performs over time Random numbers each have an equal likelihood of being selected at random

10. Distribution of Demand LAPTOPS DEMANDED FREQUENCY OF PROBABILITY OF PER WEEK, DEMAND DEMAND, P(x) CUMULATIVE 0 20 0.20 0 0 20 0.20 0 1 40 0.40 0.20 1 40 0.40 0.20 2 20 0.20 0.60 2 20 0.20 0.60 3 10 0.10 0.80 3 10 0.10 0.80 4 10 0.10 0.90 4 10 0.10 0.90 100 1.00 100 1.00

11. Roulette Wheel of Demand 90 80 60 200 x = 2 x = 0 x = 4 x = 3 x = 1

12. Generating Demand from Random Numbers DEMAND,RANGES OF RANDOM NUMBERS, xr 00-19 120-59r = 39 260-79 380-89 490-99

13. Random Number Table 39657645451990696461 73712370906597601211 72184733845167479719 75122569171795217858 37177988746352063430

14. 15 Weeks of Demand Average demand = 31/15 = 2.07 laptops/week WEEKrDEMAND (x)REVENUE (S) 13914,300 27328,600 37228,600 47528,600 53714,300 60200 787312,900 898417,200 91000 104714,300 1193417,200 122114,300 1395417,200 1497417,200 156928,600  = 31$133,300

15. Computing Expected Demand E(x) = (0.20)(0) + (0.40)(1) + (0.20)(2) + (0.10)(3) + (0.10)(4) = 1.5 laptops per week Not particularly close to simulated result of 2.07 laptops Difference is due to small number of periods analyzed

16. Random Numbers in Excel

17. Simulation in Excel Enter this formula in G6 and copy to G7:G20 Enter “=4300*G6” in H6 and copy to H7:H20 Generate random numbers for cells F6:F20 with the formula “=RAND()” in F6 and copying to F7:F20 = AVERAGE (G6:G20)

18. Simulation in Excel

19. Example of Risk Analysis PortaCom Project PortCom’s product design group has developed a prototype for a new high-quality portable printer. The new printer has an innovative design and the potential to capture a significant innovative design and the potential to capture a significant share of the portable printer market. Preliminary marketing share of the portable printer market. Preliminary marketing and financial analysis have provided the following information. Selling price = $249 per unit Administrative cost = $400,000 Advertising cost = $600,000 PortaCom believes that the costs and the demand range as follows: Unit direct labor cost = $43~$47 Unit parts cost = $80~$100 First-year demand = 1500~28,500 units

20. Simulation The advantage of simulation is that it allows us to assess the probability of a profit and the probability of a loss.The advantage of simulation is that it allows us to assess the probability of a profit and the probability of a loss. Procedure of simulation 1. Check parameters 2. Check controllable inputs 3. Check probabilistic inputs * Generate random numbers * Generate random numbers 4. Formulate a model 5. Draw a flowchart

21. Simulation 1. Check parameters Selling price = $249 per unit Administrative cost = $400,000 Advertising cost = $600,000 2. Check controllable inputs Whether or not introduce the product 3. Check probabilistic inputs Unit direct labor cost range = $43~$47 Unit parts cost range = $80~$100 First-year demand range = 1500~28,500 units

22. Simulation 4. Formulate a model Profit=(249-c1-c2)X-1,000,000 5. Draw a flowchart

23. Probability Distribution of the Direct Labor Cost Direct labor cost Probability $43 0.1 $44 0.2 $45 0.4 $46 0.2 $47 0.1

24. Probability Distribution of the Parts Costs The probability distribution for the parts cost per unit is the uniform distribution as follows:The probability distribution for the parts cost per unit is the uniform distribution as follows:

25. Probability Distribution of the First-year Demand The first-year demand is described by the normal probability distribution with mean 15,000 units and the standard deviation 45000 units as follows:The first-year demand is described by the normal probability distribution with mean 15,000 units and the standard deviation 45000 units as follows:

26. How to Generate Random Numbers Computer-generated random numbersComputer-generated random numbers * Assign ranges of random numbers to * Assign ranges of random numbers to to corresponding values of probabilistic to corresponding values of probabilistic inputs. The prob. of any input value is inputs. The prob. of any input value is identical to the prob. of its occurrence in the identical to the prob. of its occurrence in the real system. real system. * * Placing =RAND() in a cell of an Excel worksheet will result in a random number.

27. Generate Random Value for Direct Labor Cost Interval of Direct labor cost Probability random numbers $43 0.1 0.0~0.1 $43 0.1 0.0~0.1 $44 0.2 0.1~0.3 $44 0.2 0.1~0.3 $45 0.4 0.3~0.7 $45 0.4 0.3~0.7 $46 0.2 0.7~0.9 $46 0.2 0.7~0.9 $47 0.1 0.9~1.0 $47 0.1 0.9~1.0 *Excell Statement =Vlookup(Rand(),range, Col_index)

28. Generate Random Numbers for Parts Cost With a uniform probability distribution, the following relationship between the random number and the associated value of the parts cost is used. Parts cost=a+r(b-a) where r=random number a=smallest value for parts cost b=largest value for parts cost Parts cost=80+r(100-80)=80+r20

29. Generate Random Numbers for First-year Demand Because first-year demand is normally distributed, we need a procedure for generating random values from a normal distribution.Because first-year demand is normally distributed, we need a procedure for generating random values from a normal distribution. We use the following formula of Excell We use the following formula of Excell =NORMINV(RAND(),mean,standard deviation)