1. Graduate Program in Business Information Systems Simulation Aslı Sencer

2. BIS 517-Aslı Sencer Simulation – Very broad term – methods and applications to imitate or mimic real systems, usually via computer Applies in many fields and industries Very popular and powerful method

3. Advantages of Simulation Simulation can tolerate complex systems where analytical solution is not available. Allows uncertainty, nonstationarity in modeling unlike analytical models Allows working with hazardous systems Often cheaper to work with the simulated system Can be quicker to get results when simulated system is experimented. BIS 517-Aslı Sencer

4. The Bad News Don’t get exact answers, only approximations, estimates Requires statistical design and analysis of simulation experiments Requires simulation expert and compatibility with a simulation software Softwares and required hardware might be costly Simulation modeling can sometimes be time consuming.

5. BIS 517-Aslı Sencer Different Kinds of Simulation Static vs. Dynamic  Does time have a role in the model? Continuous-change vs. Discrete-change  Can the “state” change continuously or only at discrete points in time? Deterministic vs. Stochastic  Is everything for sure or is there uncertainty?

6. BIS 517-Aslı Sencer Using Computers to Simulate General-purpose languages (C, C++, Visual Basic) Simulation softwares, simulators  Subroutines for list processing, bookkeeping, time advance  Widely distributed, widely modified Spreadsheets  Usually static models  Financial scenarios, distribution sampling, etc.

7. BIS 517-Aslı Sencer Simulation Languages and Simulators Simulation languages  GPSS, SIMSCRIPT, SLAM, SIMAN  Provides flexibility in programming  Syntax knowledge is required High-level simulators  GPSS/H, Automod, Slamsystem, ARENA, Promodel  Limited flexibility — model validity?  Very easy, graphical interface, no syntax required  Domain-restricted (manufacturing, communications)

8. BIS 517-Aslı Sencer When Simulations are Used The early years (1950s-1960s)  Very expensive, specialized tool to use  Required big computers, special training  Mostly in FORTRAN (or even Assembler) The formative years (1970s-early 1980s)  Computers got faster, cheaper  Value of simulation more widely recognized  Simulation software improved, but they were still languages to be learned, typed, batch processed

9. BIS 517-Aslı Sencer When Simulations are Used (cont’d.) The recent past (late 1980s-1990s)  Microcomputer power, developments in softwares  Wider acceptance across more areas Traditional manufacturing applications Services Health care “Business processes”  Still mostly in large firms  Often a simulation is part of the “specs”

10. BIS 517-Aslı Sencer When Simulations are Used (cont’d.) The present  Proliferating into smaller firms  Becoming a standard tool  Being used earlier in design phase  Real-time control The future  Exploiting interoperability of operating systems  Specialized “templates” for industries, firms  Automated statistical design, analysis

11. BIS 517-Aslı Sencer Popularity of Simulation Consistently ranked as the most useful, popular tool in the broader area of operations research / management science  1979: Survey 137 large firms, which methods used? 1. Statistical analysis (93% used it) 2. Simulation (84%) 3. Followed by LP, PERT/CPM, inventory theory, NLP,  1980: (A)IIE O.R. division members First in utility and interest — simulation First in familiarity — LP (simulation was second)  1983, 1989, 1993: Heavy use of simulation consistently reported 1. Statistical analysis 2. Simulation

12. BIS 517-Aslı Sencer Today: Popular Topics  Real time simulation  Web based simulation  Optimization using simulation

13. BIS 517-Aslı Sencer Simulation Process Develop a conceptual model of the system  Define the system, goals, objectives, decision variables, output measures, input variables and parameters. Input data analysis:  Collect data from the real system, obtain probability distributions of the input parameters by statistical analysis Build the simulation model:  Develop the model in the computer using a HLPL, a simulation language or a simulation software

14. BIS 517-Aslı Sencer Simulation Process (cont’d.) Output Data Analysis:  Run the simulation several times and apply statistical analysis of the ouput data to estimate the performance measures Verification and Validation of the Model:  Verification: Ensuring that the model is free from logical errors. It does what it is intended to do.  Validation: Ensuring that the model is a valid representation of the whole system. Model outputs are compared with the real system outputs.

15. BIS 517-Aslı Sencer Simulation Process (cont’d.) Analyze alternative strategies on the validated simulation model. Use features like  Animation  Optimization  Experimental Design Sensitivity analysis:  How sensitive is the performance measure to the changes in the input parameters? Is the model robust?

16. BIS 517-Aslı Sencer Static Simulation: Monte-Carlo Simulation Static Simulation with no time dimension. Experiments are made by a simulation model to estimate the probability distribution of an outcome variable, that depends on several input variables. Used the evaluate the expected impact of policy changes and risk involved in decision making. Ex: What is the probability that 3-year profit will be less than a required amount? Ex: If the daily order quantity is 100 in a newsboy problem, what is his expected daily cost? (actually we learned how to answer this question analytically)

17. BIS 517-Aslı Sencer Ex1: Simulation for Dave’s Candies Dave’s Candies is a small family owned business that offers gourmet chocolates and ice cream fountain service. For special occasions such as Valentine’s day, the store must place orders for special packaging several weeks in advance from their supplier. One product, Valentine’s day chocolate massacre, is bought for $7,50 a box and sells for $12.00. Any boxes that are not sold by February 14 are discounted by 50% and can always be sold easily. Historically Dave’s candies has sold between 40-90 boxes each year with no apparent trend. Dave’s dilemma is deciding how many boxes to order for the Valentine’s day customers.

18. BIS 517-Aslı Sencer Ex1: Dave's Candies Simulation If the order quantity, Q is 70, what is the expected profit? Selling price=$12 Cost=$7.50 Discount price=$6 If D<Q Profit=selling price*D - cost*Q + discount price*(Q-D) D>Q Profit=selling price*Q-cost*Q

19. Probability Distribution for Demand YearDemand 200990 200880 200750 200660 200540 200470 200390.... Demand Distribution Demand (x i, i=1,...,6 ) Probability P(Demand=x i ) 401/6 501/6 601/6 701/6 801/6 901/6 BIS 517-Aslı Sencer

20. Generating Demands Using Random Numbers During simulation we need to generate demands so that the long run frequencies are identical to the probability distribution found. Random numbers are used for this purpose. Each random number is used to generate a demand. Excel generates random numbers between 0-1. These numbers are uniformly distributed between 0-1. Random numbers 0.12878 0.43483 0.87643 0.65711 0.03742 0.46839 0.04212 0.89900 BIS 517-Aslı Sencer

21. Generating random demands: Inverse transformation technique P(demand=x i ) (x i ) 40 50 60 70 80 90 1/6 P(demand<=x i ) (x i ) 40 50 60 70 80 90 1 5/6 4/6 3/6 2/6 1/6 U1U1 D 1 =80 U2U2 D 2 =50 1.Generate U~UNIFORM(0,1) 2.Let U=P(Demand<=D) then D=P -1 (U) BIS 517-Aslı Sencer

22. Generating Demands Demand (x i ) Probability P(Demand=x i ) Cumulative Probability P(Demand<=x i ) Random numbers 401/6 [0-1/6] 501/62/6(1/6-2/6] 601/63/6(2/6-3/6] 701/64/6(3/6-4/6] 801/65/6(4/6-5/6] 901/61(5/6-1] BIS 517-Aslı Sencer

23. Ex1: Simulation in Excel for Dave’s Candies Use the following excel functions to generate a random demand with a given distribution function.  RAND(): Generates a random number which is uniformly distributed between 0-1.  VLOOKUP(value, table range, column #): looks up a value in a table to detremine a random demand.  IF(condition, value if true, value if false): Used to calculate the total profit according to the random demand. BIS 517-Aslı Sencer

25. Dynamic Simulation: Queueing System Arrivals Departures Service is identified by: Arrival rate, interarrival time distribution Service rate, service time distribution # servers # queues Queue capacities Queue disciplines, FIFO, LIFO, etc.

26. BIS 517-Aslı Sencer M/M/1 Queueing System Arrivals Departures Service M: interarrival time is exponentially distributed M: service time is exponentially distributed 1: There is a single server

27. BIS 517-Aslı Sencer Ex3: Model Specifics Initially (time 0) empty and idle Base time units: minutes Input data (assume given for now …), in minutes: Part NumberArrival TimeInterarrival TimeService Time 10.001.732.90 21.731.351.76 33.080.713.39 43.790.624.52 54.4114.284.46 618.690.704.36 719.3915.522.07 834.913.153.36 938.061.762.37 1039.821.005.38 11 40.82...... Stop when 20 minutes of (simulated) time have passed

28. BIS 517-Aslı Sencer Queuing Simulation  Random variables:  Time between arrivals  Service time represented by probability distributions.  Events:  Arrival of a customer to the system  Departure from the system.  State variables:  # customers in the queue  Worker status {busy, idle}  Output measures:  Average waiting time in the queue  % utilization of the server  Average time spent in the system

29. BIS 517-Aslı Sencer Output Performance Measures Total production of parts over the run (P) Average waiting time of parts in queue: Maximum waiting time of parts in queue: N = no. of parts completing queue wait WQ i = waiting time in queue of ith part Know: WQ 1 = 0 (why?) N > 1 (why?)

30. BIS 517-Aslı Sencer Output Performance Measures (cont’d.) Time-average number of parts in queue: Maximum number of parts in queue: Average and maximum total time in system of parts: Q(t) = number of parts in queue at time t TS i = time in system of part i

31. BIS 517-Aslı Sencer Output Performance Measures (cont’d.) Utilization of the machine (proportion of time busy) Many others possible (information overload?)

32. BIS 517-Aslı Sencer Simulation by Hand Manually track state variables, statistical accumulators Use “given” interarrival, service times Keep track of event calendar “Lurch” clock from one event to the next Will omit times in system, “max” computations here (see text for complete details)

33. BIS 517-Aslı Sencer Simulation by Hand: Setup

34. BIS 517-Aslı Sencer Simulation by Hand: t = 0.00, Initialize

35. BIS 517-Aslı Sencer Simulation by Hand: t = 0.00, Arrival of Part 1 1

36. BIS 517-Aslı Sencer Simulation by Hand: t = 1.73, Arrival of Part 2 12

37. BIS 517-Aslı Sencer Simulation by Hand: t = 2.90, Departure of Part 1 2

38. BIS 517-Aslı Sencer Simulation by Hand: t = 3.08, Arrival of Part 3 23

39. BIS 517-Aslı Sencer Simulation by Hand: t = 3.79, Arrival of Part 4 234

40. BIS 517-Aslı Sencer Simulation by Hand: t = 4.41, Arrival of Part 5 2345

41. BIS 517-Aslı Sencer Simulation by Hand: t = 4.66, Departure of Part 2 345

42. BIS 517-Aslı Sencer Simulation by Hand: t = 8.05, Departure of Part 3 45

43. BIS 517-Aslı Sencer Simulation by Hand: t = 12.57, Departure of Part 4 5

44. BIS 517-Aslı Sencer Simulation by Hand: t = 17.03, Departure of Part 5

45. BIS 517-Aslı Sencer Simulation by Hand: t = 18.69, Arrival of Part 6 6

46. BIS 517-Aslı Sencer Simulation by Hand: t = 19.39, Arrival of Part 7 67

47. BIS 517-Aslı Sencer Simulation by Hand: t = 20.00, The End 67

48. BIS 517-Aslı Sencer Ex3:Complete Record of the Hand Simulation

49. BIS 517-Aslı Sencer Ex3: Simulation by Hand: Finishing Up Average waiting time in queue: Time-average number in queue: Utilization of drill press:

50. Randomness in Simulation The above was just one “replication” — a sample of size one (not worth much) Made a total of five replications: Confidence intervals for expected values:  In general,  For expected total production, Note substantial variability across replications BIS 517-Aslı Sencer

51. Comparing Alternatives Usually, simulation is used for more than just a single model “configuration” Often want to compare alternatives, select or search for the best (via some criterion) Simple processing system: What would happen if the arrival rate were to double?  Cut interarrival times in half  Rerun the model for double-time arrivals  Make five replications BIS 517-Aslı Sencer

52. Results: Original vs. Double-Time Arrivals Original – circles Double-time – triangles Replication 1 – filled in Replications 2-5 – hollow Note variability Danger of making decisions based on one (first) replication Hard to see if there are really differences Need: Statistical analysis of simulation output data BIS 517-Aslı Sencer