1. MIS 463 Decision Support Systems for Business Simulation-Part 1 Aslı Sencer

2. MIS 463-Aslı Sencer 2 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. MIS 463-Aslı Sencer 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.

4. MIS 463-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. MIS 463-Aslı Sencer 5 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. MIS 463-Aslı Sencer 6 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. MIS 463-Aslı Sencer 7 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. MIS 463-Aslı Sencer 8 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

9. MIS 463-Aslı Sencer 9 Today: Popular Topics Real time simulation Web based simulation Optimization using simulation

10. MIS 463-Aslı Sencer 10 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

11. MIS 463-Aslı Sencer 11 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.

12. MIS 463-Aslı Sencer 12 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?

13. MIS 463-Aslı Sencer 13 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)

14. MIS 463-Aslı Sencer 14 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.

15. MIS 463-Aslı Sencer 15 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

16. 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 MIS 463-Aslı Sencer 16

17. 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 MIS 463-Aslı Sencer Erdem MIS 463-Aslı Sencer 17

18. Generating random demands: Inverse transformation technique MIS 463-Aslı Sencer 18 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)

19. 19 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] MIS 463-Aslı Sencer

20. 20 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.

21. MIS 463-Aslı Sencer 21

22. MIS 463-Aslı Sencer 22 The System: A Simple Processing System Arriving Blank Parts Departing Finished Parts Machine (Server) Queue (FIFO) Part in Service 4567 General intent:  Estimate expected production  Waiting time in queue, queue length, proportion of time machine is busy Time units  Can use different units in different places … must declare  Be careful to check the units when specifying inputs  Declare base time units for internal calculations, outputs  Be reasonable (interpretation, roundoff error)

23. MIS 463-Aslı Sencer 23 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

24. MIS 463-Aslı Sencer 24 Goals of the Study: 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?)

25. MIS 463-Aslı Sencer 25 Goals of the Study: 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 (a.k.a. cycle time): Q(t) = number of parts in queue at time t TS i = time in system of part i

26. MIS 463-Aslı Sencer 26 Goals of the Study: Output Performance Measures (cont’d.) Utilization of the machine (proportion of time busy) Many others possible (information overload?)

27. MIS 463-Aslı Sencer 27 Pieces of a Simulation Model Entities “Players” that move around, change status, affect and are affected by other entities Dynamic objects — get created, move around, leave (maybe) Usually represent “real” things Our model: entities are the parts Can have “fake” entities for modeling “tricks” Breakdown demon, break angel Usually have multiple realizations floating around Can have different types of entities concurrently Usually, identifying the types of entities is the first thing to do in building a model

28. MIS 463-Aslı Sencer 28 Pieces of a Simulation Model (cont’d.) Attributes Characteristic of all entities: describe, differentiate All entities have same attribute “slots” but different values for different entities, for example: Time of arrival Due date Priority Color Attribute value tied to a specific entity Like “local” (to entities) variables Some automatic in Arena, some you define

29. MIS 463-Aslı Sencer 29 Pieces of a Simulation Model (cont’d.) (Global) Variables Reflects a characteristic of the whole model, not of specific entities Used for many different kinds of things Travel time between all station pairs Number of parts in system Simulation clock (built-in Arena variable) Name, value of which there’s only one copy for the whole model Not tied to entities Entities can access, change variables Writing on the wall Some built-in by Arena, you can define others

30. MIS 463-Aslı Sencer 30 Pieces of a Simulation Model (cont’d.) Resources What entities compete for People Equipment Space Entity seizes a resource, uses it, releases it Think of a resource being assigned to an entity, rather than an entity “belonging to” a resource “A” resource can have several units of capacity Seats at a table in a restaurant Identical ticketing agents at an airline counter Number of units of resource can be changed during the simulation

31. MIS 463-Aslı Sencer 31 Pieces of a Simulation Model (cont’d.) Queues Place for entities to wait when they can’t move on (maybe since the resource they want to seize is not available) Have names, often tied to a corresponding resource Can have a finite capacity to model limited space — have to model what to do if an entity shows up to a queue that’s already full Usually watch the length of a queue, waiting time in it

32. MIS 463-Aslı Sencer 32 Pieces of a Simulation Model (cont’d.) Statistical accumulators Variables that “watch” what’s happening Depend on output performance measures desired “Passive” in model — don’t participate, just watch Many are automatic in Arena, but some you may have to set up and maintain during the simulation At end of simulation, used to compute final output performance measures

33. MIS 463-Aslı Sencer 33 Pieces of a Simulation Model (cont’d.) Statistical accumulators for the simple processing system Number of parts produced so far Total of the waiting times spent in queue so far No. of parts that have gone through the queue Max time in queue we’ve seen so far Total of times spent in system Max time in system we’ve seen so far Area so far under queue-length curve Q(t) Max of Q(t) so far Area so far under server-busy curve B(t)

34. 34 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) MIS 463-Aslı Sencer

35. 35 Simulation by Hand: Setup MIS 463-Aslı Sencer

36. 36 Simulation by Hand: t = 0.00, Initialize MIS 463-Aslı Sencer

37. 37 Simulation by Hand: t = 0.00, Arrival of Part 1 1 MIS 463-Aslı Sencer

38. 38 Simulation by Hand: t = 1.73, Arrival of Part 2 12 MIS 463-Aslı Sencer

39. 39 Simulation by Hand: t = 2.90, Departure of Part 1 2 MIS 463-Aslı Sencer

40. 40 Simulation by Hand: t = 3.08, Arrival of Part 3 23 MIS 463-Aslı Sencer

41. 41 Simulation by Hand: t = 3.79, Arrival of Part 4 234 MIS 463-Aslı Sencer

42. 42 Simulation by Hand: t = 4.41, Arrival of Part 5 2345 MIS 463-Aslı Sencer

43. 43 Simulation by Hand: t = 4.66, Departure of Part 2 345 MIS 463-Aslı Sencer

44. 44 Simulation by Hand: t = 8.05, Departure of Part 3 45 MIS 463-Aslı Sencer

45. 45 Simulation by Hand: t = 12.57, Departure of Part 4 5 MIS 463-Aslı Sencer

46. 46 Simulation by Hand: t = 17.03, Departure of Part 5 MIS 463-Aslı Sencer

47. 47 Simulation by Hand: t = 18.69, Arrival of Part 6 6 MIS 463-Aslı Sencer

48. 48 Simulation by Hand: t = 19.39, Arrival of Part 7 67 MIS 463-Aslı Sencer

49. 49 Simulation by Hand: t = 20.00, The End 67

50. MIS 463-Aslı Sencer 50 Simulation by Hand: Finishing Up Average waiting time in queue: Time-average number in queue: Utilization of drill press:

51. MIS 463-Aslı Sencer 51 Event-Based Simulation Table

52. Entity-Based Simulation Table Since simulation ends at 20th minute, 6th item’s process will not be Completed! The last thing occurs in a simulation will be arrival of 7th item! MIS 463-Aslı Sencer 52

53. MIS 463-Aslı Sencer 53 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

54. MIS 463-Aslı Sencer 54 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

55. MIS 463-Aslı Sencer 55 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