Graduate Program in Business Information Systems Simulation Aslı

Graduate Program in Business Information Systems Simulation Aslı Sencer

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

Advantages of Simulation n n 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

The Bad News n n n 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. BIS 517 -Aslı Sencer

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

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

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

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

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

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

Popularity of Simulation n 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 n First in utility and interest — simulation n First in familiarity — LP (simulation was second) ¨ 1983, 1989, 1993: Heavy use of simulation consistently reported 1. Statistical analysis 2. Simulation BIS 517 -Aslı Sencer

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

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

Simulation Process (cont’d. ) n Output Data Analysis: ¨ Run the simulation several times and apply statistical analysis of the ouput data to estimate the performance measures n 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. BIS 517 -Aslı Sencer

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

Static Simulation: Monte-Carlo Simulation n n 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) BIS 517 -Aslı Sencer

Ex 1: Simulation for Dave’s Candies n 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. BIS 517 -Aslı Sencer

Ex 1: 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 n If D<Q Profit=selling price*D - cost*Q + discount price*(Q-D) n D>Q Profit=selling price*Q-cost*Q BIS 517 -Aslı Sencer

Probability Distribution for Demand Year Demand Distribution 2009 90 Demand (xi, i=1, . . . , 6) 2008 80 40 1/6 2007 50 50 1/6 2006 60 60 1/6 2005 40 70 1/6 2004 70 80 1/6 2003 90 90 1/6 . . BIS 517 -Aslı Sencer Probability P(Demand=xi)

Generating Demands Using Random Numbers n n n 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

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

Generating Demands Demand (xi) Probability P(Demand=xi) Cumulative Probability P(Demand<=xi) 40 1/6 [0 -1/6] 50 1/6 2/6 (1/6 -2/6] 60 1/6 3/6 (2/6 -3/6] 70 1/6 4/6 (3/6 -4/6] 80 1/6 5/6 (4/6 -5/6] 90 1/6 1 (5/6 -1] BIS 517 -Aslı Sencer Random numbers

Ex 1: 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

BIS 517 -Aslı Sencer

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. 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 BIS 517 -Aslı Sencer

Ex 3: Model Specifics n n n Initially (time 0) empty and idle Base time units: minutes Input data (assume given for now …), in minutes: Part Number 1 2 3 4 5 6 7 8 9 10 11. . n Arrival Time 0. 00 1. 73 3. 08 3. 79 4. 41 18. 69 19. 39 34. 91 38. 06 39. 82 40. 82. . Interarrival Time 1. 73 1. 35 0. 71 0. 62 14. 28 0. 70 15. 52 3. 15 1. 76 1. 00. . . Service Time 2. 90 1. 76 3. 39 4. 52 4. 46 4. 36 2. 07 3. 36 2. 37 5. 38. . . Stop when 20 minutes of (simulated) time have passed 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 § BIS 517 -Aslı Sencer

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

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

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

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

Simulation by Hand: Setup BIS 517 -Aslı Sencer

Simulation by Hand: t = 0. 00, Initialize BIS 517 -Aslı Sencer

Simulation by Hand: t = 0. 00, Arrival of Part 1 1 BIS 517 -Aslı Sencer

Simulation by Hand: t = 1. 73, Arrival of Part 2 2 1 BIS 517 -Aslı Sencer

Simulation by Hand: t = 2. 90, Departure of Part 1 2 BIS 517 -Aslı Sencer

Simulation by Hand: t = 3. 08, Arrival of Part 3 3 2 BIS 517 -Aslı Sencer

Simulation by Hand: t = 3. 79, Arrival of Part 4 4 3 2 BIS 517 -Aslı Sencer

Simulation by Hand: t = 4. 41, Arrival of Part 5 5 4 3 2 BIS 517 -Aslı Sencer

Simulation by Hand: t = 4. 66, Departure of Part 2 5 4 3 BIS 517 -Aslı Sencer

Simulation by Hand: t = 8. 05, Departure of Part 3 5 4 BIS 517 -Aslı Sencer

Simulation by Hand: t = 12. 57, Departure of Part 4 5 BIS 517 -Aslı Sencer

Simulation by Hand: t = 17. 03, Departure of Part 5 BIS 517 -Aslı Sencer

Simulation by Hand: t = 18. 69, Arrival of Part 6 6 BIS 517 -Aslı Sencer

Simulation by Hand: t = 19. 39, Arrival of Part 7 7 6 BIS 517 -Aslı Sencer

Simulation by Hand: t = 20. 00, The End 7 6 BIS 517 -Aslı Sencer

Ex 3: Complete Record of the Hand Simulation BIS 517 -Aslı Sencer

Ex 3: Simulation by Hand: Finishing Up n Average waiting time in queue: n Time-average number in queue: n Utilization of drill press: BIS 517 -Aslı Sencer

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

Comparing Alternatives n n n 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

Results: Original vs. Double-Time Arrivals n n n n BIS 517 -Aslı Sencer 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