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Published byDoris Miles Modified over 9 years ago
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1 Outline Model 05-01 problem statement detailed ARENA model model technique Output Analysis
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2 Model 5-1: An Automotive Maintenance and Repair Shop additional maintenance and repair facility in the suburban area customer orders (calls) by appointments, from one to three days in advance calls arrivals ~ Poisson process, mean 25 calls/day distribution of calls: 55% for the next day; 30% for the days after tomorrow; 15% for two days after tomorrow response missing a desirable day: 90% choose the following day; 10% leave
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3 An Automotive Repair and Maintenance Shop service Book Time, (i.e., estimated service time) ~ 44 + 90*BETA(2, 3) min Book Time also for costing promised wait time to customers wait time = Book Time + one hour allowance actual service time ~ GAMM(book time/1.05, 1.05) min first priority to wait customers customer behavior 20% wait, 80% pick up cars later about 60% to 70% of customers arrive on time 30% to 40% arrive within 3 hours of appointment time
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4 Costs and Revenues schedule rules at most five wait customers per day no more than 24 book hours scheduled per day (three bays, eight hours each) normal cost: $45/hour/bay, 40-hour per week overtime costs $120/hour/bay, at most 3 hours revenue from customers: $78/ book hour penalty cost each incomplete on-going car at the end of a day: $35 no penalty for a car whose service not yet started
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5 System Performance simulate the system 20 days to get average daily profit average daily book time average daily actual service time average daily overtime average daily number of wait appointments not completed on time
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6 Relationship Between Models Model 5-1: An Automotive Maintenance and Repair Shop a fairly complicated model non-queueing type Model 5-2: Enhancing the Automotive Shop Model two types of repair bays for different types of cars customer not on time
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7 The Structure of the ARENA Model Five parts Control Logic to initialize variables and count days Generate appointment calls, including a representative initial condition Make appointments, considering priority of jobs Service activities Update performance variables
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8 Details of Model 05-01 logic control and submodels for each day first simulate the calls for appointments (of future days) then simulate the work of the day vectors variables and expressions
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9 Steps to Prepare a Simulation Program assumption: already formulated the problem, i.e., fully understood how the system works for a simple problem: use the crude to detailed pseudo code approach to build the flow of the model for a complicated problem first play around with a simplified problem use paper and pencil to simulate
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10 An Illustration for Model 05-01 a simplified version of Model 05-01 a week of three days reservations made two days in advance Book Time = 1 w.p. 3/4 and = 2 w.p. 1/4 actual Service time = 1.2 Book Time w.p. 1/3 = 0.8 Book Time w.p. 2/3
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11 An Illustration for Model 05-01 each customer equally likely to be leave or wait every day 4 hours, with at most 1 hour OT at most 1 customer to leave his car number of customers in each day = 2 w.p. 1/3 and = 3 w.p. 2/3 simulation duration: 4 days
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12 Before Simulation terminating or non-terminating process? non-terminating typically simulated for a long time and the initial condition being unimportant how to set the initial condition if a non- terminating system is simulated for a short time? empty: is it representative? not empty: how to make it representative?
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13 To Generate a Representative Initial Condition representative initial condition day 1: appointments made in previous two days, i.e., day -1 and day 0 day 2: appointments made in day 0 idea generate calls for day -1 and then for day 0 whenever applicable, schedule appointments on days 1 and 2 implicitly drop appointments for days -1 and 0
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14 Paper and Pencil Simulation of the Simplified System Day0 123 4
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15 Very Crude Pseudo-Code 1 Generate a representative initial condition 2 Simulate the system for 4 days assumption for the model: ignore the time of calls, assuming that all happen in the morning
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16 Refinement of the First Step of the Pseudo-Code Generate a representative initial condition Start with an empty 6-day schedule Generate Book Times and schedule them for calls in Day -1 Generate number of calls for Day -1 Generate Book Times and schedule them for calls in Day 0 Generate number of calls for Day 0
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17 Refinement of the Second Step of the Pseudo-Code Refinement of the Second Step of the Pseudo-Code
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18 To Implement in ARENA need further refinement of the pseudo-code need modifying the pseudo-code to suit the structure of ARENA, e.g., what are the entities in the ARENA model? what are the correspondence between the steps in paper and pencil simulation and ARENA? ….. lots of details
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19 Output Analysis simulation: estimate = E(X) by observing sample values from the distribution of X output analysis point estimator of ? unbiased estimator of ? variance of estimator? efficient estimator of ? confidence on the range estimator? # of simulation runs (replications) required?
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20 Desirable Functions of Software interval estimation comparing alternatives automatic statistical tests handy housekeeping for scenarios automatic searching for optimal all features available in ARENA
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21 Output Analysis two types of estimates, point and interval theoretical basis point estimates: SLLN interval estimate: CLT
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22 Strong Law of Large Numbers i.i.d. random variables X 1, X 2, … finite mean and variance 2 define = E(X) (X 1 + … + X n )/n
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23 Additional Facts X 1, X 2,..., X n be i.i.d.; finite mean and variance 2 unbiased estimator of unbiased estimator of 2
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24 Central Limit Theorem i.i.d. random variables X 1, X 2, … finite mean and variance 2
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25 Central Limit Theorem - Basis to Analyze Terminating Systems t, 2, and F: useful distributions for range estimation and hypothesis testing of normal random variables X i ’ s CLT: statsitics approximately normal for “ large enough ” n can use t, 2, and F for (approximate) range estimation and hypothesis testing
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26 Differences Between Terminating and Non-Terminating Processes Differences Between Terminating and Non-Terminating Processes termination condition and run length terminating: well-defined, i.i.d. replications non-terminating: no well-defined length initial condition terminating: clear, defined by the problem non-terminating: unclear, biased by any fixed initial value random variables for estimation i.i.d. random variables stationary version of random variables
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27 Non-Terminating Processes time
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28 Terminating Processes standard outputs interval estimate of mean Model 05-02Model 05-02 hypothesis testing of mean Model 05-02Model 05-02 number of runs Model 06-01Model 06-01 saving results in an output file for further processing export from Output Analyzer to a text file Model 06-02Model 06-02 processed by first by Excel and then Input Analyzer to analyze the output data Model 06-02Model 06-02 confidence intervals by Output Analyzer Model 06-02Model 06-02 comparison by Output Analyzer Model 06-03Model 06-03 sequential determination of number of runs comparison by Output Analyzer Model 12-03Model 12-03
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29 Non-Terminating Processes non-terminating process Model 07-02Model 07-02 Output Analyzer replication/deletion Model 07-03 replication/deletionModel 07-03 batch means sequential batch means auto-correlation regenerative simulation
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