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14. Simulation and Factory Physics

14. Simulation and Factory Physics. @Risk: Harriet Hotel and Overbooking Problems Introduction to Simulation Methods of modeling uncertainty Monte Carlo simulation Managing production lines without variability Managing production lines with variability

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14. Simulation and Factory Physics

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  1. 14. Simulation and Factory Physics • @Risk: Harriet Hotel and Overbooking Problems • Introduction to Simulation • Methods of modeling uncertainty • Monte Carlo simulation • Managing production lines without variability • Managing production lines with variability • Throughput rate, flow time and inventory levels • Line balancing • Single machine stations vs. parallel machines

  2. Overbooking Problem • Common practice in • Difference between overbooking problems and newsvendor problems

  3. Harriet Hotel Note: HarrietHotel.xls is available on CourseInfo 100 125 30 0.95 200 =B2-B3  try different values =RiskBinomial(B7, B4) =MIN(B1,B8) =B8-B9 =RiskOutput() +B6*B9-B5*B10 • First, start @Risk. Excel will start automatically. • Make “Actual Arrivals" a Binomial Random Variable: • Menu: Insert, Function, @RiskDistribution, RiskBinomial • Make "Nightly Profit" an Output: Menu: @Risk, Model, Add Output • Set Iterations & Sampling: Menu: @Risk, Simulation, Settings • Run the Simulation: Menu: @Risk, Simulation, Start • Analyze the Results: Results Window: Results, Results Settings or Quick Report

  4. @Risk Simulation Settings.Menu: @Risk, Simulation, Settings • Number of times the simulation is repeated for each scenario. • Number of Scenarios. • use 1 if you enter a single value for “Number of Reservations Accepted", or • use 7 if use RiskSimTable with seven different values. “Monte Carlo” causes @Risk to show randomly generated values when you press function key F9. A "fixed seed" causes @Risk to use the same random numbers every time a run is repeated. This means that all simulations will face the same “Actual Arrivals”.

  5. @Risk Report SettingsResults Window:Results, Report Settings Specify the reports you are interested in. For example, you can put these results on an Excel spreadsheet. Generate the selective reposts.

  6. Using the @Risk Simulation Add-in for Excel • Open @Risk. (Excel will be opened for you.) • Create your model and think about what are the • Performance measures (output cells) • Decision variables (under your control) • Random variables (input cells) • Use probability functions to represent your random variables • Go to Insert | Function and select @Risk Distribution, or • go to@Risk | Model | Define Distributions • Identify the performance measures you wish to gather data on • Go to@Risk | Add Output, orsimply type in Riskoutput() • You can see the list of your input and output cells by going to @Risk | Model | List of Outputs and Inputs • Specify simulation settings: @Risk | Simulation | Settings • Iterations: # iterations and # simulations • sampling • Start the simulation (@Risk | Simulation | Start) • Analyze results

  7. Selecting a Distribution (p. 550) • Quantifying Uncertainty • Mean and Standard Deviation • Shape (skewness) • Min, mostlikely, max • Discrete Probability Distributions: • RiskIntUniform (x,y) • RiskDuniform({x1,x2,…,xn}) • RiskDiscrete ({x1,x2,…,xn}, {p1,p2,…,pn}) • RiskBinomial(n,p) • Continuous Probability Distributions: • RiskUniform(x,y) • RiskNormal(m,s) • RiskLogNorm(m,s) • RiskTriang(min, most likely, max) You can also go to @Risk | Model | Define Distributions, which is helpful in choosing among the different probability distributions.

  8. Analyzing Simulation Results • After the simulation runs, the Results Window will automatically open, showing summary statistics for • the output cells and • the input cells if you’ve chosen to collect them in the Sampling tab of Simulation Settings • You can move back and forth between the results and your spreadsheet through the “Show Excel Window” button and the “Show Result Window” button (or through @Risk | Results). • From the Results Window: • Copy the simulation results to an Excel worksheet for further analysis and safekeeping by going to Results | Report Setting or Quick Report • To generate a graph, right-click on an output (or input) cell and then choose the type of graph you want (histogram or cumulative). Right-click on any graph to change its format or to copy it into a standard Excel graph. • To simulate for different values of a decision variable (One variable at a time!): • Use RiskSimTable({x1,x2,…xn}); x1, x2, … xn can be cells or numbers. • type n in “# of simulations” under @Risk | Simulation | Settings • Reports: mean, std, percentiles

  9. Some Tips • @Risk will run all the models that are open. If you are only interested in results from one model, close all other models. • @Risk can handle multiple random variables. • @Risk allows formulas such as: B1*(1+RiskNormal(10,9))+B3 • @Risk can handle multiple output cells

  10. Introduction to Simulation • Approaches to analyzing uncertainty: • Monte Carlo simulation using computers • Why important? • Disadvantages

  11. Factory Physics • Managing production lines without variability • Managing production lines with variability • Throughput rate, flow time and inventory levels • Line balancing • Single machine stations vs. parallel machines • Sources of variability

  12. punch press cuts penny blanks stamps Lincoln’s face places a rim on the penny cleans away any burrs The Penny Fab A production line that makes giant one-cent pieces. The line consists of four machines in sequence. Capacity of each machine is one penny every two hours. (A balanced line with no variability.) • Theoretical flow time (hours) T0 = • Bottleneck rate per hour R0= • To achieve R0, Inventory needed is: I0=

  13. Penny Fab One 2 hrs 2 hrs 2 hrs 2 hrs T = Flow Time for each Penny R = Throughput Rate for System Critical WIP level I0

  14. Throughput and Flow Time vs. Inventory .5 20 Throughput Rate (Jobs/hr) .4 16 Flow Time (Hours) .3 12 Flow time (Hours) Throughput (Jobs/hr) .2 8 .1 4 0 0 0 2 4 6 8 10 12 14 Inventory (jobs) To achieve the Theoretical Throughput Rate R0 = The minimum Inventory needed is I0 = 0.5 jobs per hour 4.0 jobs

  15. Penny Fab Two 2 hr 5 hr 3 hr 10 hr Station 1 Station 2 Station 3 Station 4

  16. Penny Fab Two R0 = T0 = _______________ I0 = ________________ Station 1 Station 2 Station 3 Station 4 # of jobs Utilization

  17. 5 jobs/shift 2.5 jobs/shift on each machine Line Balancing • Processing rate at station 1: 1 job/shift 50% of the time, 4 jobs/shift 50% of the time; avg 2.5 jobs/shift • Processing rate at station 2: 2 jobs/shift 50% of the time, 8 jobs/shift 50% of the time; avg 5 jobs/shift => Extra capacity at the first station!

  18. Line Balancing (cont.) The expected output rate = jobs/shift

  19. Line Balancing (cont.) • If we shut down one of the machines at station 1, the expected output rate jobs/shift. What is the capacity of a line with variability?

  20. 0.5 without variability 0.4 with variability 0.3 Throughput Rate, R 0.2 0.1 0 2 4 6 8 10 12 14 16 18 20 22 24 26 Inventory, I Penny Fab Two Throughput Rate With variability • Simulation is the tool to find R(I) and T(I) !! • To get close to the bottleneck rate R0 you might need a huge inventory!!

  21. Penny Fab Two Flow Time 80 70 60 With variability 50 Flow Time, T T 40 30 without variability 20 10 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 Inventory, I

  22. c = 1 c = 1 c = 1 c = 1 2 hrs 2 hrs 2 hrs 2 hrs c = 2 c = 1 c = 1 2 hrs 2 hrs 4 hrs Penny Fab One • Single Machine Stations • Parallel Machines

  23. Internal Benchmarking Example Large Panel Line:

  24. Internal Benchmarking • Best inventory level without variability = 126.5  33.1 = 4,187 • Actual Values: • Benchmark: • T = 34 days = 816 hours – Theoretical FT= 33.1 hours • I = 37,400 panels – “best inv level” = 4,187 panels • R = 45.8 panels/hour – Bottleneck rate = 126.5 panels/hr • Conclusions: • Throughput is 36% of capacity • WIP is 8.9 times the “best inventory level” • Flow Time is 24.6 times theoretical flow time • Why?

  25. Takeaways • @Risk • Spreadsheet model: performance measures, decision variables, random variables • Probability functions for representing random variables, e.g., RiskNormal(m,s) • Decision variables: RiskSimTable (one variable at a time!) • Output cells for performance measures (Riskoutput) • Simulation settings (run length, desired reports) • Reports (mean, std., percentiles) • Simulation • Methods of modeling uncertainty • Monte Carlo simulation: random number generation

  26. Takeaways • Managing production lines without variability • There exists an optimal Inventory level = bottleneck rate  theoretical flow time • Managing production lines with variability • Throughput rate increases as inventory increases • Throughput rate < bottleneck rate • Unbalance Lines • Single machine stations vs. parallel machines

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