1. 1 Lecture 6 MGMT 650 Simulation – Chapter 13

2. 2 Announcements  HW #4 solutions and grades posted in BB  HW #4 average = 111.30  Final exam today  Open book, open notes….  Proposed class structure for today  Lecture – 6:00 – 7:50  Class evaluations – 7:50 – 8:00  Break – 8:00 – 8:30  Final – 8:30 – 9:45

3. 3 Lecture 6 Simulation Chapter 13

4. 4 Simulation Is …  Simulation – very broad term  methods and applications to imitate or mimic real systems, usually via computer  Applies in many fields and industries  Simulation models complex situations  Models are simple to use and understand  Models can play “what if” experiments  Extensive software packages available  ARENA, ProModel  Very popular and powerful method

5. 5 Applications  Manufacturing facility  Bank operation  Airport operations (passengers, security, planes, crews, baggage, overbooking)  Hospital facilities (emergency room, operating room, admissions)  Traffic flow in a freeway system  Waiting lines - fast-food restaurant, supermarkets  Emergency-response system  Military

6. 6 Example – Simulating Machine Breakdowns  The manager of a machine shop is concerned about machine breakdowns.  Historical data of breakdowns over the last 100 days is as follows  Simulate breakdowns for the manager for a 10-day period Number of BreakdownsFrequency 010 130 225 320 410 55

7. 7 Simulation Procedure Expected number of breakdowns = 1.9 per day

8. 8 Statistical Analysis 95 % confidence interval for mean breakdowns for the 10-day period is given by:

9. 9 Monte Carlo Simulation Monte Carlo method: Probabilistic simulation technique used when a process has a random component  Identify a probability distribution  Setup intervals of random numbers to match probability distribution  Obtain the random numbers  Interpret the results

10. 10 Example 2 – Simulating a Reorder Policy  The manager of a truck dealership wants to acquire some insight into how a proposed policy for reordering trucks might affect order frequency  Under the new policy, 2 trucks will be ordered every time the inventory of trucks is 5 or lower  Due to proximity between the dealership and the local office, orders can be filled overnight  The “historical” probability for daily demand is as follows  Simulate a reorder policy for the dealer for the next 10 days  Assume a beginning inventory of 7 trucks Demand (x)P(x) 00.50 10.40 20.10

11. 11 Example 2 Solutions

12. 12 In-class Example using MS-Excel  The time between mechanics’ requests for tools in a AAMCO facility is normally distributed with a mean of 10 minutes and a standard deviation of 1 minute.  The time to fill requests is also normal with a mean of 9 minutes and a standard deviation of 1 minute.  Mechanics’ waiting time represents a cost of $2 per minute.  Servers represent a cost of $1 per minute.  Simulate arrivals for the first 9 mechanic requests and determine  Service time for each request  Waiting time for each request  Total cost in handling all requests  Assume 1 server only

13. 13 AAMCO Solutions

14. 14 Discrete Event Simulation Example 1 - A Simple Processing System

15. 15 Discrete Event Simulation Example 2 - Electronic Assembly/Test System  Produce two different sealed elect. units (A, B)  Arriving parts: cast metal cases machined to accept the electronic parts  Part A, Part B – separate prep areas  Both go to Sealer for assembly, testing – then to Shipping (out) if OK, or else to Rework  Rework – Salvaged (and Shipped), or Scrapped

16. 16 Part A  Interarrivals: expo (5) minutes  From arrival point, proceed immediately to Part A Prep area  Process = (machine + deburr + clean) ~ tria (1,4,8) minutes  Go immediately to Sealer  Process = (assemble + test) ~ tria (1,3,4) min.  91% pass, go to Shipped; Else go to Rework  Rework: (re-process + testing) ~ expo (45)  80% pass, go to Salvaged; Else go to Scrapped

17. 17 Part B  Interarrivals: batches of 4, expo (30) min.  Upon arrival, batch separates into 4 individual parts  From arrival point, proceed immediately to Part B Prep area  Process = (machine + deburr +clean) ~ tria (3,5,10)  Go to Sealer  Process = (assemble + test) ~ weib (2.5, 5.3) min., different from Part A, though at same station  91% pass, go to Shipped; Else go to Rework  Rework: (re-process + test) = expo (45) min.  80% pass, go to Salvaged; Else go to Scrapped

18. 18 Run Conditions, Output  Start empty & idle, run for four 8-hour shifts (1,920 minutes)  Collect statistics for each work area on  Resource utilization  Number in queue  Time in queue  For each exit point (Shipped, Salvaged, Scrapped), collect total time in system (a.k.a. cycle time)

19. 19 Simulation Models Are Beneficial  Systematic approach to problem solving  Increase understanding of the problem  Enable “what if” questions  Specific objectives  Power of mathematics and statistics  Standardized format  Require users to organize

20. 20 Simulation Process 1. Identify the problem 2. Develop the simulation model 3. Test the model 4. Develop the experiments 5. Run the simulation and evaluate results 6. Repeat 4 and 5 until results are satisfactory

21. 21 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?  Most operational models:  Dynamic, Discrete-change, Stochastic

22. 22 Advantages of Simulation  Solves problems that are difficult or impossible to solve mathematically  Flexibility to model things as they are (even if messy and complicated)  Allows experimentation without risk to actual system  Ability to model long-term effects  Serves as training tool for decision makers

23. 23 Limitations of Simulation  Does not produce optimum solution  Model development may be difficult  Computer run time may be substantial  Monte Carlo simulation only applicable to random systems

24. 24 Fitting Probability Distributions to Existing Data Data Summary Number of Data Points= 187 Min Data Value = 3.2 Max Data Value = 12.6 Sample Mean = 6.33 Sample Std Dev = 1.51 Histogram Summary Histogram Range = 3 to 13 Number of Intervals= 13

25. 25 ARENA – Input Analyzer Distribution Summary Distribution:Gamma Expression:3 + GAMM(0.775, 4.29) Square Error:0.003873 Chi Square Test Number of intervals= 7 Degrees of freedom = 4 Test Statistic = 4.68 Corresponding p-value= 0.337 Kolmogorov-Smirnov Test Test Statistic= 0.0727 Corresponding p-value> 0.15 Data Summary Number of Data Points= 187 Min Data Value = 3.2 Max Data Value = 12.6 Sample Mean = 6.33 Sample Std Dev = 1.51 Histogram Summary Histogram Range = 3 to 13 Number of Intervals= 13

26. 26 Simulation in Industry

27. 27 Course Conclusions  Recognize that not every tool is the best fit for every problem  Pay attention to variability  Forecasting  Inventory management - Deliveries from suppliers  Build flexibility into models  Pay careful attention to technology  Opportunities  Improvement in service and response times  Risks  Costs involved  Difficult to integrate  Need for periodic updates  Requires training  Garbage in, garbage out  Results and recommendations you present are only as reliable as the model and its inputs  Most decisions involve tradeoffs  Not a good idea to make decisions to the exclusion of known information