Closed-book part (total time for parts I and II: 100 minutes) + 10 minutes for those with roll-over minutes from Test 1.

Transcription

1 Closed-book part (total time for parts I and II: 100 minutes) + 10 minutes for those with roll-over minutes from Test 1. Part I: Use α of 5% for all problems. Problem 1 (20 points) An IE is to conduct a simulation of a manufacturing cell. The company s production line uses 5 different parts. During the data collection process manufacturing plant engineer informs the IE that the arrival percentage follows the rates below. Part Type % The IE has also collected 65 random observations during a day and has recorded the following observations on the number of parts: Part Type Count Stipulate what the IE can do with the data and form a hypothesis and conclude from your analysis. Problem 1 Alternative (20 points) A compost manufacturer adds used coffee to its compost to add additional nutrients to the compost for gardening. He has an agreement with several major coffee shops to collect their used ground coffee without any expenses. This is a win-win situation for both sides as the coffee shop does not have to pay for trash collection and the compost manufacturer gets it free. The agreement calls for the compost manufacturer to provide a large collector bin at the trash location of the store and must remove it every other day. For the compost manufacturer the agreement is justified if they can collect 160 Kg of coffee every other day. The compost manufacturer would like to simulate the collection process and evaluate different scenarios.

2 The record for the past 18 pickups indicates the following pickups in Kg: 144, 132, 158, 172, 156, 180, 146, 152, 162, 138, 155, 174, 186, 145, 153, 163, 164, compute a 95% confidence interval of μ and provide an interpretation of your interval. 2. Is there a strong evidence that μ is greater than 160? Problem 2 (30 points) A part manufacturer suspects that simulation model of his production line may be affected by two identical machines on the manufacturing floor which are supposed to be producing the at the same rate but in reality producing differently. In fact, he notices that machine 1 on the average produces 3 more units than machine 2 and that is why the simulation results cannot be verified by real results. He further believes that this is due to the changes in variance. To test his hypothesis, he checks the hourly production of each machine during the yesterday s two shifts. For Machine 1, which worked both shifts, production per hour numbers are: 9, 12, 11, 8, 10, 13, 9, 10, 12, 11, 13, 14, 7, 9, 11, and 12. For Machine 2, which worked only the first shift, production per hour numbers are: 8, 13, 6, 8, 9, 11, 7, and 10. Is the manufacturer right in his assumption? Problem 2 Alternative (30 points) Cases arrive at Supreme Court of Matunga with an exponential inter-arrival distribution of 3 per week. There are 7 judges and the court is in session for 40 weeks per year. Cases are assigned to judges randomly for evaluation which takes another exponentially distributed time with the mean of two weeks. When new cases arrive and no judge is available to be assigned to the case, 4 special assistants to Chief Justice, will work on those cases, each at most one case. When all judges are busy and the assistants have the cases, no new case is accepted for that term. Assistants keep working on the cases until a judge becomes available to be assigned to the case. When review of a case is completed it is schedule for full court hearing. Based on the provided information what is the expected average number of cases in the system? What is the expected average waiting time of the cases before they can be heard by the full court? Part II: SIMIO Model (50 points) A proposed production system consists of five serial automatic workstations. The processing times at each workstation are constant 11, 10, 11, 11, and 12 (in minutes). The part interarrival times are U(13, 15.1). There is an unlimited buffer in front of all workstations. Transfer times are negligible. At workstations 2 through 5 there is a chance that the part need to be reprocessed by the workstation that precedes it. The probability of revisiting a workstation is independent in that the same part could be sent back many times with no change in the

3 probability. At present it is estimated that this probability, the same for all workstations, is between 5% and 10%. Develop a simulation model and make 6 runs of 10,000 minutes each for probabilities of 5, 6, 7, 8, 9, and 10%. What should the analysis consist of? No actual SIMIO model needs to be developed. You need to draw and fully explain what to change and where.

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