Operations Management, FARE*3310 - Fall 2017: Assignment 2 Last Name First Name 222 333 333 333 333 333 333 333 333 333 STUDENT ID NUMBER INSTRUCTIONS: 1. Your name and student number must be clearly displayed on this cover page and on each page of all your answer sheets; and number the pages. 2. This assignment contains FOUR questions with subparts. 3. If you have any queries the instructor or the GTAs will try to help you. 4. This assignment booklet contains 3 pages, including this cover page. 5. The assignment will count for 7.5 percent of your final grade. You are required to answer ALL questions. The point value of each question is shown at the beginning of the question. 6. SHOW YOUR WORK FOR FULL CREDIT. 7. Please round your calculations to THREE decimal places (e.g. 0.001). 8. If you have to, make reasonable assumptions, but explain/justify any assumptions made in your answers. 9. Please note that late assignments will be given a zero grade. 10. Due Date: Friday, October 27, 2017, beginning of the class. 11. Please attach this cover page to the front of your assignment. Question 1 2 3 4 Total Maximum 20 20 20 15 75 Your Score 1 Grader Comments 1. [Chapter S6: 20 points] A customer service centre wants to develop control charts for its service waiting time. The following table shows waiting time (in minutes) for four samples for five customers for customer service call centre. Table 1 Customer waiting times (in minutes) Samples #1 #2 1 4.5 4.2 2 4.6 4.5 3 4.5 4.6 4 4.7 4.6 #3 4.2 4.4 4.4 4.8 #4 4.3 4.7 4.4 4.5 #5 4.3 4.3 4.6 4.9 , and the ranges, R, of these measurements for each a) Use the data in Table 1 to calculate the averages, . (5) , and the average range, sample. Next, calculate the overall average, b) Set up three-sigma control limits for average and range. Plot the appropriate data on the control charts and determine whether the process distribution appears to be in control? (6) c) One more sample results in the following customer waiting times: 4.6, 4.7, 4.9, 4.8, 4.9. Use the control limits determined in part (b) to decide if the process distribution is in control. (3) d) Suppose that the standard deviation of the waiting time process distribution is 0.1 minutes. If customer service wants to answer all calls within 4.5 0.4 minutes, what are the upper and lower specification limits? The process is known to operate at a mean of 4.5 minutes. What are the Cp and Cpk for this process? About what percentage of all units of the product will meet specifications? If each nonconforming customer service costs the customer service centre $5, and the annual service volume is 500,000 customers, what is the annual total cost of nonconforming customer services? Is the process capable of delivering a six-sigma service quality? If not, what should the standard deviation of the process be to meet sigma six quality? (6) 2. [Chapter S6: 20 points] A medical facility does MRIs for sports injuries. Occasionally a test yields inconclusive results and must be repeated. Using the following fifteen sample results for the number of retests in 50 observations (n=50) each: Sample (day) Number of retests 1 1 2 2 3 2 4 0 5 2 6 1 7 2 8 0 9 2 10 7 11 3 12 2 13 1 14 0 15 5 a) Calculate the proportion of retests in each sample, calculate the average proportion of retest, and calculate three-sigma upper and lower control limits. (5) b) Construct a control chart for the proportion of retests using three-sigma limits. Is the process in control? Why? (4) c) Would your conclusion in (2.b) change if you use four-sigma control limits? Why? What about twosigma? (3) d) In addition to the test results, the medical centre wants to monitor the number of complaints received from its patients. The quality control manager collected and summarized the following number of complaints per week, for fifteen weeks. The complaints for the fifteen weeks are recorded as follows: Calculate the average number of complaints. Construct a three-sigma c-chart for this process and indicate if the process was out of control at any time. (6) Sample (day) # of complaints 1 4 2 10 3 14 4 8 5 9 6 6 7 5 8 11 9 12 10 7 11 6 12 4 13 2 14 10 15 0 e) If 16 complaints are received today (day 16), use the control limits determined in part (d) to decide if the process is in control. (2) 2 3. [Chapter 4: 20 points] A local commercial farm sells pumpkins for Halloween to grocery stores within a 100-kilometer radius of its farm. The operation manager of the farm recognizes that pumpkin business is competitive and risky, and the ability to correctly predict demand for the next season and deliver orders promptly is a big factor in getting new customers and maintaining old ones. Customers typically don't place an order in advance. The operation manager of the farm wants to be certain that enough drivers and vehicles are available to deliver orders promptly and that they grow enough pumpkins for the season. The operation manager wants to be able to forecast the demand for 2017. From previous orders, the farm has the following information for 2007 through 2016. Month 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 Orders 8,000 7,200 8,000 10,000 8,800 4,000 6,000 6,400 4,400 7,200 a) Forecast orders for 2010 through 2017 using (i) naive method, (ii) a 2-month moving average; (iii) a 3-month moving average, (iv) a 3-month weighted moving average. Use weights of 4, 3, and 2, with the heavier weights on the more recent months, (v) exponential smoothing with = 0.4. Assume that the initial forecast for 2009 was 8,000. (10) b) Compute the mean absolute deviation (MAD) for 2010 through 2016 for each of the methods used. Which method would you recommend to forecast orders for 2017? Why? What would be the forecast for 2017? If = 0.5 for the exponential smoothing method, would your recommendation change? Why? (10) 4. [Chapter 17 and Chapter S6: 15 points] a) [Ch. 17] With the booming world economy, the sand and building stones consumed in the construction industry are considerably increasing. To obtain the sand that meets the quality requirements of the construction engineering, various types of mechanical sand washing systems are developed and used to clean the sea sand. Based on the structural characteristic of the mechanical sand washing system, the following reliability diagram is established. What is the reliability of the system? (5) b) [Ch. 17] A system for the electric motor power of the sand washing machine has four sensitive components connected in series with reliabilities of 0.95, 0.92, 0.94 and 0.96. According to the quality department of the manufacturer of the electric motor, the current system lacks reliability. At the manufacturing plant, the engineers have proposed to improve the reliability of the system. The new system still has four components, but the motor has a backup for each component. The four backup components all have a reliability of 0.95. What is the reliability of the series (old) system? What is the reliability of the new (proposed) motor? If you pay a premium, the manufacturer can improve all four of the backup units to 0.98 (the third option). What is the reliability of the third option? (5) c) [Ch. S6] The manufacturer of the sand washing machine motor receives an average of 25 returns per month from its customers due to nonconformities. What type of control chart would you use to monitor this process? Using a three-sigma control chart, would thirty-six returns in a month warrant action? Why? (5) 3