Some tasks and the order in which they must be performed according to their assembly requirements are shown in the following table. These are to be combined into workstations to create an assembly line. The assembly line operates 71?2 hours per day. The output requirement is 1,000 units per day. Preceding Time Preceding Time Task Preceding Tasks Time (Seconds) Task Preceding Task Time (Seconds) A - 15 G C 11 B A 24 H D 9 C A 6 I E 14 D B 12 J F,G 7 E B 18 K H,I 15 F C 7 L J,K 10 a. What is the workstation cycle time required to produce 1,000 units per day? b. Balance the line using the longest task time based on the 1,000-unit forecast, stating which tasks would be done in each workstation. c. For (b), what is the efficiency of your line balance, assuming it is running at the cycle time from part (a)? d. After production was started, Marketing realized that it understated demand and must increase output to 1,100 units. What action would you take? Be specific and quantitative in your answer. 8. An initial solution has been given to the following workcenter layout problem. Given the fl ows described and a cost of $2.00 per unit per foot, compute the total cost for the layout. Each location is 100 feet long and 50 feet wide as shown in the following fi gure. Use the centers of departments for distances and measure distance using metropolitan-rectilinear distance. Department A B C D A 0 10 25 55 Department B 0 10 5 C 0 15 D 0 100' 100' 100' 50' A B C 50' D 50' CHAPTER 12 7. The following table lists all costs of quality incurred by Sam's Surf Shop last year. What was Sam's appraisal cost for quality last year? Annual inspection costs $ 155,000 Annual cost of scrap materials 286,000 Annual rework cost 34,679 Annual cost of quality training 456,000 Annual warranty cost 1,546,000 Annual testing cost 543,000 10. A manufacturing company has been inspecting units of output from a process. Each product inspected is evaluated on fi ve criteria. If the unit does not meet standards for the criteria it counts as a defect for the unit. Each unit could have as few as zero defects, and as many as fi ve. After inspecting 2,000 units, they discovered 33 defects. What is the DPMO measure for this process? CHAPTER 13 6. C-Spec, Inc., is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of 4+6 .003 inches. After a trial run on this machine, C-Spec has determined that the machine has a sample mean of 4.001 inches with a standard deviation of .002 inch. a. Calculate the Cpk for this machine. b. Should C-Spec use this machine to produce this part? Why? 7. Ten samples of 15 parts each were taken from an ongoing process to establish a p-chart for control. The samples and the number of defectives in each are shown in the following table: Number of Number of Defective Items Defective Items Sample n in the Sample Sample n in the Sample 1 15 3 6 15 2 2 15 1 7 15 0 3 15 0 8 15 3 4 15 0 9 15 1 5 15 0 10 15 0 a. Develop a p-chart for 95 percent confi dence (1.96 standard deviation). b. Based on the plotted data points, what comments can you make? 8. A shirt manufacturer buys cloth by the 100-yard roll from a supplier. For setting up a control chart to manage the irregularities (e.g., loose threads and tears), the following data were collected from a sample provided by the supplier. Sample 1 2 3 4 5 6 7 8 9 1 0 Irregularities 3 5 2 6 5 4 6 3 4 5 a. Using these data, set up a c-chart with z 5 2. b. Suppose the next five rolls from the supplier had three, two, five, three, and seven irregularities. Is the supplier process under control? 9. Resistors for electronic circuits are manufactured on a high-speed automated machine. The machine is set up to produce a large run of resistors of 1,000 ohms each. To set up the machine and to create a control chart to be used throughout the run, 15 samples were taken with four resistors in each sample. The complete list of samples and their measured values are as follows: Sample Number Readings (in ohms) 1 1010 991 985 986 2 995 996 1009 994 3 990 1003 1015 1008 4 1015 1020 1009 998 5 1013 1019 1005 993 6 994 1001 994 1005 7 989 992 982 1020 8 1001 986 996 996 9 1006 989 1005 1007 10 992 1007 1006 979 11 996 1006 997 989 12 1019 996 991 1011 13 981 991 989 1003 14 999 993 988 984 15 1013 1002 1005 992 Develop an X-chart and an R-chart and plot the values. From the charts, what comments can you make about the process? (Use three-sigma control limits as in Exhibit 13.7.) Your company assembles five different models of a motor scooter that is sold in specialty stores in the United States. The company uses the same engine for all five models. You have been given the assignment of choosing a supplier for these engines for the coming year. Due to the size of your warehouse and other administrative restrictions, you must order the engines in lot sizes of 1,500 each. Because of the unique characteristics of the engine, special tooling is needed during the manufacturing process which you agree to reimburse the supplier. Your assistant has obtained quotes from two reliable engine suppliers and you need to decide which to use. The following data has been collected: Requirements (annual forecast) 18,000 units Weight per engine 25 pounds Order processing cost $120 per order Inventory carry cost 25 percent of the average value of inventory per year Note:Assume that half of lot size is in inventory on average (1,500/2 = 750 units). Two qualified suppliers have submitted the following quotations: Unit Price Supplier 1 Supplier 2 1 to 1,499 units/order $510.00 $505.00 1,500 to 2,999 units/order 500.00 505.00 3,000 + units/order 490.00 488.00 Tooling costs $22,000 20,000 Distance 1125 miles 100 miles Your assistant has obtained the following freight rates from your carrier: Truckload (40,000lbs. each load): $0.80 per ton-mile Less-than-truckload: $1.20 per ton-mile Note:Per ton-mile = 2,000 lbs. per mile A. Perform a total cost of ownership analysis and select a supplier. B. Would it make economic sense to order in truckload quantities? Would your supplier selection change if you ordered truckload quantities? Jill’s Job Shop buys two parts (Tegdiws and Widgets) for use in its production system from two different suppliers. The parts are needed throughout the entire 52-week year. Tegdiws are used at a relatively constant rate and are ordered whenever the remaining quantity drops to the reorder level. Widgets are ordered from a supplier who stops by every three weeks. Data for both products are as follows: ITEM Annual demand Holding cost (% of item cost) Setup or order cost Lead time Safety stock Item cost TEGDIW WIDGET $10,000 $5,000 20% 20% $150.00 $25.00 4 weeks 1 week 55 units 5 units $10.00 $2.00 a. What is the inventory control system for Tegdiws? That is, what is the reorder quantity and what is the reorder point? Item X is a standard item stocked in a company’s inventory of component parts. Each year the firm, on a random basis, uses about 2,000 of item X, which costs $25 each. Storage costs, which include insurance and cost of capital, amount to $5 per unit of average inventory. Every time an order is placed for more item X, it costs $10. a. Whenever item X is ordered, what should the order size be? b. What is the annual cost for ordering item X? c. What is the annual cost for storing item X? In the past, Taylor Industries has used a fixed-time period inventory system that involved taking a complete inventory count of all items each month. However, increasing labor costs are forcing Taylor Industries to examine alternative ways to reduce the amount of labor involved in inventory stockrooms, yet without increasing other costs, such as shortage costs. Here is a random sample of 20 of Taylor’s items. Item Annual Item Annual Number Usage Number Usage __________________________________________________________ 1 $1,500 11 $13,000 2 12,000 12 600 3 2,200 13 42,000 4 50,000 14 9,000 5 9,600 15 1,200 6 750 16 10,200 7 2,000 17 4,000 8 11,000 18 61,000 9 800 19 3,500 10 15,000 20 2,900 a. What would you recommend Taylor do to cut back its labor cost? (Illustrate using an ABC plan.) b. Item 15 is critical to continued operations. How would you recommend it be classified?