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  ME 451 S. G. Kapoor Homework #7 Due: 12/7/2017 1.   A manufacturing company has received an order for 500 gears. The primary dimensional control that the company has to worry about is the pitch circle diameter of the gear that should be within 3 +/-0.002 in. Because this item is being used in a number of products, the company wants to explore the possibility of using alternative technologies for its manufacture. A preliminary analysis indicates that a universal milling machine, a  broaching machine with a form type of broaching center, and a hobbing machine are available within the company. Estimate the unit cost of production, manufacturing lead time and expected number of defective gears produced on all these machine tools. The available data are shown in Table 2. The other data are: Unit raw material cost = $10.00 Unit salvage value = $ 2.00 Process average = 3.0002 in. Table 2 Type of machine tools Standard deviation (in.)Processing Cost per unit ($/unit)Processing Time per unit (min/unit)Universal milling machine 0.001 20.00 1.00 Broaching machine 0.000730.000.80 Hobbing machine 0.000132.000.70 2.   The steel rods of 40 cm long and 7 cm in diameter are turned on a CNC lathe at a feed rate of 0.2 mm per revolution and depth of cut of 2 mm. A lot of 1000 units of steel rods is machined. The tool life is given by V T 0.25  = 190. The other data are: Machine labor rate = $10/hour Machine overhead time = 200% of labor Grinding Labor time = $10/hour Grinding overhead rate = 300% of grinding labor Loading and unloading time = 2 min/piece Two types of carbide tools can be used for the turning operation: brazed inserts and throwaway inserts. The data related to the tools are:  Brazed Inserts Original cost of the tool = $25.00 Grinding Time = 3 min Tool changing time = 1 min The tool can be ground only five times before it is discarded. Throwaway Inserts Tool cost = $15.00   Tool changing time = 0.5 min Determine the following (assuming a single pass): (a)   Optimum tool life and optimum cutting speed to maximize the production rate (b)   Lead time to process the lot for the criterion of maximum production rate (c)   Which tool should be recommended for maximum production rate criterion? 3.   Consider the machine-component matrix of eight parts and five machines. Components Machines 1 2 34567 8 M1 1 111 1M2 1 1 11 1M3 1 1111 1M4 1 11 M5 1 1111 1 (a)   Determine similarity coefficients between all pairs of machines (b)   Analyze all the cell configurations in the similarity range 0.5 to 0.8. (c)   Assuming that intercell moves cost five times intracell moves, determine the optimal cell configuration to minimize the total cost of inter- and intracell material handling. 4.   A department manufactures three different products using a Kanban system. Data for the individual products are given in the following table. Setup time is negligible. (a)   Find the minimum number of Kanbans required for each part type assuming replenishment lead time is always four hours. (b)   Suppose that lead time is exponentially distributed with a mean of four hours. How many Kanbans are required for each part type to ensure that parts are available for at least 99% of the time that they are requested? Product Demand/hour Container size Unit processing time (hours) A 20 5 0.02 B 40 10 0.01 C 10 5 0.01 5.   A production center is used to manufacture several similar part types. Each set-up costs $150 and takes 3 hours. Economic Manufactured Quantity (EMQ) model is employed to decide the batch size. Processing time is deterministic with a capacity of 4,000 units per year. Production batches flow through the system with only minimal waiting time. Demand occurs at a constant rate of 1,000 units per year. The carrying cost rate is 40%/year and the raw material cost per item is $10. The production center is charged out at $30 per hour, including labor and the machining time is 60 minutes. Determine the impact on batch size, batch throughput time, number of set-ups, and total relevant inventory cost for a 30% reduction in set-up time and cost. The plant operated 2400 hours  per year.
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