HW-02-03-10s-Ch2_3-1

HW-02-03-10s-Ch2_3-1 - IE 131 Solutions for Problems due...

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IE 131 Solutions for Problems due Feb 3 (Chs 2 and 3) 2.18 The standard time to produce a certain part in a worker-machine system is 9.0 min. A rush order has been received to supply 1000 units of the part within five working days (40 hours). How many worker-machine systems must be diverted from other production to satisfy this order? Each machine must be set up at the beginning of production of parts for the order, and the setup time per machine is 5.0 hours. Fraction defect rate is 5%, and worker efficiency is 100%. Availability is expected to be 98% during setup and production. How many machines and machine operators are required during the week? Solution : Production workload WL p = 1,000(9.0)/60(1 – 0.05) = 157.9 hr/wk Setup workload WL su = 5.0 n Total workload WL = 157.9 + 5.0 n Available time (production and setup) AT = 40(0.98) = 39.2 hr/wk per machine n = (157.9 + 5.0 n )/39.2 39.2 n = 157.9 + 5.0 n 34.2 n = 157.9 n = 4.62 rounded up to 5 machines and 5 operators 2.25 In a worker-machine cell, the appropriate number of production machines to assign to the worker is to be determined. Let n = the number of machines. Each production machine is identical and has an automatic processing time T m = 4.0 min to produce one piece. Servicing time T s = 12 sec for each machine. The full cycle time for each machine in the cell is T c = T s + T m . The walk time (repositioning time) for the worker is given by T r = 5 + 3 n , where T r is in seconds. T r increases with n because the distance between machines increases with more machines. (a) Determine the maximum number of machines in the cell if no machine idle time is allowed. For your answer, compute (b) the cycle time, (c) the worker idle time expressed as a percentage of the cycle time, and (d) the production rate of the machine cluster. Solution : (a) T c = T m + T s = 4.0(60) + 12 = 252 sec Worker time per machine = T s + T r = 12 + 5 + 3 n = 17 + 3 n n = 252/(17 + 3 n ) n (17 + 3 n ) = 252 17 n + 3 n 2 = 252 Setting this up to use the quadratic equation, 3
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HW-02-03-10s-Ch2_3-1 - IE 131 Solutions for Problems due...

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