1. The ABC Company is planning a new product line and a new plant to produce the parts for the line. The product line will include 8 different models. Annual production of each model is expected to be 900 units. Each product will be assembled of 180 components. All processing of parts will be accomplished in the new plant. On average, 6 processing operations are required to produce each component, and each operation takes an average of 1.0 min (including an allowance for setup time and part handling). All processing operations are performed at workstations, each of which includes a production machine and a human worker. The plant operates one shift. Determine the number of (a) components, (b) processing operations, and (c) workers that will be needed to accomplish the processing operations if each worker works 2000 hr/yr.
2. One million units of a certain product are to be manufactured annually on dedicated production machines that run 24 hours per day, five days per week, 50 weeks per year. (a) If the cycle time of a machine to produce one part is 1.0 minute, how many of the dedicated machines will be required to keep up with demand? Assume that availability, utilization, worker efficiency = 100%, and that no setup time will be lost. (b) Solve part (a) except that availability = 0.90.
3. A mass-production plant has six machines and currently operates one 8-hour shift per day, 5 days per week, 50 weeks per year. The six machines produce the same part each at a rate of 12 parts per hour. (a) Determine the annual production capacity of this plant. (b) If the plant were to operate three 8-hour shifts per day, 7 days per week, 52 weeks per year, determine the annual percentage increase in plant capacity?
4. A job shop has four machines and operates 40 hours per week. During the most recent week, machine 1 processed part A for 25 hours at a production rate of 10 parts per hour, and part B for 12 hours at a rate of 7 parts per hour. Machine 2 processed part C for 37 hours at a rate of 14 parts per hour, and was idle 3 hours. Machine 3 processed part D for 15 hours at a rate of 20 parts per hour, and part E for 25 hours at a rate of 15 parts per hour. Machine 4 processed part F for 13 hours at a rate of 9 parts per hour, part G for 12 hours at a rate of 18 parts per hour, and was idle the rest of the week. Determine (a) weekly production output of the shop and (b) average utilization of equipment.
5. The table below presents production data for three batches of parts processed through a batch production plant. Production rates (Rp) are given in parts per hour. Utilization fractions (f) are the fractions of time during the 40-hour week that the machine is devoted to the production of these parts. The parts do not proceed through the machines in the same order. Determine (a) weekly production rate, (b) workload, and (c) average utilization of this set of equipment. A spreadsheet calculator is recommended for this problem.
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Machine 1
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Machine 2
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Machine 3
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Machine 4
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Part
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Rp1
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f1
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Rp2
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f2
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Rp3
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f3
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Rp4
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f4
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A
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15
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0.3
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22.5
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0.2
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30
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0.15
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7.5
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0.6
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B
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10
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0.5
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12.5
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0.4
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8
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0.625
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C
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30
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0.2
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15
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0.4
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20
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0.3
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6. A batch production plant processes an average of 35 batches of parts per week. Five of those part styles have been selected as a sample for analysis to assess the production performance of the plant. The five parts are considered to be representative of the population of parts processed by the plant. Any machine in the plant can be set up for any type of batch processed in the plant. Batch quantities, numbers of operations in the processing sequence, setup times, and cycle times for the parts are listed in the table below. The average nonoperation time per batch per operation is 11.5 hours. The plant operates 40 hours per week. Use this sample to determine the following measures of plant performance: (a) manufacturing lead time for an average part, (b) plant capacity if all machines could be operated at 100% utilization, and (c) work-in-process (number of parts- in-process). Use of a spreadsheet calculator is recommended for this problem.
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Part j
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Qi
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noj
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Tsuij (hr)
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Tcij / (min)
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Tno (hr)
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A
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100
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6
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5.0
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9.3
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11.5
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B
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240
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3
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3.8
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8.4
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11.5
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C
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85
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4
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4.0
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12.0
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11.5
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D
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250
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8
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6.1
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5.7
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11.5
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E
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140
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7
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3.5
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3.2
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11.5
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7. In the operation of a certain production machine, one worker is required at a direct labor rate = $10/hr. Applicable labor factory overhead rate = 50%. Capital investment in the system = $250,000, expected service life = 10 years, no salvage value at the end of that period, and the applicable machine factory overhead rate = 30%. The work cell will operate 2000 hr/yr. Use a rate of return of 25% to determine the appropriate hourly rate for this work cell.
8. The break-even point is to be determined for two production methods, one a manual method and the other automated. The manual method requires two workers at $9.00/hr each. Together, they produce at a rate of 36 units/hr. The automated method has an initial cost of $125,000, a 4-year service life, no salvage value, and annual maintenance costs = $3000. No labor (except for maintenance) is required to operate the machine, but the power required to run the machine is 50 kW (when running). Cost of electric power is $0.05/kWh. If the production rate for the automated machine is 100 units/hr, determine the break-even point for the two methods, using a rate of return = 25%.
9. A customer has requested a quotation for a machining job consisting of 80 parts. The starting work part is a casting that will cost $17.00 per casting. The average production time of the job is 13.80 min on an automatic machine whose equipment cost rate is $66.00 per hour. This rate does not include any overhead costs. Tooling cost is $0.35 per part. The factory overhead rate is 128% and the corporate overhead rate is 230%. These rates are applied only to time and toooling costs, not starting material costs. The company uses a 15% markup on total cost for its price quotes. What is the quoted price for this job?
10. A part is processed through six operations in a batch production plant. Cost of the starting material for each unit is $5.85. Batch quantity = 40 parts. The table below presents time and cost data for the six operations: Tsu= setup time, Th= part handling time, To= operation processing time, Tt = tool handling time where applicable, Tno= nonoperation time, Co = operating cost of the work center, and Ct = tool costs where applicable. Determine the total production cost for this part. A spreadsheet calculator is recommended for this problem.
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Operation
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Tsu
(hr)
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Th
(min/Pc)
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To
(min/Pc)
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Ts
(min/Pc)
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Tno
(hr)
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Co
($/hr)
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Cs
($/pc)
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1
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2.5
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0.25
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1.25
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0
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10
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32.88
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0
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2
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1.3
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0.22
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2.50
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0.25
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10
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65.50
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0.22
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3
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4.1
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0.30
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1.75
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0
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10
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48.25
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0
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4
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1.7
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0.25
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0.85
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0.10
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10
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72.15
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0.16
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5
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1.4
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0.18
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1.67
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0
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10
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45.50
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0
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6
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0.8
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0.33
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0.95
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0.15
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10
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29.75
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0.18
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