Machining Cost Optimization Involving Shift and Overtime Work

[+] Author and Article Information
Esko Niemi

Department of Mechanical Engineering, Lappeenranta University of Technology, P.O. Box 20, FIN-53851 Lappeenranta, Finlande-mail: Esko.Niemi@lut.fi

J. Manuf. Sci. Eng 122(4), 790-794 (Jan 01, 2000) (5 pages) doi:10.1115/1.1314600 History: Received July 01, 1999; Revised January 01, 2000
Copyright © 2000 by ASME
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Hourly labor cost as a function of annual machine occupation time
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Cost minimizing cutting speeds at different production volumes. The parameter values are: n=0.25,C=200 m/min (15 min)0.25=394,s=7670 m,tc=3 min,ct=8.4 EUR and th=15 min. Two labor cost categories exist, w1=16.5 EUR/hour,w2=100.9 EUR/hour,Δt1=50 h and Δt2=50 h; see notation of Eq. (1).
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The minimized total cutting cost per unit for different production volumes. The unit cost shown does not include the fixed cost or such variable cost that is constant per unit produced.
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Cutting speeds for the long-run example. “Optimal” is the minimum cost cutting speed determined at each production rate. The fixed 160 m/min cutting speed shown is used in the cost comparisons in Fig. 5. The parameter values are: n=0.25,C=200 m/min (15 min)0.25=394,s=11 930 m,tc=3 min,ct=8.4 EUR,th=15 min. The maximum total annual process hours are assumed to be 8500. The labor costs and corresponding hours at annual level are shown in Table 1. An hourly variable cost of 3.4 EUR is assumed.
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Average manufacturing costs for the example machining process at the cost minimizing cutting speed at each production volume and at 160 m/min constant speed. The two lower lines show those variable costs that affect the optimization. The two upper lines show the total unit costs, where the fixed cost is included. The capital investment in machinery etc. is 673 kEUR, interest rate 7 percent and depreciation time 10 years. There are no other fixed costs and the variable cost directly related to volume is set to zero. The other parameter values are given under Fig. 4. The minimum of the optimized total cost curve is at the production volume of 4590 units and the minimum of the constant cutting speed curve is at 4830 units in this case.
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Cutting speeds for the short-run example. The fixed 132 m/min cutting speed shown for comparison is the speed that produces minimum cost for two-shift work in the earlier long-run example. The cost parameters are the same as in the long-run example except as follows: the hourly variable cost is zero since such costs are taken to be fixed within the short planning time considered. Four labor cost categories exist, w1 (regular time)=0, w2=25.2 EUR/hour, w3=33.6 EUR/hour, w4=50.5 EUR/hour, Δt1=80 h, Δt2=10 h, Δt3=20 h and Δt4=20 h.
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Average manufacturing costs for the short-run example machining process. The lines show those variable costs that affect the optimization. The parameter values are given in Fig. 6.
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The minimum cost cutting speeds for the example with several tool types. The parameter values are: n1=0.25,C1=200 m/min (15 min)0.25=394,s1=5369 m,tc1=3 min,ct1=8.4 EUR, n2=0.50,C2=500 m/min (15 min)0.5=1936,s2=8000 m,tc2=3 min,ct2=16.8 EUR,n3=0.30,C3=250 m/min (15 min)0.30=563,s3=4000 m,tc3=3 min,ct3=6.7 EUR and th=21 min. The maximum total annual process hours are assumed to be 8500. The labor costs and corresponding hours at annual level are the ones shown in Table 1. An hourly variable cost of 3.4 EUR is assumed.



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