Performance Metrics for a GT Cell A group-technology cell has three machines and is used to process a family of four similar parts. The table below lists production quantities (Qj), production times (Tpij), and machine fractions for each family member (fij). Assume the nonoperation times (Tno) are

Question

Performance Metrics for a GT Cell
A group-technology cell has three machines and is used to process a family of four similar parts. The table below lists production quantities [latex](Q_{j})[/latex], production times [latex](T_{pij})[/latex], and machine fractions for each family member [latex](f_{ij})[/latex]. Assume the nonoperation times [latex](T_{no})[/latex] are all the same at 30 min per machine. Determine (a) average hourly production rate for the cell, (b) utilization of each machine and average utilization of the cell, (c) manufacturing lead time, and (d) work-in-process.

		Machine 1		Machine 2		Machine 3
Part	[latex](Q_{j})[/latex]	[latex](T_{p1})[/latex] (min)	[latex](f_{1j})[/latex]	[latex](T_{p2})[/latex] (min)	[latex](f_{2j})[/latex]	[latex](T_{p3})[/latex] (min)	[latex](f_{3j})[/latex]
A	1	3.0	0.2	4.5	0.3	2.25	0.15
B	1	2.0	0.2	4.0	0.4	3.0	0.3
C	1	5.0	0.25	4.0	0.2	3.0	0.15
D	1	4.0	0.3	1.333	0.1	2.667	0.2

Accepted Answer

A spreadsheet calculator was used to perform the calculations. Hourly
production rates for each machine and family member were computed using Equation (18.2).

[latex]R_{pij} = \frac{60}{T_{pij}}[/latex]

The quantities of each family member produced in 1 hr were [latex]Q_{ij} = f_{ij}R_{pij}[/latex]. The total for each column represents the hourly output of all parts from each machine (17.5 pc/hr). Finally, the MLT values were obtained from [latex]MLT_{j} = T_{p1j} + T_{p 2j} + T_{p3j} + 3T_{no}[/latex]. These were averaged to obtain 99.7 min = 1.661 hr.

[latex]R_{p1}[/latex]	[latex]R_{p2}[/latex]	[latex]R_{p3}[/latex]	[latex]Q_{1}[/latex]	[latex]Q_{2}[/latex]	[latex]Q_{3}[/latex]	MLT
20.00	13.33	26.67	4.00	4.00	4.00	99.75
30.00	15.00	20.00	6.00	6.00	6.00	99.00
12.00	15.00	20.00	3.00	3.00	3.00	102.00
15.00	45.00	22.50	4.50	4.50	4.50	68.00
			17.50	17.50	17.50	398.75
				Average MLT = 99.7

Summary: (a) Hourly production rate for each machine and for the cell [latex]R_{p} = 17.5[/latex] parts /hr
Note that all three machines have the same production rate, which means that the workload in the cell is balanced.
(b) Utilization for each machine is given by [latex]\sum{f_{ij} }[/latex] for each machine i. Thus,
[latex]U_{1} = 0.95, U_{2} = 1.0,[/latex] and [latex]U_{3} = 0.80[/latex]. Average cell utilization U = 0.917.
(c) Average manufacturing lead time MLT = 99.7 min = 1.661 hr
(d) Average work-in-process WIP = (17.5 parts/hr)(1.661 hr) = 29.1 parts

Question 18.4: Performance Metrics for a GT Cell A group-technology cell ha...

Related Answered Questions

Rank-order Clustering Technique Apply the rank-order clustering technique to the part-machine incidence matrix in Table 18.3. ...

Verified Answer:

Rating Machine Sequences Compute (a) the percentage of in-sequence moves, (b) the percentage of bypassing moves, and (c) the percentage of backtracking moves for the solution in Example 18.2. ...

Verified Answer:

Group-technology Machine Sequence Using the Hollier Method A GT cell has four machines: 1, 2, 3, and 4. An analysis of 50 parts processed on these machines has been summarized in the from–to chart in Table 18.7. Additional information: 50 parts enter the machine grouping at machine 3, 20 parts ...

Verified Answer: