Question

Changeover of fixtures on a machine takes 35 minutes. Following the changeover, an average
of four parts must be produced and discarded to make adjustment before the correct setting is
achieved. For each part the processing time is two minutes and the material cost is $1.50. The
labor cost for a skilled setup person to do the changeover and adjustment is $15.50 per hour.
The labor cost of the machine operator is $10.50 per hour. Currently, the part is produced in
batches of 50 units. Suppose the setup procedure could be simplified so that the operator would
be able to do it and not have to make any adjustment in the setting. What must the fixture
changeover time be reduced to such that a batch size of 20 units could be produced for the same
average per-unit cost as the present cost? Assume the per-unit cost includes labor and material
costs of setup and production; also, assume the machine’s excess capacity is ample and is not
a consideration.

Answer 1

Current Scenario:

Change over cost = changeover labour price*change over time = 15.5*35/60 = $9.04

Labour cost = No. of units made(54: 4 discarded)* operating labour price*time taken per unit = 54*10.5*2/60 = $18.9

Material Cost = No. of units*cost of material per unit = 54*1.5 = $81

Total cost = sum of above three costs: $108.94

This cost is averaged over 50 units. So per unit average cost = 108.94/50 =$2.1788 ....(1)

Future Scenario: 4 units won't be wasted in setup and setup will require no adjustments

only 20 units will be produced.

Material cost = 20*1.5 = $30

Labour cost = 20*2*10.5/60= $7

Suppose changeover time be 'x' minutes. Changeover cost = 15.5*x/60= 0.258333*x

Total cost = 37 + .258333x

Average cost per unit = (37 + .258333x)/20 ...... (2)

As per question, these two average costs in (1) and (2) should be equal.

Hence, x = (2.1788*20-37)/.258333 = 25.46 minutes

Hence, required changeover time is 25.46 minutes.