Question

In the molding shop, there are 11 machines capable of molding the one part done in-house, but historically one machine is always being maintained or repaired at any given time. Each machine requires a full-time operator who earns an hourly wage of $15, though only 50 minutes of a molding operator's typical hour is occupied with the tasks of loading, unloading, actively monitoring, and adjusting the machine. The machines can each produce 25 parts per hour. The workers will work overtime at a 50% wage premium. There are currently only 6 operators dedicated to molding this automobile component. An additional 4 operators are available from a labor pool within the company.

In the final assembly shop, purchased parts and those molded in-house are assembled by 15 workers working an eight-hour shift on an assembly line that moves at the rate of 150 components per hour. Each assembly worker earns a wage of $10 per hour, though on average only 37.5 minutes of an assembly worker's typical hour is spent working directly on components. Management believes that they could hire 15 more workers for a second shift if necessary.

The size of inventories represented in the figure depend on many factors, including the degree of synchronization in the scheduling that takes place in molding and in purchasing. It may be reasonable to assume that, in order to have uninterrupted final assembly, there are always some molded and purchased parts in inventory.

Question:

Determine the rate of output (or capacity) of the component operation. Assume the department purchasing parts has virtually unlimited capacity, i.e., it can provide any reasonable number of parts each week. Determine the direct labor content, direct labor utilization and labor cost of the molding and assembly tasks.

Answer 1

Answer:

 

Given data,

 

Component workers

	Ti	1/Ti	Ci	Ci/Ti
Component Worker	2.5 parts per min	1 /2.5 = .4	15 workers	15 / .4 =6

 

Effective Capacity of Component 8 hr day

 

6 * 480 mins = 2880

1200/2880 = 0.4166

(150 components * 8 hr = 1200)

Capacity Utilization = 41.66%

Molding Direct Labor Cost

($15/ 1 hour) / (25/hr)

.25/.41 = $.6 per minute    0.6* 60 mins = $36

$36 per hour * 6 = $216 per hour direct labor cost

Direct Labor Content

50 mins on machine * 6 workers = 300 min per hour

Labor Utility

50 min/ 60 min =0.83 per hour

Labor Utility = 83% per hour

 

Assembly workers

Direct Labor Cost

($10/ hr) / (150 components/ hr)

(10/60) / (150/60)

0.166/ 2.5 = 0.0664

0.0664 * 60 mins = $4 per hour

4*15 workers = $60 for direct labor cost for 15 workers

 

Direct Labor Content

 

37.5 min on machine * 15 workers = 562.5 mins of Direct Labor content

Avg. labor utility

562.5*(562.5 + 337.5 mins idle) =0.625

(all 15 workers accounted for)

Average labor utility = 62.5%