Chapter 13, Problem 9E

Computador has a manufacturing plant in Des Moines that has the theoretical capability to produce 243,000 laptops per quarter but currently produces 91,125 units. The conversion cost per quarter is $7,290,000. There are 60,750 production hours available within the plant per quarter. In addition to the processing minutes per unit used, the production of the laptops uses 10 minutes of move time, 20 minutes of wait time, and 5 minutes of rework time. (All work is done by cell workers.)

Required:

1. 1. Compute the theoretical and actual velocities (per hour) and the theoretical and actual cycle times (minutes per unit produced).
2. 2. Compute the ideal and actual amounts of conversion cost assigned per laptop.
3. 3. Calculate MCE. How does MCE relate to the conversion cost per laptop?

To determine

Calculate the theoretical and actual velocities and the theoretical and actual cycle times.

Explanation of Solution

Cycle time: “Cycle time and velocity are two operational measures of responsiveness. Cycle time is the span of time taken to produce a unit of output from the time the materials are received till the good is supplied to finished goods inventory. Therefore, cycle time is the time taken to produce a product”.

Velocity: “Velocity is the number of units of output that can be produced within a given period of time”.

Calculate the theoretical velocity:

$\begin{array}{c}\text{Theoretical}\text{velocity}\text{=}\frac{\text{Laptops}\text{produced}\text{per}\text{quarter}}{\text{Production}\text{hours}\text{available}}\\ \text{=}\frac{\text{243,000}\text{units}}{\text{60,750}\text{hours}}\\ \text{=}\text{4}\text{laptops}\text{per}\text{hour}\end{array}$

Calculate actual velocity:

$\begin{array}{c}\text{Actual}\text{velocity}\text{=}\frac{\text{Laptops}\text{produced}\text{currently}}{\text{Production}\text{hours}\text{available}}\\ \text{=}\frac{\text{91,125}\text{units}}{\text{60,750}\text{hours}}\\ \text{=}\text{1}\text{.5}\text{laptops}\text{per}\text{hour}\end{array}$

Calculate theoretical cycle time:

$\begin{array}{c}\text{Theoretical}\text{cycle}\text{time}\text{=}\frac{\text{Time}\text{taken}}{\text{Units}\text{produced}}\\ \text{=}\frac{\text{60}\text{minutes}}{\text{4}\text{laptops}}\\ \text{=}\text{15}\text{minutes}\text{per}\text{laptop}\end{array}$

Calculate actual cycle time:

$\begin{array}{c}\text{Actual}\text{cycle}\text{time}\text{=}\frac{\text{Time}\text{taken}}{\text{Units}\text{produced}}\\ \text{=}\frac{\text{60}\text{minutes}}{\text{1}\text{.5}\text{laptops}}\\ \text{=}\text{40}\text{minutes}\text{per}\text{laptop}\end{array}$

Conclusion

Therefore, from the above calculations, it is ascertained that:

• The theoretical velocity is 4 laptops per hour.
• The actual velocity is 1.5 laptops per hour.
• The theoretical cycle time is 15 minutes per laptop.
• The actual cycle time is 40 minutes per laptop.

To determine

Calculate the ideal and actual amounts of conversion cost assigned per laptop.

Explanation of Solution

Calculate the ideal amount of conversion cost assigned per laptop:

$\begin{array}{c}\begin{array}{l}\text{Ideal (Theoretical}\text{)amount of }\\ \text{conversion cost assigned per laptop}\end{array}\}\text{=}\text{Conversion}\text{cost}\text{rate}\text{×}\text{Theoretical}\text{cycle}\text{time}\\ \text{=}\text{\$2}\text{(1)}\text{×}\text{15}\text{minutes}\\ \text{=}\text{\$30}\text{per}\text{laptop}\end{array}$

Therefore, the ideal (theoretical) amount of conversion cost assigned per laptop is $30 per laptop

Calculate the actual amount of conversion cost assigned per laptop:

$\begin{array}{c}\begin{array}{l}\text{Actual amount of conversion }\\ \text{cost assigned per laptop}\end{array}\}\text{=}\text{Conversion}\text{cost}\text{rate}\text{×}\text{Actual}\text{cycle}\text{time}\\ \text{=}\text{\$}\text{2}(1)\text{×}\text{40}\text{minutes}\text{per}\text{laptop}\\ \text{=}\text{\$80}\text{per laptop}\end{array}$

Therefore, the ideal (theoretical) amount of conversion cost assigned per laptop is $80 per laptop

Working note:

(1)Calculate the conversion cost rate:

$\begin{array}{c}\text{Conversion}\text{cost}\text{rate}\text{=}\frac{\text{Conversion}\text{cost}\text{per}\text{quarter}}{\left(\begin{array}{l}\text{Production}\text{hours}\text{available}\text{×}\\ \text{Time}\text{taken}\text{per}\text{hour}\end{array}\right)}\\ \text{=}\frac{\text{\$7,290,000}}{\text{60,750}\text{hours}\text{×}\text{60}\text{minutes}}\\ \text{=}\frac{\text{\$7,290,000}}{\text{3,645,000}\text{minutes}}\\ \text{=}\text{\$}\text{2}\text{per}\text{minute}\end{array}$

To determine

Calculate manufacturing cycle efficiency (MCE) and explain the manner in which MCE relate to conversion cost per laptop.

Explanation of Solution

Manufacturing cycle efficiency: Manufacturing cycle efficiency is a measure of Just-In-Time (JIT) manufacturing system and it expresses the time spent in value-added activities as a percentage of total cycle time or it is defined as processing time divided by the sum of the inspection time, waiting time, processing time and move time.

Calculate manufacturing cycle efficiency (MCE):

$\begin{array}{c}\begin{array}{l}\text{Manufacturing cycle}\\ \text{ efficiency }\left(\text{MCE}\right)\end{array}\}\text{=}\frac{\text{Process}\text{time}}{\left(\begin{array}{l}\text{Process}\text{time}\text{+Wait}\text{time}\\ \text{+}\text{Move}\text{time+}\text{Rework}\text{time}\end{array}\right)}\\ \text{=}\frac{\text{15}\text{minutes}}{\left(\begin{array}{l}\text{15 minutes+}\text{10}\text{minutes}\text{+}\\ \text{20}\text{minutes+}\text{5}\text{minutes}\end{array}\right)}\\ \text{=}\frac{\text{15}}{\text{50}}\\ \text{=}\text{0}\text{.3}\end{array}$

Increase in manufacturing cycle efficiency will decrease the “actual process time” by decreasing non-value-added time and this will decrease the ‘conversion cost per unit”.