Chapter 15, Problem 1CE

Anderson Company has the following departmental manufacturing structure for one of its products:

After some study, the production manager of Anderson recommended the following revised cellular manufacturing approach:

Required:

1. 1. Calculate the total time it takes to produce a batch of 20 units using Anderson’s traditional departmental structure.
2. 2. Using cellular manufacturing, how much time is saved producing the same batch of 20 units? Assuming the cell operates continuously, what is the production rate? Which process controls this production rate?
3. 3. What if the processing times of molding, welding, and assembly are all reduced to six minutes each? What is the production rate now, and how long will it take to produce a batch of 20 units?

To determine

Compute the total time taken for the production of a batch of 20 units using the traditional departmental structure.

Explanation of Solution

Traditional departmental structure: The traditional departmental structure refers to the conventional manufacturing approach, wherein the manufacturing is a process which includes lots of lead time.

Compute the total time taken for the production of a batch of 20 units using the traditional departmental structure.

Batch Time:
Processing time:
Molding (1)	150 mins
Welding (2)	300 mins
Polishing (3)	240 mins
Assembly (4)	140 mins
Total Processing Time	830 mins
Move and wait time (5)	75 mins
Total Batch Time	905 mins

 Table (1)

Working Notes (1):

Calculate the processing time for Molding:

$\begin{array}{c}\text{Molding = Number of units }\times \text{ Process Time}\\ \text{= }20\text{ units }\times \text{7}\text{.5 mins}\\ =1\text{50 mins}\end{array}$

Working Notes (2):

Calculate the processing time for Welding:

$\begin{array}{c}\text{Welding = Number of units }\times \text{ Process Time}\\ \text{= }20\text{ units }\times \text{15 mins}\\ =30\text{0 mins}\end{array}$

Working Notes (3):

Calculate the processing time for Polishing:

$\begin{array}{c}\text{Polishing = Number of units }\times \text{ Process Time}\\ \text{= }20\text{ units }\times 12\text{mins}\\ =24\text{0 mins}\end{array}$

Working Notes (4):

Calculate the processing time for Assembly:

$\begin{array}{c}\text{Assembly = Number of units }\times \text{ Process Time}\\ \text{= }20\text{ units }\times \text{7 mins}\\ =1\text{40 mins}\end{array}$

Working Notes (5):

Calculate the Move and wait time:

$\begin{array}{c}\begin{array}{l}\text{Move and}\\ \text{wait time}\end{array}\}\text{= }\left(\begin{array}{l}\text{Move and wait time for Molding + }\\ \text{Move and wait time for Welding + }\\ \text{Move and wait time for Polishing + }\\ \text{Move and wait time for Assembly}\end{array}\right)\\ \text{= 15 mins + 18 mins + }22.\text{5 mins + 19}\text{.5 mins}\\ =7\text{5 mins}\end{array}$

To determine

Compute the total time taken for the production of a batch of 20 units using the cellular manufacturing approach and the production rate if it’s a continuous production and identify the process which controls the production rate.

Explanation of Solution

Cellular manufacturing: The cellular manufacturing refers to the manufacturing approach, wherein the various equipments related to the various processes of production are clustered together to avoid any move time and enable faster manufacturing of the goods.

Compute the total time taken for the production of a batch of 20 units using the cellular manufacturing.

Batch Time:
Processing time:
For First Unit	45 mins
Second unit	60 mins
Third Unit	75 mins
Fourth unit	90 mins
Fifth Unit	105 mins
Sixth unit	120 mins
Seventh Unit	135 mins
Eighth unit	150 mins
Ninth Unit	165 mins
Tenth unit	180 mins
Eleventh Unit	195 mins
Twelfth unit	210 mins
Thirteenth Unit	225 mins
Fourteenth Unit	240 mins
Fifteenth Unit	255 mins
Sixteenth Unit	270 mins
Seventeenth Unit	285 mins
Eighteenth Unit	300 mins
Nineteenth Unit	315 mins
Twentieth Unit	330 mins
Total Processing Time	330 mins

 Table (2)

The total processing time of 1 unit is 45 minutes (refer Working Notes (6)). The production of the second unit starts once in every fifteen minutes, so that the production process can go on without stopping in middle. Thus 15 mins is added to the processing time of previous every unit, to get the processing time of the present unit.

The production time for a batch of 20 units using cellular manufacturing is 330 mins. The production of 20 units under the traditional departmental structure has a production time is 905 mins. Hence, the total production time saved using the cellular manufacturing approach is 605 mins $\left(\text{905 mins}-300\text{ mins}\right)$.

The production rate uses the processing time of the process with the longest processing time, thus the Welding process with 15 mins processing time is used.

The new Production rate is 4 units per hour $\left(\frac{60\text{ mins}}{15\text{ mins}}\right)$.

The production of every unit starts once in fifteen minutes and for 20 units the production time is 300 mins $\left(\frac{20\text{ units}}{4\text{ units}}\times \text{60 mins}\right)$.

The production starts once in every fifteen minutes, as Welding process takes 15 mins to be completed and is the bottleneck process in the production, as it controls the production rate.

Working Notes (6):

Calculate the total Processing time:

$\begin{array}{c}\text{Processing time = }\left(\begin{array}{l}\text{Processing time for Molding + }\\ \text{Processing time for Welding + }\\ \text{Processing time for Polishing + }\\ \text{Processing time for Assembly}\end{array}\right)\\ \text{= 15 mins + 7}\text{.5 mins + }12\text{ mins + 10}\text{.5 mins}\\ =4\text{5 mins}\end{array}$

To determine

Identify the new processing time and the production rate if the processing time for welding, molding and assembly are reduced by 6 minutes each.

Explanation of Solution

The production rate uses the processing time of the process with the longest processing time, thus the Polishing process with 12 mins processing time is used.

The new Production rate is 5 units per hour$\left(\frac{60\text{ mins}}{12\text{ mins}}\right)$.

The production of every unit starts once in twelve minutes and for 20 units the production time is 240 mins$\left(\frac{20\text{ units}}{5\text{ units}}\times \text{60 mins}\right)$.

Compute the new total processing time for the production of a batch of 20.

Batch Time:
Processing time:
For First Unit	27 mins
Second unit	39 mins
Third Unit	51 mins
Fourth unit	63 mins
Fifth Unit	75 mins
Sixth unit	87 mins
Seventh Unit	99 mins
Eighth unit	111 mins
Ninth Unit	123 mins
Tenth unit	135 mins
Eleventh Unit	147 mins
Twelfth unit	159 mins
Thirteenth Unit	171 mins
Fourteenth Unit	183 mins
Fifteenth Unit	195 mins
Sixteenth Unit	207 mins
Seventeenth Unit	219 mins
Eighteenth Unit	231 mins
Nineteenth Unit	243 mins
Twentieth Unit	255 mins
Total Processing Time	255 mins

 Table (3)

The total processing time of 1 unit is 27 minutes (refer Working Notes (7)). The production of the second unit starts once in every twelfth minutes, so that the production process can go on without stopping in middle. Thus 12 mins is added to the processing time of previous every unit, to get the processing time of the present unit.

The production time for a batch of 20 units using cellular manufacturing is 255 mins.

Working Notes (7):

Calculate the total Processing time:

$\begin{array}{c}\text{Processing time = }\left(\begin{array}{l}\text{Processing time for Molding + }\\ \text{Processing time for Welding + }\\ \text{Processing time for Polishing + }\\ \text{Processing time for Assembly}\end{array}\right)\\ \text{= 9 mins + 1}\text{.5 mins + }12\text{ mins + 4}\text{.5 mins}\\ =27\text{ mins}\end{array}$