The maker of the world-famous Chocolate Chip Cookies needs to design a product layout for a new product, Mint Chocolate Chip. The company plans to use this new production line eight hours a day in order to meet projected demand of 1,440 cases per day. The following table describes the tasks involved in the production of a Mint Chocolate Chip Cookie. $$\begin{array} { l l l }
\text { Task } & \text { Time } ( \text { secs } ) & \text { Immediate Predecessor } \
\hline \mathrm { u } & 4 & \text { none } \
\mathrm { v } & 14 & \mathrm { u } \
\mathrm { w } & 12 & \mathrm {~V} \
\mathrm { x } & 12 & \mathrm {~V} \
\mathrm { y } & 6 & \mathrm { w } \
\mathrm { z } & 8 & \mathrm { x } , \mathrm { y }
\end{array}$$ For output to equal projected demand, what should be the actual cycle time for this production line?
A) 54 seconds
B) 27 seconds
C) 20 seconds
D) 18 seconds
E) 14 seconds

Question

The maker of the world-famous Chocolate Chip Cookies needs to design a product layout for a new product, Mint Chocolate Chip. The company plans to use this new production line eight hours a day in order to meet projected demand of 1,440 cases per day. The following table describes the tasks involved in the production of a Mint Chocolate Chip Cookie. $$\begin{array} { l l l } 
\text { Task } & \text { Time } ( \text { secs } ) & \text { Immediate Predecessor } \
\hline \mathrm { u } & 4 & \text { none } \
\mathrm { v } & 14 & \mathrm { u } \
\mathrm { w } & 12 & \mathrm {~V} \
\mathrm { x } & 12 & \mathrm {~V} \
\mathrm { y } & 6 & \mathrm { w } \
\mathrm { z } & 8 & \mathrm { x } , \mathrm { y }
\end{array}$$ For output to equal projected demand, what should be the actual cycle time for this production line?
A) 54 seconds
B) 27 seconds
C) 20 seconds
D) 18 seconds
E) 14 seconds

Quizplus · Accepted Answer

To determine the cycle time, we need to first calculate the theoretical maximum output rate (TMOR) by finding the time of the longest path through the network diagram. The critical path for this project is given by the sequence:

u → v → w → y → z

The time to complete this path is: 4 s + 14 s + 12 s + 6 s + 8 s = 44 s

The TMOR is the reciprocal of this time: 1 ÷ 44 s = 0.0227 units/sec

To find the cycle time, we need to divide the production time available per day (8 hours or 28,800 seconds) by the demand rate (1,440 cases per day), and the result should not be less than the TMOR:

Cycle time = Production time available per day ÷ Demand rate per day
Cycle time = 28,800 s ÷ 1,440 cases
Cycle time = 20 s

Therefore, the actual cycle time for this production line should be 20 seconds, which is the best choice (C).

The Maker of the World-Famous Chocolate Chip Cookies Needs to Design