A firm is planning to set up an assembly line to assemble 40 units per hour, and 57 minutes per hour are productive. The time to perform each task and the tasks which precede each task are:
$A−−.69BA.55CB.92DB.59EB.70FB1.10GC,D,E.75HG,F.43IH.29\begin{array} { | c | c | c | } \hline \text { Task } & \begin{array} { c } \text { Preceding } \\\text { Task }\end{array} & \begin{array} { c } \text { Time to } \\\text { perform (min.) }\end{array} \\\hline \mathrm { A } & - - & .69 \\\hline \mathrm { B } & \mathrm { A } & .55 \\\hline \mathrm { C } & \mathrm { B } & .92 \\\hline \mathrm { D } & \mathrm { B } & .59 \\\hline \mathrm { E } & \mathrm { B } & .70 \\\hline \mathrm { F } & \mathrm { B } & 1.10 \\\hline \mathrm { G } & \mathrm { C } , \mathrm { D } , \mathrm { E } & .75 \\\hline \mathrm { H } & \mathrm { G } , \mathrm { F } & .43 \\\hline \mathrm { I } & \mathrm { H } & .29 \\\hline\end{array}$ a. Draw a network diagram of precedence relationships.
b. Compute the required cycle time per unit in minutes.
c. Compute the theoretical minimum number of workstations required to produce 40 units per hour.
d. Balance this line using longest processing time.
e. What is the efficiency of the line obtained in part d?

Question

A firm is planning to set up an assembly line to assemble 40 units per hour, and 57 minutes per hour are productive. The time to perform each task and the tasks which precede each task are:

A−−.69BA.55CB.92DB.59EB.70FB1.10GC,D,E.75HG,F.43IH.29\begin{array} { | c | c | c | } \hline \text { Task } & \begin{array} { c } \text { Preceding } \\\text { Task }\end{array} & \begin{array} { c } \text { Time to } \\\text { perform (min.) }\end{array} \\\hline \mathrm { A } & - - & .69 \\\hline \mathrm { B } & \mathrm { A } & .55 \\\hline \mathrm { C } & \mathrm { B } & .92 \\\hline \mathrm { D } & \mathrm { B } & .59 \\\hline \mathrm { E } & \mathrm { B } & .70 \\\hline \mathrm { F } & \mathrm { B } & 1.10 \\\hline \mathrm { G } & \mathrm { C } , \mathrm { D } , \mathrm { E } & .75 \\\hline \mathrm { H } & \mathrm { G } , \mathrm { F } & .43 \\\hline \mathrm { I } & \mathrm { H } & .29 \\\hline\end{array}

a. Draw a network diagram of precedence relationships.
b. Compute the required cycle time per unit in minutes.
c. Compute the theoretical minimum number of workstations required to produce 40 units per hour.
d. Balance this line using longest processing time.
e. What is the efficiency of the line obtained in part d?

swapnil mohane · Accepted Answer

Final Answer :  (a) The appropriate diagram appears below. (b) Cycle time is 57/40 = 1.425 minutes. (c) The theoretical minimum number of stations required is 6.02/1.425 = 4.22 or 5. (d) The balanced line appears in the software output panel below. (e) The line's efficiency is 6.02 / 8.55 = 70.4%      Station   Task   Time   (minutes)   Time left   (minutes)   Ready   tasks  A 1  A  0.69 0.735   B B 0.55 0.185 C , D , E , F 2   F 1.1 0.325 C , D , E 3 C 0.92 0.505 D , E 4 E 0.7 0.725 D D 0.59 0.135 G 5 G 0.75 0.675 H H 0.43 0.245 I 6 I 0.29 1.135  Summary Statistics   Cycle time  1.425  minutes   Time allocated (cycle   time*#)  8.549999  minutes/cycle   Time needed (sum of   task times)  6.02  minutes/unit   Tdle time (allocated-   needed)  − . 529999  minutes/cycle   Efficiency   (needed/allocated)  70.40936 %  Balance Delay (1-   efficiency)  29.59064 %  Min (theoretical) # of   stations  5 \begin{array}{|l|l|l|l|l|}\hline	ext { Station }  &  	ext { Task }  &  \begin{array}{l}	ext { Time } \	ext { (minutes) }\end{array}  &  \begin{array}{l}	ext { Time left } \	ext { (minutes) }\end{array}  &  \begin{array}{l}	ext { Ready } \	ext { tasks }\end{array} \\hline  &   &   &   &  \mathbf{A} \\hline 1  &  	ext { A }  &  0.69  &  0.735  &  \mathrm{~B} \\hline &  \mathrm{B}  &  0.55  &  0.185  &  \mathrm{C}, \mathrm{D}, \mathrm{E}, \mathrm{F} \\hline 2  &  \mathrm{~F}  &  1.1  &  0.325  &  \mathrm{C}, \mathrm{D}, \mathrm{E} \\hline 3  &  \mathrm{C}  &  0.92  &  0.505  &  \mathrm{D}, \mathrm{E} \\hline 4  &  \mathrm{E}  &  0.7  &  0.725  &  \mathrm{D} \\hline  &  \mathrm{D}  &  0.59  &  0.135  &  \mathrm{G} \\hline 5  &  \mathrm{G}  &  0.75  &  0.675  &  \mathrm{H} \\hline  &  \mathrm{H}  &  0.43  &  0.245  &  \mathrm{I} \\hline 6  &  \mathrm{I}  &  0.29  &  1.135  &  \\hline 	ext { Summary Statistics }  &   &   &   &  \\hline 	ext { Cycle time }  &  1.425  &  	ext { minutes }  &   &  \\hline	ext { Time allocated (cycle }  &   &   &   &  \	ext { time*\#) }  &  8.549999  &  	ext { minutes/cycle }  &   &  \\hline 	ext { Time needed (sum of }  &   &   &   &  \	ext { task times) }  &  6.02  &  	ext { minutes/unit }  &   &  \\hline 	ext { Tdle time (allocated- }  &   &  \	ext { needed) }  &  -.529999  &  	ext { minutes/cycle } \\hline 	ext { Efficiency }  &   &  \	ext { (needed/allocated) }  &  70.40936 \%  &  \\hline 	ext { Balance Delay (1- }  &   &  \	ext { efficiency) }  &  29.59064 \%  &  \\hline \begin{array}{l}	ext { Min (theoretical) \# of } \	ext { stations }\end{array}  &  5 & \\hline\end{array}  Station  1 2 3 4 5 6  Summary Statistics   Cycle time   Time allocated (cycle   time*#)   Time needed (sum of   task times)   Tdle time (allocated-   needed)   Efficiency   (needed/allocated)   Balance Delay (1-   efficiency)   Min (theoretical) # of   stations  ​ ​  Task   A  B   F C E D G H I 1.425 8.549999 6.02 − .529999 70.40936% 29.59064% 5 ​  Time   (minutes)  ​ 0.69 0.55 1.1 0.92 0.7 0.59 0.75 0.43 0.29  minutes   minutes/cycle   minutes/unit   minutes/cycle  ​  Time left   (minutes)  ​ 0.735 0.185 0.325 0.505 0.725 0.135 0.675 0.245 1.135 ​  Ready   tasks  ​ A   B C , D , E , F C , D , E D , E D G H I ​ ​

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