Use Johnson's rule to determine the optimal sequencing for the five jobs to be processed on two machines in a fixed order (Machine 1 before Machine 2). The processing times in hours are given in the table below.
a. What is the optimal sequence?
b. What is the total makespan for this sequence?
c. What is the total idle time for Machine 2?.
$25\begin{array} { | l | r | r | } \hline & \text { Machine 1 } & \text { Machine 2 } \\\hline \text { A } & 6 & 17 \\\hline \text { B } & 8 & 4 \\\hline \text { C } & 5 & 8 \\\hline \text { D } & 4 & 6 \\\hline \text { E } & 2 & 5 \\\hline\end{array}$

Question

Use Johnson's rule to determine the optimal sequencing for the five jobs to be processed on two machines in a fixed order (Machine 1 before Machine 2). The processing times in hours are given in the table below.
a. What is the optimal sequence?
b. What is the total makespan for this sequence?
c. What is the total idle time for Machine 2?.

25\begin{array} { | l | r | r | } \hline & \text { Machine 1 } & \text { Machine 2 } \\\hline \text { A } & 6 & 17 \\\hline \text { B } & 8 & 4 \\\hline \text { C } & 5 & 8 \\\hline \text { D } & 4 & 6 \\\hline \text { E } & 2 & 5 \\\hline\end{array}

April Barrow · Accepted Answer

Final Answer :  (a,b)  Job   Machine 1 time   Machine 1   end time   Machine 2   time   Machine 2   end time   Machine 2   idle time   E  2 2 5 7 2  D  4 6 6 13 0  C  5 11 8 21 0  A 6 17 17 38 0  B  8 25 4 42 0  Makespan  42  Total  2 \begin{array} { | c | r | r | r | r | r | } \hline 	ext { Job }  &  	ext { Machine 1 time }  &  \begin{array} { c } 	ext { Machine 1 } \	ext { end time }\end{array}  &  \begin{array} { c } 	ext { Machine 2 } \	ext { time }\end{array}  &  \begin{array} { c } 	ext { Machine 2 } \	ext { end time }\end{array}  &  \begin{array} { c } 	ext { Machine 2 } \	ext { idle time }\end{array} \\hline 	ext { E }  &  2  &  2  &  5  &  7  &  2 \\hline 	ext { D }  &  4  &  6  &  6  &  13  &  0 \\hline 	ext { C }  &  5  &  11  &  8  &  21  &  0 \\hline 	ext { A}  &  6  &  17  &  17  &  38  &  0 \\hline 	ext { B } &  8  &  25  &  4  &  42  &  0 \\hline\\hline 	ext { Makespan }  &  42 &   &   &  	ext { Total } & 2 \\hline\end{array}  Job   E   D   C   A  B   Makespan  ​  Machine 1 time  2 4 5 6 8 42 ​  Machine 1   end time  ​ 2 6 11 17 25 ​  Machine 2   time  ​ 5 6 8 17 4 ​  Machine 2   end time  ​ 7 13 21 38 42  Total  ​  Machine 2   idle time  ​ 2 0 0 0 0 2 ​ ​   (c) 2 Days.

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