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 are given in the table below.
a. What is the optimal sequence?
b. What is the total flow time for this sequence?
$817N149O137P108\begin{array} { | c | c | c | } \hline \text { Job } & \text { Machine 1 } & \text { Machine 2 } \\\hline \text { L } & 10 & 11 \\\hline \text { M } & 8 & 17 \\\hline \mathrm { N } & 14 & 9 \\\hline \mathrm { O } & 13 & 7 \\\hline \mathrm { P } & 10 & 8 \\\hline\end{array}$

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 are given in the table below.
a. What is the optimal sequence?
b. What is the total flow time for this sequence?

817N149O137P108\begin{array} { | c | c | c | } \hline \text { Job } & \text { Machine 1 } & \text { Machine 2 } \\\hline \text { L } & 10 & 11 \\\hline \text { M } & 8 & 17 \\\hline \mathrm { N } & 14 & 9 \\\hline \mathrm { O } & 13 & 7 \\\hline \mathrm { P } & 10 & 8 \\\hline\end{array}

Zybrea Knight · Accepted Answer

Final Answer :  (a,b) The optimal sequence is M-L-N-P-O, and the total flow time is 62. Details are contained in the solution table below.    Machine 1   Machine 2   Order   Done 1   Done 2   (flow time)   L  10. 11.  second  18. 36. M 8. 17.  first  8. 25. N 14. 9.  third  32. 45. O 13. 7.  fith  55. 62.  P  10. 8.  fourth  42. 53.  Makespan  62. \begin{array}{|r|r|r|r|r|r|}\hline  &  	ext { Machine 1 }  &  	ext { Machine 2 }  &  	ext { Order }  &  	ext { Done 1 }  &  \begin{array}{r}	ext { Done 2 } \	ext { (flow time) }\end{array} \\hline 	ext { L }  &  10 .  &  11 .  &  	ext { second }  &  18 .  &  36 . \\hline M  &  8 .  &  17 .  &  	ext { first }  &  8 .  &  25 . \\hline N &  14 .  &  9 .  &  	ext { third }  &  32 .  &  45 . \\hline O  &  13 .  &  7 .  &  	ext { fith }  &  55 .  &  62 . \\hline 	ext { P }  &  10 .  &  8 .  &  	ext { fourth }  &  42 .  &  53 . \\hline 	ext { Makespan }  &   &   &   &   &  62 . \\hline\end{array}  L  M N O  P   Makespan  ​  Machine 1  10. 8. 14. 13. 10. ​  Machine 2  11. 17. 9. 7. 8. ​  Order   second   first   third   fith   fourth  ​  Done 1  18. 8. 32. 55. 42. ​  Done 2   (flow time)  ​ 36. 25. 45. 62. 53. 62. ​ ​  Sequence: M, L, N, P.  O 	ext { Sequence: M, L, N, P. } \mathbf{O}  Sequence: M, L, N, P.  O

Definitions

Learning Objectives

Learning Objectives

Related questions