The operations manager of a body and paint shop has five cars to schedule for repair. He would like to minimize the throughput time (makespan) to complete all work on these cars. Each car requires body work prior to painting. The estimates of the times required to do the body and paint work on each are as follows:
$125\begin{array} { | c | c | c | } \hline \text { Car } & \begin{array} { c } \text { Body Work } \\\text { (Hours) }\end{array} & \text { Paint (Hours) } \\\hline \text { A } & 8 & 7 \\\hline \text { B } & 9 & 4 \\\hline \text { C } & 7 & 9 \\\hline \text { D } & 3 & 4 \\\hline \text { E } & 12 & 5 \\\hline\end{array}$ a. Chart the progress of these five jobs through the two centres on the basis of the arbitrary order
A→B→C→D→E.
b. After how many hours will all jobs be completed?
$5101520253035404550\begin{array} { | l | l | l | l | l | l | l | l | l | l | l | } \hline \text { Body Work } & & & & & & & & & & \\\hline \text { Paint } & & & & & & & & & & \\\hline & 5 & 10 & 15 & 20 & 25 & 30 & 35 & 40 & 45 & 50 \\\hline\end{array}$ c. Use Johnson's rule to sequence these five jobs for minimum total duration. Show your work in
determining the job sequence.
d. The optimal sequence is ________.
e. Chart the progress of the five jobs in this optimal sequence.
f. After how many hours will all jobs be completed?

Question

The operations manager of a body and paint shop has five cars to schedule for repair. He would like to minimize the throughput time (makespan) to complete all work on these cars. Each car requires body work prior to painting. The estimates of the times required to do the body and paint work on each are as follows:

125\begin{array} { | c | c | c | } \hline \text { Car } & \begin{array} { c } \text { Body Work } \\\text { (Hours) }\end{array} & \text { Paint (Hours) } \\\hline \text { A } & 8 & 7 \\\hline \text { B } & 9 & 4 \\\hline \text { C } & 7 & 9 \\\hline \text { D } & 3 & 4 \\\hline \text { E } & 12 & 5 \\\hline\end{array}

a. Chart the progress of these five jobs through the two centres on the basis of the arbitrary order
A→B→C→D→E.
b. After how many hours will all jobs be completed?

5101520253035404550\begin{array} { | l | l | l | l | l | l | l | l | l | l | l | } \hline \text { Body Work } & & & & & & & & & & \\\hline \text { Paint } & & & & & & & & & & \\\hline & 5 & 10 & 15 & 20 & 25 & 30 & 35 & 40 & 45 & 50 \\\hline\end{array}

c. Use Johnson's rule to sequence these five jobs for minimum total duration. Show your work in
determining the job sequence.
d. The optimal sequence is ________.
e. Chart the progress of the five jobs in this optimal sequence.
f. After how many hours will all jobs be completed?

Irisha Naziha · Accepted Answer

Final Answer :  (a,b) Arbitrary order:   (c,d) The sequence of jobs is Car D, Car C, Car A, Car E, Car B. Makespan = 43 as per the POM for Windows solution below.    Body Work   Paint   Order   Done 1   Done 2   (flow time)   A   8.   7.   third   18.  26.  B   9.   4.   fifth  39. 43. C 7  9.   second  10. 19. D 3. 4.  first  3. 7. E 12.  5.   fourth  30. 35.  Makespan  43. \begin{array}{|l|r|r|r|r|r|}\hline  &  	ext { Body Work }  &  	ext { Paint }  &  	ext { Order }  &  	ext { Done 1 }  &  \begin{array}{r}	ext { Done 2 } \	ext { (flow time) }\end{array} \\hline 	ext { A }  &  	ext { 8. }  &  	ext { 7. }  &  	ext { third }  &  	ext { 18. }  &  26 . \\hline 	ext { B }  &  	ext { 9. }  &  	ext { 4. }  &  	ext { fifth }  &  39 .  &  43 . \\hline \mathbf{C}  &  \mathbf{7}  &  	ext { 9. }  &  	ext { second }  &  10 .  &  19 . \\hline \mathbf{D}  &  3 .  &  4 .  &  	ext { first }  &  \mathbf{3 .}  &  \mathbf{7} . \\hline \mathbf{E}  &  12 .  &  	ext { 5. }  &  	ext { fourth }  &  30 .  &  35 . \\hline 	ext { Makespan }  &   &   &   &   &  \mathbf{4 3 .} \\hline\end{array}  A   B  C D E  Makespan  ​  Body Work   8.   9.  7 3. 12. ​  Paint   7.   4.   9.  4.  5.  ​  Order   third   fifth   second   first   fourth  ​  Done 1   18.  39. 10. 3. 30. ​  Done 2   (flow time)  ​ 26. 43. 19. 7 . 35. 43. ​ ​  Sequence: D, C, A, E, B  	ext { Sequence: D, C, A, E, B }  Sequence: D, C, A, E, B    (c) Johnson's method sequence of steps    Step   Job   Position  1  D  1. 2  B   5.  3  E  4. 4  A  3. 5  C  2. \begin{array} { | l | r | r | } \hline 	ext { Step }  &  	ext { Job }  &  	ext { Position } \\hline 1  &  	ext { D }  &  1 . \\hline 2  &  	ext { B }  &  	ext { 5. } \\hline 3  &  	ext { E }  &  4 . \\hline 4  &  	ext { A }  &  3 . \\hline 5  &  	ext { C }  &  2 . \\hline\end{array}  Step  1 2 3 4 5 ​  Job   D   B   E   A   C  ​  Position  1.  5.  4. 3. 2. ​ ​   (e,f)

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