Asked by Archit Barua on May 03, 2024
Verified
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:
Car Body Work (Hours) Paint (Hours) A 87 B 94 C 79 D 34 E 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} Car A B C D E Body Work (Hours) 897312 Paint (Hours) 74945 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?
Body Work Paint 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} Body Work Paint 5101520253035404550 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?
Throughput Time
The time it takes for a product to go through the production process with no waiting. It is the time of the longest path through the system.
Body Work
This term refers to physical manipulations and repairs carried out on the body of a vehicle by auto repair professionals.
Paint Work
The application of paint, varnish, lacquer, or other finishes to surfaces as a finite operation in manufacturing, maintenance, or artistic production.
- Employ Johnson's rule to identify the optimal arrangement of tasks aimed at minimizing the total completion time in a dual-machine setup.
- Critique the functionality of multiple scheduling strategies by referencing average flow time, work-in-process, lateness, and makespan.
- Assess how job subdivision influences the decrease in overall duration within an industrial operation.
Verified Answer
Sequence: D, C, A, E, B \text { 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 \text { Step } & \text { Job } & \text { Position } \\\hline 1 & \text { D } & 1 . \\\hline 2 & \text { B } & \text { 5. } \\\hline 3 & \text { E } & 4 . \\\hline 4 & \text { A } & 3 . \\\hline 5 & \text { C } & 2 . \\\hline\end{array} Step 12345 Job D B E A C Position 1. 5. 4.3.2. (e,f)
Learning Objectives
- Employ Johnson's rule to identify the optimal arrangement of tasks aimed at minimizing the total completion time in a dual-machine setup.
- Critique the functionality of multiple scheduling strategies by referencing average flow time, work-in-process, lateness, and makespan.
- Assess how job subdivision influences the decrease in overall duration within an industrial operation.
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