Asked by Andrea Anguiano on Apr 30, 2024
Verified
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?
Job Machine 1 Machine 2 L 1011 M 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} Job L M NOP Machine 1 108141310 Machine 2 1117978
Johnson's Rule
A scheduling technique used to minimize the total time required to complete a group of jobs on two machines or in two stages.
Optimal Sequence
The most efficient order or arrangement of steps or actions to achieve a specific goal.
Total Flow Time
The cumulative amount of time taken for a unit of work or a product to flow through a system, including both processing and waiting times.
- Use Johnson's rule to establish the prime sequence of operations to decrease the makespan in a two-machine scenario.
- Audit the operational performance of numerous scheduling protocols, highlighting average flow time, work-in-process, lateness, and makespan.
Verified Answer
Sequence: M, L, N, P. O\text { Sequence: M, L, N, P. } \mathbf{O} Sequence: M, L, N, P. O
Learning Objectives
- Use Johnson's rule to establish the prime sequence of operations to decrease the makespan in a two-machine scenario.
- Audit the operational performance of numerous scheduling protocols, highlighting average flow time, work-in-process, lateness, and makespan.
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