Asked by Patrick Garland on May 03, 2024
Verified
At Morgan's Transformer Rebuilding, a set of five jobs is ready for dispatching to a machine centre. The processing times and due dates for the jobs are given in the table below. Use shortest processing time to sequence the jobs, and calculate the average completion time, the average job lateness, and the average number of jobs in the machine centre.
Job Work Time (days) Due Date (days) A 1538 B 1328 C 720 D 1850 E 915\begin{array} { | c | c | c | } \hline \text { Job } & \text { Work Time (days) } & \text { Due Date (days) } \\\hline \text { A } & 15 & 38 \\\hline \text { B } & 13 & 28 \\\hline \text { C } & 7 & 20 \\\hline \text { D } & 18 & 50 \\\hline \text { E } & 9 & 15 \\\hline\end{array} Job A B C D E Work Time (days) 15137189 Due Date (days) 3828205015
Shortest Processing Time
A rule in production scheduling where jobs are sequenced based on ascending order of their processing times, with the shortest first.
Average Completion Time
The average duration taken to complete all tasks or processes within a specified set of operations or activities.
Job Lateness
The amount of time by which the completion of a job exceeds its originally scheduled or planned delivery time.
- Absorb key regulations of dispatching and how they inform schedule creation.
- Appraise the performance metrics of assorted scheduling rules, focusing on average flow time, work-in-process, lateness, and makespan.
- Calculate the mean lateness, total completion time, and count of tasks within the system.
Verified Answer
ZS
Zelia SantosMay 07, 2024
Final Answer :
The optimal sequence is C-E-B-A-D. The average completion time is 31.6 days. The average lateness is 4 days. The average jobs in system is 2.548. Details appear in the table below.
SPT ‾ Time Due Date Slack Flow time Late days C7201370E9156161B132815291A153823446D1850326212 Total 15820 Average 31.64\begin{array}{|c|c|c|c|c|c|}\hline\underline{\text { SPT }} & \text { Time } & \frac{\text { Due }}{\text { Date }} & \text { Slack } & \text { Flow time } & \text { Late days } \\\hline \mathrm{C} & 7 & 20 & 13 & 7 & 0\\\hline \mathrm{E} & 9 & 15 & 6 & 16 & 1 \\\hline \mathrm{B} & 13 & 28 & 15 & 29 & 1 \\\hline \mathrm{A} & 15 & 38 & 23 & 44 & 6 \\\hline \mathrm{D} & 18 & 50 & 32 & 62 & 12 \\\hline & & & \text { Total } & 158 & 20 \\\hline & & & \text { Average } & 31.6 & 4 \\\hline\end{array} SPT CEBAD Time 79131518 Date Due 2015283850 Slack 136152332 Total Average Flow time 71629446215831.6 Late days 011612204 Average number of jobs in system: 2.548
SPT ‾ Time Due Date Slack Flow time Late days C7201370E9156161B132815291A153823446D1850326212 Total 15820 Average 31.64\begin{array}{|c|c|c|c|c|c|}\hline\underline{\text { SPT }} & \text { Time } & \frac{\text { Due }}{\text { Date }} & \text { Slack } & \text { Flow time } & \text { Late days } \\\hline \mathrm{C} & 7 & 20 & 13 & 7 & 0\\\hline \mathrm{E} & 9 & 15 & 6 & 16 & 1 \\\hline \mathrm{B} & 13 & 28 & 15 & 29 & 1 \\\hline \mathrm{A} & 15 & 38 & 23 & 44 & 6 \\\hline \mathrm{D} & 18 & 50 & 32 & 62 & 12 \\\hline & & & \text { Total } & 158 & 20 \\\hline & & & \text { Average } & 31.6 & 4 \\\hline\end{array} SPT CEBAD Time 79131518 Date Due 2015283850 Slack 136152332 Total Average Flow time 71629446215831.6 Late days 011612204 Average number of jobs in system: 2.548
Learning Objectives
- Absorb key regulations of dispatching and how they inform schedule creation.
- Appraise the performance metrics of assorted scheduling rules, focusing on average flow time, work-in-process, lateness, and makespan.
- Calculate the mean lateness, total completion time, and count of tasks within the system.