Asked by Taylor Morrison on May 20, 2024
Verified
A firm that specializes in desktop publishing for local charities has agreed to take on the following jobs. The firm has not decided which dispatching rule to apply in order to prioritize the jobs and fix them into the schedule. All dates are specified as days from Today.
Time Due Date Tob 1 2025 Tob 2 1520 Tob 3 716 Job 4 2550 Tob 5 3133 Job 6 4355\begin{array} { | l | l | l | } \hline & \text { Time } & \text { Due Date } \\\hline \text { Tob 1 } & 20 & 25 \\\hline \text { Tob 2 } & 15 & 20 \\\hline \text { Tob 3 } & 7 & 16 \\\hline \text { Job 4 } & 25 & 50 \\\hline \text { Tob 5 } & 31 & 33 \\\hline \text { Job 6 } & 43 & 55 \\\hline\end{array} Tob 1 Tob 2 Tob 3 Job 4 Tob 5 Job 6 Time 20157253143 Due Date 252016503355 a. Complete the following table. Show your supporting calculations below.
b. Which dispatching rule has the best score for flow time?
c. Which dispatching rule has the best score for work-in-process (jobs in the system)?
d. Which dispatching rule has the best score for lateness?
Dispatching Rule Job Sequence Average Flow Time Average Number of Jobs Average Lateness FCFS EDD SPT LPT \begin{array} { | l | c | c | c | c | } \hline \begin{array} {c } \text { Dispatching } \\\text { Rule }\end{array} & \text { Job Sequence } & \begin{array} { c } \text { Average } \\\text { Flow Time }\end{array} & \begin{array} { c } \text { Average } \\\text { Number of } \\\text { Jobs }\end{array} & \begin{array} { c } \text { Average } \\\text { Lateness }\end{array} \\\hline \text { FCFS } & & & & \\\hline \text { EDD } & & & & \\\hline \text { SPT } & & & & \\\hline \text { LPT } & & & & \\\hline\end{array} Dispatching Rule FCFS EDD SPT LPT Job Sequence Average Flow Time Average Number of Jobs Average Lateness
Dispatching Rule
A guideline or criterion used to determine the scheduling and order in which jobs should be processed in manufacturing or service operations.
Flow Time
The time taken for a unit to move through an entire system or process, from start to finish.
Work-In-Process
Items or materials that are in the stage of production but have not yet been completed.
- Familiarize oneself with the essential aspects of dispatching and their application in planning.
- Analyze the comparative effectiveness of various scheduling directives regarding average flow time, work-in-process, lateness, and makespan.
- Find the leading scheduling technique tailored to specific performance expectations.
Verified Answer
BC
Bryleigh CollinsMay 21, 2024
Final Answer :
(a) The table of results appears below. A supporting table for each dispatch rule also follows.
Dispatching Rule Job Sequence Average Flow Time Average Number of Jobs Average Lateness FCFS 1−2−3−4−5−667.22.8634.8 EDD 3−2−1−5−4−663.82.7132.2 SPT 3−2−1−4−5−662.82.6731.2 LPT 6−5−4−1−2−3101.74.3370.5\begin{array} { | l | c | c | c | c | } \hline \begin{array} { c } \text { Dispatching } \\\text { Rule }\end{array} & \text { Job Sequence } & \begin{array} { c } \text { Average } \\\text { Flow Time }\end{array} & \begin{array} { c } \text { Average } \\\text { Number of } \\\text { Jobs }\end{array} & \begin{array} { c } \text { Average } \\\text { Lateness }\end{array} \\\hline \text { FCFS } & 1 - 2 - 3 - 4 - 5 - 6 & 67.2 & 2.86 & 34.8 \\\hline \text { EDD } & 3 - 2 - 1 - 5 - 4 - 6 & 63.8 & 2.71 & 32.2 \\\hline \text { SPT } & 3 - 2 - 1 - 4 - 5 - 6 & 62.8 & 2.67 & 31.2 \\\hline \text { LPT } & 6 - 5 - 4 - 1 - 2 - 3 & 101.7 & 4.33 & 70.5 \\\hline\end{array} Dispatching Rule FCFS EDD SPT LPT Job Sequence 1−2−3−4−5−63−2−1−5−4−63−2−1−4−5−66−5−4−1−2−3 Average Flow Time 67.263.862.8101.7 Average Number of Jobs 2.862.712.674.33 Average Lateness 34.832.231.270.5 (b,c,d) The SPT rule is best for flow time, for average jobs in system, and for lateness. FCFS Time Due Date Slack Flow time Late days Job 1 20255200 Job 2 ‾152053515 Job 3 ‾71694226 Job 4 ‾2550256717 Job 5 ‾313329865 Job 6 ‾435512141‾86‾ Total 403209 Average 67.1734.83\begin{array}{|l|c|c|l|c|c|c|}\hline \text { FCFS } & \text { Time } & \frac{\text { Due }}{\text { Date }} & & \text { Slack } & \text { Flow time } &\text { Late days } \\\hline \text { Job 1 } & 20 & 25 & & 5 & 20 & 0 \\\hline \underline{\text { Job 2 }} & 15 & 20 & & 5 & 35 & 15 \\\hline \underline{\text { Job 3 }} & 7 & 16 & & 9 & 42 & 26 \\\hline \underline{\text { Job 4 }} & 25 & 50 & & 25 & 67 & 17 \\\hline \underline{\text { Job 5 }} & 31 & 33 & & 2 & 98 & 65 \\\hline \underline{\text { Job 6 }} & 43 & 55 & & 12 & \underline{141} & \underline{86} \\\hline & & & & \text { Total } & 403 & 209 \\\hline & & & & \text { Average } & 67.17 & 34.83 \\\hline\end{array} FCFS Job 1 Job 2 Job 3 Job 4 Job 5 Job 6 Time 20157253143 Date Due 252016503355 Slack 55925212 Total Average Flow time 203542679814140367.17 Late days 0152617658620934.83
Average number of jobs in system: 2.858\text { Average number of jobs in system: } 2.858 Average number of jobs in system: 2.858
EDD Time Due Date Slack Flow time Late davs Job3 716970 Job 2 15205222 Job 1 202554217 Job 5 313327340 Job 4 2550259848 Job 6 435512141‾86‾ Total 383193 Average 63.8332.17\begin{array}{|c|c|c|c|c|c|c|}\hline \text { EDD } & \text { Time } & \frac{\text { Due }}{\text { Date }} & & \text { Slack } & \text { Flow time } & \text { Late davs } \\\hline \text { Job3 } & 7 & 16 & & 9 & 7 & 0 \\\hline \text { Job 2 } & 15 & 20 & & 5 & 22 & 2 \\\hline \text { Job 1 } & 20 & 25 & & 5 & 42 & 17 \\\hline \text { Job 5 } & 31 & 33 & & 2 & 73 & 40 \\\hline \text { Job 4 } & 25 & 50 & & 25 & 98 & 48 \\\hline \text { Job 6 } & 43 & 55 & & 12 & \underline{141} & \underline{86} \\\hline & & & & \text { Total } & 383 & 193 \\\hline & & & & \text { Average } & 63.83 & 32.17 \\\hline\end{array} EDD Job3 Job 2 Job 1 Job 5 Job 4 Job 6 Time 71520312543 Date Due 162025335055 Slack 95522512 Total Average Flow time 72242739814138363.83 Late davs 021740488619332.17
Average number of jobs in system: 2.716\text { Average number of jobs in system: } 2.716 Average number of jobs in system: 2.716 SPT ‾ Time Due Date Slack Flow time Late days Job 3 716970 Job 2 ‾15205222 Job 1 ‾202554217 Job 4 ‾2550256717 Job 5 ‾313329865 Job 6 ‾435512141‾86‾ Total 377187 Average 62.8331.17\begin{array}{|c|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 \text { Job 3 } & 7 & 16 & & 9 & 7 & 0 \\\hline \overline{\text { Job 2 }} & 15 & 20 & & 5 & 22 & 2 \\\hline \underline{\text { Job 1 }} & 20 & 25 & & 5 & 42 & 17 \\\hline \underline{\text { Job 4 }} & 25 & 50 & & 25 & 67 & 17 \\\hline \underline{\text { Job 5 }} & 31 & 33 & & 2 & 98 & 65 \\\hline \underline{\text { Job 6 }} & 43 & 55 & & 12 & \underline{141} & \underline{86} \\\hline & & & & \text { Total } & 377 & 187 \\\hline & & & & \text { Average } & 62.83 & 31.17 \\\hline\end{array} SPT Job 3 Job 2 Job 1 Job 4 Job 5 Job 6 Time 71520253143 Date Due 162025503355 Slack 95525212 Total Average Flow time 72242679814137762.83 Late days 021717658618731.17
Average number of jobs in system: 2.674\text { Average number of jobs in system: } 2.674 Average number of jobs in system: 2.674
LPT Time Due Date Slack Flow time Late days Job 6 435512430 Job 5 313327441 Job 4 2550259949 Job 1 2025511994 Job 2 15205134114 Job 3 7169141125‾ Total 610423 Average 101.6770.5\begin{array}{|c|c|c|l|c|c|c|}\hline \text { LPT } & \text { Time } & \begin{array}{c}\text { Due } \\\text { Date }\end{array} & & \text { Slack } & \text { Flow time } & \text { Late days } \\\hline \text { Job 6 } & 43 & 55 & & 12 & 43 & 0 \\\hline \text { Job 5 } & 31 & 33 & & 2 & 74 & 41 \\\hline \text { Job 4 } & 25 & 50 & & 25 & 99 & 49 \\\hline \text { Job 1 } & 20 & 25 & & 5 & 119 & 94 \\\hline \text { Job 2 } & 15 & 20 & & 5 & 134 & 114 \\\hline \text { Job 3 } & 7 & 16 & & 9 & 141 & \underline{125} \\\hline & & & & \text { Total } & 610 & 423 \\\hline & & & & \text { Average } & 101.67 & 70.5 \\\hline\end{array} LPT Job 6 Job 5 Job 4 Job 1 Job 2 Job 3 Time 43312520157 Due Date 553350252016 Slack 12225559 Total Average Flow time 437499119134141610101.67 Late days 041499411412542370.5
Average number of jobs in svstem: 4.326\text { Average number of jobs in svstem: } 4.326 Average number of jobs in svstem: 4.326
Dispatching Rule Job Sequence Average Flow Time Average Number of Jobs Average Lateness FCFS 1−2−3−4−5−667.22.8634.8 EDD 3−2−1−5−4−663.82.7132.2 SPT 3−2−1−4−5−662.82.6731.2 LPT 6−5−4−1−2−3101.74.3370.5\begin{array} { | l | c | c | c | c | } \hline \begin{array} { c } \text { Dispatching } \\\text { Rule }\end{array} & \text { Job Sequence } & \begin{array} { c } \text { Average } \\\text { Flow Time }\end{array} & \begin{array} { c } \text { Average } \\\text { Number of } \\\text { Jobs }\end{array} & \begin{array} { c } \text { Average } \\\text { Lateness }\end{array} \\\hline \text { FCFS } & 1 - 2 - 3 - 4 - 5 - 6 & 67.2 & 2.86 & 34.8 \\\hline \text { EDD } & 3 - 2 - 1 - 5 - 4 - 6 & 63.8 & 2.71 & 32.2 \\\hline \text { SPT } & 3 - 2 - 1 - 4 - 5 - 6 & 62.8 & 2.67 & 31.2 \\\hline \text { LPT } & 6 - 5 - 4 - 1 - 2 - 3 & 101.7 & 4.33 & 70.5 \\\hline\end{array} Dispatching Rule FCFS EDD SPT LPT Job Sequence 1−2−3−4−5−63−2−1−5−4−63−2−1−4−5−66−5−4−1−2−3 Average Flow Time 67.263.862.8101.7 Average Number of Jobs 2.862.712.674.33 Average Lateness 34.832.231.270.5 (b,c,d) The SPT rule is best for flow time, for average jobs in system, and for lateness. FCFS Time Due Date Slack Flow time Late days Job 1 20255200 Job 2 ‾152053515 Job 3 ‾71694226 Job 4 ‾2550256717 Job 5 ‾313329865 Job 6 ‾435512141‾86‾ Total 403209 Average 67.1734.83\begin{array}{|l|c|c|l|c|c|c|}\hline \text { FCFS } & \text { Time } & \frac{\text { Due }}{\text { Date }} & & \text { Slack } & \text { Flow time } &\text { Late days } \\\hline \text { Job 1 } & 20 & 25 & & 5 & 20 & 0 \\\hline \underline{\text { Job 2 }} & 15 & 20 & & 5 & 35 & 15 \\\hline \underline{\text { Job 3 }} & 7 & 16 & & 9 & 42 & 26 \\\hline \underline{\text { Job 4 }} & 25 & 50 & & 25 & 67 & 17 \\\hline \underline{\text { Job 5 }} & 31 & 33 & & 2 & 98 & 65 \\\hline \underline{\text { Job 6 }} & 43 & 55 & & 12 & \underline{141} & \underline{86} \\\hline & & & & \text { Total } & 403 & 209 \\\hline & & & & \text { Average } & 67.17 & 34.83 \\\hline\end{array} FCFS Job 1 Job 2 Job 3 Job 4 Job 5 Job 6 Time 20157253143 Date Due 252016503355 Slack 55925212 Total Average Flow time 203542679814140367.17 Late days 0152617658620934.83
Average number of jobs in system: 2.858\text { Average number of jobs in system: } 2.858 Average number of jobs in system: 2.858
EDD Time Due Date Slack Flow time Late davs Job3 716970 Job 2 15205222 Job 1 202554217 Job 5 313327340 Job 4 2550259848 Job 6 435512141‾86‾ Total 383193 Average 63.8332.17\begin{array}{|c|c|c|c|c|c|c|}\hline \text { EDD } & \text { Time } & \frac{\text { Due }}{\text { Date }} & & \text { Slack } & \text { Flow time } & \text { Late davs } \\\hline \text { Job3 } & 7 & 16 & & 9 & 7 & 0 \\\hline \text { Job 2 } & 15 & 20 & & 5 & 22 & 2 \\\hline \text { Job 1 } & 20 & 25 & & 5 & 42 & 17 \\\hline \text { Job 5 } & 31 & 33 & & 2 & 73 & 40 \\\hline \text { Job 4 } & 25 & 50 & & 25 & 98 & 48 \\\hline \text { Job 6 } & 43 & 55 & & 12 & \underline{141} & \underline{86} \\\hline & & & & \text { Total } & 383 & 193 \\\hline & & & & \text { Average } & 63.83 & 32.17 \\\hline\end{array} EDD Job3 Job 2 Job 1 Job 5 Job 4 Job 6 Time 71520312543 Date Due 162025335055 Slack 95522512 Total Average Flow time 72242739814138363.83 Late davs 021740488619332.17
Average number of jobs in system: 2.716\text { Average number of jobs in system: } 2.716 Average number of jobs in system: 2.716 SPT ‾ Time Due Date Slack Flow time Late days Job 3 716970 Job 2 ‾15205222 Job 1 ‾202554217 Job 4 ‾2550256717 Job 5 ‾313329865 Job 6 ‾435512141‾86‾ Total 377187 Average 62.8331.17\begin{array}{|c|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 \text { Job 3 } & 7 & 16 & & 9 & 7 & 0 \\\hline \overline{\text { Job 2 }} & 15 & 20 & & 5 & 22 & 2 \\\hline \underline{\text { Job 1 }} & 20 & 25 & & 5 & 42 & 17 \\\hline \underline{\text { Job 4 }} & 25 & 50 & & 25 & 67 & 17 \\\hline \underline{\text { Job 5 }} & 31 & 33 & & 2 & 98 & 65 \\\hline \underline{\text { Job 6 }} & 43 & 55 & & 12 & \underline{141} & \underline{86} \\\hline & & & & \text { Total } & 377 & 187 \\\hline & & & & \text { Average } & 62.83 & 31.17 \\\hline\end{array} SPT Job 3 Job 2 Job 1 Job 4 Job 5 Job 6 Time 71520253143 Date Due 162025503355 Slack 95525212 Total Average Flow time 72242679814137762.83 Late days 021717658618731.17
Average number of jobs in system: 2.674\text { Average number of jobs in system: } 2.674 Average number of jobs in system: 2.674
LPT Time Due Date Slack Flow time Late days Job 6 435512430 Job 5 313327441 Job 4 2550259949 Job 1 2025511994 Job 2 15205134114 Job 3 7169141125‾ Total 610423 Average 101.6770.5\begin{array}{|c|c|c|l|c|c|c|}\hline \text { LPT } & \text { Time } & \begin{array}{c}\text { Due } \\\text { Date }\end{array} & & \text { Slack } & \text { Flow time } & \text { Late days } \\\hline \text { Job 6 } & 43 & 55 & & 12 & 43 & 0 \\\hline \text { Job 5 } & 31 & 33 & & 2 & 74 & 41 \\\hline \text { Job 4 } & 25 & 50 & & 25 & 99 & 49 \\\hline \text { Job 1 } & 20 & 25 & & 5 & 119 & 94 \\\hline \text { Job 2 } & 15 & 20 & & 5 & 134 & 114 \\\hline \text { Job 3 } & 7 & 16 & & 9 & 141 & \underline{125} \\\hline & & & & \text { Total } & 610 & 423 \\\hline & & & & \text { Average } & 101.67 & 70.5 \\\hline\end{array} LPT Job 6 Job 5 Job 4 Job 1 Job 2 Job 3 Time 43312520157 Due Date 553350252016 Slack 12225559 Total Average Flow time 437499119134141610101.67 Late days 041499411412542370.5
Average number of jobs in svstem: 4.326\text { Average number of jobs in svstem: } 4.326 Average number of jobs in svstem: 4.326
Learning Objectives
- Familiarize oneself with the essential aspects of dispatching and their application in planning.
- Analyze the comparative effectiveness of various scheduling directives regarding average flow time, work-in-process, lateness, and makespan.
- Find the leading scheduling technique tailored to specific performance expectations.