Asked by Emily_ nicole on May 12, 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 Day 1.
Start day 1 Data Received Time Due Date A 12319 B 11833 C 1615D11154 E 11214 F 1429\begin{array} { | r | r | r | r | } \hline \text { Start day } & 1 & & \\\hline \text { Data } & & & \\\hline & \text { Received } & \text { Time } & \text { Due Date } \\\hline \text { A } & 1 & 23 & 19 \\\hline \text { B } & 1 & 18 & 33 \\\hline \text { C } & 1 & 6 & 15 \\\hline \mathrm { D } & 1 & 11 & 54 \\\hline \text { E } & 1 & 12 & 14 \\\hline \text { F } & 1 & 4 & 29 \\\hline\end{array} Start day Data A B C D E F 1 Received 111111 Time 2318611124 Due Date 193315541429 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 Average Flow Time Average Number of Jobs Number of Jobs Late Average Lateness FCFS SPT LPT EDD SLACK CR \begin{array} { | l | l | l | l | l | } \hline \begin{array} { l } \text { Dispatching } \\\text { Rule }\end{array} & \begin{array} { l } \text { Average } \\\text { Flow Time }\end{array} & \begin{array} { l } \text { Average Number } \\\text { of Jobs }\end{array} & \begin{array} { l } \text { Number of } \\\text { Jobs Late }\end{array} & \begin{array} { l } \text { Average } \\\text { Lateness }\end{array} \\\hline \text { FCFS } & & & & \\\hline \text { SPT } & & & & \\\hline\text { LPT } & & & & \\\hline \text { EDD } & & & & \\\hline \text { SLACK } & & & & \\\hline \text { CR } & & & &\\\hline\end{array} Dispatching Rule FCFS SPT LPT EDD SLACK CR Average Flow Time Average Number of Jobs Number of Jobs Late Average Lateness
Dispatching Rule
A set of guidelines or criteria used for determining the sequence of tasks or the allocation of resources in a production process.
Flow Time
The total time a product spends in a manufacturing or service process from start to finish.
Work-In-Process
Items or components that are in the process of being manufactured but are not yet completed products.
- Gain an understanding of crucial dispatching principles and how they are applied in scheduling tasks.
- Examine the performance outcomes of diverse scheduling rules by considering average flow time, work-in-process, lateness, and makespan.
- Ascertain the most effective scheduling strategy according to predefined performance metrics.
Verified Answer
GB
Gagandeep BhanguMay 13, 2024
Final Answer :
a)
Method Average Flow Time Average number of jobs insystem Utilization Number of late jobs AverageLate Time FCFS 52.166674.229730.236422624.83333 SPT 32.166672.6081080.38342315.33333 LPT 54.166674.3918920.227692626.83333 Due Date 42.166673.4189190.29249515.16667 Slack 49.166673.9864860.250847621.83333 Crit Ratio 52.333334.2432430.235669625\begin{array}{rrrrrr}\text { Method }&\begin{array} { l } \text {Average }\\ \text {Flow Time }\\\end{array}&\begin{array} { l } \text { Average}\\ \text { number of}\\ \text { jobs in}\\ \text {system }\\\end{array}&\text { Utilization }&\begin{array} { l } \text {Number of }\\ \text { late jobs}\\\end{array}&\begin{array} { l } \text { Average}\\ \text {Late Time }\\\end{array}\\\text { FCFS } & 52.16667 & 4.22973 & 0.236422 & 6 & 24.83333 \\\text { SPT } & 32.16667 & 2.608108 & 0.38342 & 3 & 15.33333 \\\text { LPT } & 54.16667 & 4.391892 & 0.227692 & 6 & 26.83333 \\\text { Due Date } & 42.16667 & 3.418919 & 0.29249 & 5 & 15.16667 \\\text { Slack } & 49.16667 & 3.986486 & 0.250847 & 6 & 21.83333 \\\text { Crit Ratio } & 52.33333 & 4.243243 & 0.235669 & 6 & 25\end{array} Method FCFS SPT LPT Due Date Slack Crit Ratio Average Flow Time 52.1666732.1666754.1666742.1666749.1666752.33333 Average number of jobs insystem 4.229732.6081084.3918923.4189193.9864864.243243 Utilization 0.2364220.383420.2276920.292490.2508470.235669Number of late jobs636566 AverageLate Time 24.8333315.3333326.8333315.1666721.8333325 b) SPT
c) SPT
d) EDD
Method Average Flow Time Average number of jobs insystem Utilization Number of late jobs AverageLate Time FCFS 52.166674.229730.236422624.83333 SPT 32.166672.6081080.38342315.33333 LPT 54.166674.3918920.227692626.83333 Due Date 42.166673.4189190.29249515.16667 Slack 49.166673.9864860.250847621.83333 Crit Ratio 52.333334.2432430.235669625\begin{array}{rrrrrr}\text { Method }&\begin{array} { l } \text {Average }\\ \text {Flow Time }\\\end{array}&\begin{array} { l } \text { Average}\\ \text { number of}\\ \text { jobs in}\\ \text {system }\\\end{array}&\text { Utilization }&\begin{array} { l } \text {Number of }\\ \text { late jobs}\\\end{array}&\begin{array} { l } \text { Average}\\ \text {Late Time }\\\end{array}\\\text { FCFS } & 52.16667 & 4.22973 & 0.236422 & 6 & 24.83333 \\\text { SPT } & 32.16667 & 2.608108 & 0.38342 & 3 & 15.33333 \\\text { LPT } & 54.16667 & 4.391892 & 0.227692 & 6 & 26.83333 \\\text { Due Date } & 42.16667 & 3.418919 & 0.29249 & 5 & 15.16667 \\\text { Slack } & 49.16667 & 3.986486 & 0.250847 & 6 & 21.83333 \\\text { Crit Ratio } & 52.33333 & 4.243243 & 0.235669 & 6 & 25\end{array} Method FCFS SPT LPT Due Date Slack Crit Ratio Average Flow Time 52.1666732.1666754.1666742.1666749.1666752.33333 Average number of jobs insystem 4.229732.6081084.3918923.4189193.9864864.243243 Utilization 0.2364220.383420.2276920.292490.2508470.235669Number of late jobs636566 AverageLate Time 24.8333315.3333326.8333315.1666721.8333325 b) SPT
c) SPT
d) EDD
Learning Objectives
- Gain an understanding of crucial dispatching principles and how they are applied in scheduling tasks.
- Examine the performance outcomes of diverse scheduling rules by considering average flow time, work-in-process, lateness, and makespan.
- Ascertain the most effective scheduling strategy according to predefined performance metrics.