Asked by Alexis Rampey on May 03, 2024
Verified
Jack's Refrigeration Repair is under contract to repair, recondition, and/or refurbish commercial and industrial icemakers from restaurants, seafood processors, and similar organizations. Jack currently has five jobs to be scheduled, shown in the order in which they arrived.
Job Processing Time (hours) Due (hours) V2050W1035X5090Y1535Z5575\begin{array} { | c | c | c | } \hline \text { Job } & \text { Processing Time (hours) } & \text { Due (hours) } \\\hline \mathrm { V } & 20 & 50 \\\hline \mathrm { W } & 10 & 35 \\\hline \mathrm { X } & 50 & 90 \\\hline \mathrm { Y } & 15 & 35 \\\hline \mathrm { Z } & 55 & 75 \\\hline\end{array} Job VWXYZ Processing Time (hours) 2010501555 Due (hours) 5035903575 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?
e. What dispatching rule would you select? Support your decision.
Dispatching Rule Job Sequence Average Flow Time Average Number of Jobs Average Lateness FCFS SPT EDD CR \begin{array} { | c | c | c | c | c | } \hline \begin{array} { c } \text { Dispatching } \\\text { Rule }\end{array} & \text { Job Sequence } & \begin{array} { c } \text { Average Flow } \\\text { 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 { SPT } & & & & \\\hline \text { EDD } & & & & \\\hline \text { CR } & & & & \\\hline\end{array} Dispatching Rule FCFS SPT EDD CR Job Sequence Average Flow Time Average Number of Jobs Average Lateness
Commercial Icemakers
Machines designed for industrial or commercial use that produce large quantities of ice cubes or flakes for various business needs, such as in restaurants, bars, and healthcare facilities.
Industrial Icemakers
Machines specifically designed for large-scale production of ice, commonly used in industries such as food, hospitality, and healthcare.
Dispatching Rule
relates to guidelines or criteria used in manufacturing and operations management to prioritize and allocate tasks or resources, optimizing workflow and productivity.
- Understand key dispatching rules and their application in scheduling.
- Evaluate the performance of different scheduling rules based on average flow time, work-in-process, lateness, and makespan.
Verified Answer
ZK
Zybrea KnightMay 05, 2024
Final Answer :
(a) A summary of calculations appears in the table below.
Dispatching Rule Job Sequence Average Flow Time Average Number of Jobs Average Lateness FCFS V,W,X,Y,Z752.5027 SPT W, Y, V, X, Z 652.1716 EDD W, Y, V, Z, X 662.2017 CR Z, X, Y, V, W 1143.8061\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 Flow } \\\text { 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 } & \mathrm { V } , \mathrm { W } , \mathrm { X } , \mathrm { Y } , \mathrm { Z } & 75 & 2.50 & 27 \\\hline \text { SPT } & \text { W, Y, V, X, Z } & 65 & 2.17 & 16 \\\hline \text { EDD } & \text { W, Y, V, Z, X } & 66 & 2.20 & 17 \\\hline \text { CR } & \text { Z, X, Y, V, W } & 114 & 3.80 & 61 \\\hline\end{array} Dispatching Rule FCFS SPT EDD CR Job Sequence V,W,X,Y,Z W, Y, V, X, Z W, Y, V, Z, X Z, X, Y, V, W Average Flow Time 756566114 Average Number of Jobs 2.502.172.203.80 Average Lateness 27161761 (b,c,d) SPT is best on all three criteria: flow time, work-in-process, and lateness. (e) Most students will select SPT as quite obvious, but EDD is a close second in all criteria. Supporting calculations for each priority rule appear in the tables below. SPT Machine Due Date Flow Time Late W1035100Y1535250V2050450X5090955 Z 557515075 Total 32580 Average 6516\begin{array}{|c|c|c|c|c|}\hline \text { SPT } & \text { Machine } & \text { Due Date } & \text { Flow Time } & \text { Late } \\\hline \mathrm{W} & 10 & 35 & 10 & 0 \\\hline \mathrm{Y} & 15 & 35 & 25 & 0 \\\hline \mathrm{V} & 20 & 50 & 45 & 0 \\\hline \mathrm{X} & 50 & 90 & 95 & 5 \\\hline \text { Z } & 55 & 75 & 150 & 75 \\\hline \text { Total } & & & 325 & 80 \\\hline \text { Average } & & & 65 & 16 \\\hline\end{array} SPT WYVX Z Total Average Machine 1015205055 Due Date 3535509075 Flow Time 1025459515032565 Late 0005758016
Average # jobs in system =2.17\text { Average } \# \text { jobs in system }=2.17 Average # jobs in system =2.17
FCFS Machinel Due Date Flow Time Late V2050200W1035300X5090800Y15359560 Z 557515075 Total 375135 Average 7527\begin{array}{|c|c|c|c|c|}\hline \text { FCFS } & \text { Machinel } & \text { Due Date } & \text { Flow Time } & \text { Late } \\\hline \mathrm{V} & 20 & 50 & 20 & 0 \\\hline \mathrm{W} & 10 & 35 & 30 & 0 \\\hline \mathrm{X} & 50 & 90 & 80 & 0 \\\hline \mathrm{Y} & 15 & 35 & 95 & 60 \\\hline \text { Z } & 55 & 75 & 150 & 75 \\\hline \text { Total } & & & 375 & 135 \\\hline \text { Average } & & & 75 & 27 \\\hline\end{array} FCFS VWXY Z Total Average Machinel 2010501555 Due Date 5035903575 Flow Time 2030809515037575 Late 000607513527
Average # jobs in system =2.5\text { Average \# jobs in system }=2.5 Average # jobs in system =2.5 EDD Machine l Due Date Flow Time Late W1035100Y1535250V2050450Z557510025X509015060 Total 33085 Average 6617\begin{array}{|c|c|c|c|c|}\hline \text { EDD } & \text { Machine l } & \text { Due Date } & \text { Flow Time } & \text { Late } \\\hline \mathrm{W} & 10 & 35 & 10 & 0 \\\hline \mathrm{Y} & 15 & 35 & 25 & 0 \\\hline \mathrm{V} & 20 & 50 & 45 & 0 \\\hline \mathrm{Z} & 55 & 75 & 100 & 25 \\\hline \mathrm{X} & 50 & 90 & 150 & 60 \\\hline \text { Total } & & & 330 & 85 \\\hline \text { Average } & & & 66 & 17 \\\hline\end{array} EDD WYVZX Total Average Machine l 1015205550 Due Date 3535507590 Flow Time 10254510015033066 Late 00025608517
Average # jobs in system =2.20\text { Average } \# \text { jobs in system }=2.20 Average # jobs in system =2.20
CR Machinel Due Date CR Flow Time Late Z 55751.36550X50901.810515Y15352.3312085V20502.514090W10353.5150115 Total 570305 Average 1146\begin{array}{|c|c|c|c|c|c|}\hline \text { CR } & \text { Machinel } & \text { Due Date } & \text { CR } & \text { Flow Time } & \text { Late } \\\hline \text { Z } & 55 & 75 & 1.36 & 55 & 0 \\\hline \mathrm{X} & 50 & 90 & 1.8 & 105 & 15 \\\hline \mathrm{Y} & 15 & 35 & 2.33 & 120 & 85 \\\hline \mathrm{V} & 20 & 50 & 2.5 & 140 & 90 \\\hline \mathrm{W} & 10 & 35 & 3.5 & 150 & 115 \\\hline \text { Total } & & & & 570 & 305 \\\hline \text { Average } & & & & 114 & 6 \\\hline\end{array} CR Z XYVW Total Average Machinel 5550152010 Due Date 7590355035 CR 1.361.82.332.53.5 Flow Time 55105120140150570114 Late 01585901153056
Average # jobs in system =3.80\text { Average \# jobs in system }=3.80 Average # jobs in system =3.80
Dispatching Rule Job Sequence Average Flow Time Average Number of Jobs Average Lateness FCFS V,W,X,Y,Z752.5027 SPT W, Y, V, X, Z 652.1716 EDD W, Y, V, Z, X 662.2017 CR Z, X, Y, V, W 1143.8061\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 Flow } \\\text { 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 } & \mathrm { V } , \mathrm { W } , \mathrm { X } , \mathrm { Y } , \mathrm { Z } & 75 & 2.50 & 27 \\\hline \text { SPT } & \text { W, Y, V, X, Z } & 65 & 2.17 & 16 \\\hline \text { EDD } & \text { W, Y, V, Z, X } & 66 & 2.20 & 17 \\\hline \text { CR } & \text { Z, X, Y, V, W } & 114 & 3.80 & 61 \\\hline\end{array} Dispatching Rule FCFS SPT EDD CR Job Sequence V,W,X,Y,Z W, Y, V, X, Z W, Y, V, Z, X Z, X, Y, V, W Average Flow Time 756566114 Average Number of Jobs 2.502.172.203.80 Average Lateness 27161761 (b,c,d) SPT is best on all three criteria: flow time, work-in-process, and lateness. (e) Most students will select SPT as quite obvious, but EDD is a close second in all criteria. Supporting calculations for each priority rule appear in the tables below. SPT Machine Due Date Flow Time Late W1035100Y1535250V2050450X5090955 Z 557515075 Total 32580 Average 6516\begin{array}{|c|c|c|c|c|}\hline \text { SPT } & \text { Machine } & \text { Due Date } & \text { Flow Time } & \text { Late } \\\hline \mathrm{W} & 10 & 35 & 10 & 0 \\\hline \mathrm{Y} & 15 & 35 & 25 & 0 \\\hline \mathrm{V} & 20 & 50 & 45 & 0 \\\hline \mathrm{X} & 50 & 90 & 95 & 5 \\\hline \text { Z } & 55 & 75 & 150 & 75 \\\hline \text { Total } & & & 325 & 80 \\\hline \text { Average } & & & 65 & 16 \\\hline\end{array} SPT WYVX Z Total Average Machine 1015205055 Due Date 3535509075 Flow Time 1025459515032565 Late 0005758016
Average # jobs in system =2.17\text { Average } \# \text { jobs in system }=2.17 Average # jobs in system =2.17
FCFS Machinel Due Date Flow Time Late V2050200W1035300X5090800Y15359560 Z 557515075 Total 375135 Average 7527\begin{array}{|c|c|c|c|c|}\hline \text { FCFS } & \text { Machinel } & \text { Due Date } & \text { Flow Time } & \text { Late } \\\hline \mathrm{V} & 20 & 50 & 20 & 0 \\\hline \mathrm{W} & 10 & 35 & 30 & 0 \\\hline \mathrm{X} & 50 & 90 & 80 & 0 \\\hline \mathrm{Y} & 15 & 35 & 95 & 60 \\\hline \text { Z } & 55 & 75 & 150 & 75 \\\hline \text { Total } & & & 375 & 135 \\\hline \text { Average } & & & 75 & 27 \\\hline\end{array} FCFS VWXY Z Total Average Machinel 2010501555 Due Date 5035903575 Flow Time 2030809515037575 Late 000607513527
Average # jobs in system =2.5\text { Average \# jobs in system }=2.5 Average # jobs in system =2.5 EDD Machine l Due Date Flow Time Late W1035100Y1535250V2050450Z557510025X509015060 Total 33085 Average 6617\begin{array}{|c|c|c|c|c|}\hline \text { EDD } & \text { Machine l } & \text { Due Date } & \text { Flow Time } & \text { Late } \\\hline \mathrm{W} & 10 & 35 & 10 & 0 \\\hline \mathrm{Y} & 15 & 35 & 25 & 0 \\\hline \mathrm{V} & 20 & 50 & 45 & 0 \\\hline \mathrm{Z} & 55 & 75 & 100 & 25 \\\hline \mathrm{X} & 50 & 90 & 150 & 60 \\\hline \text { Total } & & & 330 & 85 \\\hline \text { Average } & & & 66 & 17 \\\hline\end{array} EDD WYVZX Total Average Machine l 1015205550 Due Date 3535507590 Flow Time 10254510015033066 Late 00025608517
Average # jobs in system =2.20\text { Average } \# \text { jobs in system }=2.20 Average # jobs in system =2.20
CR Machinel Due Date CR Flow Time Late Z 55751.36550X50901.810515Y15352.3312085V20502.514090W10353.5150115 Total 570305 Average 1146\begin{array}{|c|c|c|c|c|c|}\hline \text { CR } & \text { Machinel } & \text { Due Date } & \text { CR } & \text { Flow Time } & \text { Late } \\\hline \text { Z } & 55 & 75 & 1.36 & 55 & 0 \\\hline \mathrm{X} & 50 & 90 & 1.8 & 105 & 15 \\\hline \mathrm{Y} & 15 & 35 & 2.33 & 120 & 85 \\\hline \mathrm{V} & 20 & 50 & 2.5 & 140 & 90 \\\hline \mathrm{W} & 10 & 35 & 3.5 & 150 & 115 \\\hline \text { Total } & & & & 570 & 305 \\\hline \text { Average } & & & & 114 & 6 \\\hline\end{array} CR Z XYVW Total Average Machinel 5550152010 Due Date 7590355035 CR 1.361.82.332.53.5 Flow Time 55105120140150570114 Late 01585901153056
Average # jobs in system =3.80\text { Average \# jobs in system }=3.80 Average # jobs in system =3.80
Learning Objectives
- Understand key dispatching rules and their application in scheduling.
- Evaluate the performance of different scheduling rules based on average flow time, work-in-process, lateness, and makespan.