Bob Dresser operates a major appliance warranty service centre. His operation has two check stations that are required at the end of every repair task performed by his appliance repair staff. These are the Functionality Review (FR) and the Overall Scan (OS). The FR must be performed successfully before the OS is begun. On Friday morning, six repair jobs are completed, awaiting these two inspection activities. Processing times are given in minutes.
$1025\begin{array} { | c | c | c | } \hline \text { Job } & \text { FR } & \text { OS } \\\hline \text { A } & 50 & 30 \\\hline \text { B } & 35 & 55 \\\hline \text { C } & 25 & 20 \\\hline \text { D } & 20 & 35 \\\hline \text { E } & 15 & 10 \\\hline \text { F } & 10 & 25 \\\hline\end{array}$ a. What is the optimal sequence of jobs for the objective of minimizing the total flow time?
b. Show your work, and document the sequence.
c. Chart the solution to this problem.
d. What jobs are being processed at time period 90?
e. What is the total flow time of this problem?
$FROS20406080100120140160180200\begin{array} { | l | l | l | l | l | l | l | l | l | l | l | } \hline \mathrm { FR } & & & & & & & & & & \\\hline \mathrm { OS } & & & & & & & & & & \\\hline & 20 & 40 & 60 & 80 & 100 & 120 & 140 & 160 & 180 & 200 \\\hline\end{array}$

Question

Bob Dresser operates a major appliance warranty service centre. His operation has two check stations that are required at the end of every repair task performed by his appliance repair staff. These are the Functionality Review (FR) and the Overall Scan (OS). The FR must be performed successfully before the OS is begun. On Friday morning, six repair jobs are completed, awaiting these two inspection activities. Processing times are given in minutes.

1025\begin{array} { | c | c | c | } \hline \text { Job } & \text { FR } & \text { OS } \\\hline \text { A } & 50 & 30 \\\hline \text { B } & 35 & 55 \\\hline \text { C } & 25 & 20 \\\hline \text { D } & 20 & 35 \\\hline \text { E } & 15 & 10 \\\hline \text { F } & 10 & 25 \\\hline\end{array}

a. What is the optimal sequence of jobs for the objective of minimizing the total flow time?
b. Show your work, and document the sequence.
c. Chart the solution to this problem.
d. What jobs are being processed at time period 90?
e. What is the total flow time of this problem?

FROS20406080100120140160180200\begin{array} { | l | l | l | l | l | l | l | l | l | l | l | } \hline \mathrm { FR } & & & & & & & & & & \\\hline \mathrm { OS } & & & & & & & & & & \\\hline & 20 & 40 & 60 & 80 & 100 & 120 & 140 & 160 & 180 & 200 \\\hline\end{array}

Jabaar Mohamud · Accepted Answer

Final Answer :

(a) The optimal sequence is F-D-B-A-C-E.
(b) Supporting work appears in the table below.

185.\begin{array}{|r|r|r|r|r|r|}\hline & \text { FR } & \text { OS } & \text { Order } & \text { Done 1 } & \begin{array}{r}\text { Done 2 } \\\text { (flow time) }\end{array} \\\hline \text { A } & 50 . & 30 . & \text { fourth } & 115 . & 155 . \\\hline \mathbf{B} & 35 . & 55 . & \text { third } & 65 . & 125 . \\\hline \mathrm{C} & 25 . & 20 . & \text { fifth } & 140 . & 175 . \\\hline \mathrm{D} & 20 . & 35 . & \text { second } & 30 . & 70 . \\\hline \mathrm{E} & 15 . & 10 . & \text { sixth } & 155 . & 185 . \\\hline \text { F } & 10 . & 25 . & \text { first } & 10 . & 35 . \\\hline \text { Makespan } & & && & 185 . \\\hline\end{array}

\text { Sequence: F, D, B, A, C, E }

(c) The schedule appears in the chart below. (d) Job A is being processed at FR (Machine 1), while Job B is being processed at OS (e) Total flow time for the schedule is 185. $(a) The optimal sequence is F-D-B-A-C-E. (b) Supporting work appears in the table below. \begin{array}{|r|r|r|r|r|r|} \hline & \text { FR } & \text { OS } & \text { Order } & \text { Done 1 } & \begin{array}{r} \text { Done 2 } \\ \text { (flow time) } \end{array} \\ \hline \text { A } & 50 . & 30 . & \text { fourth } & 115 . & 155 . \\ \hline \mathbf{B} & 35 . & 55 . & \text { third } & 65 . & 125 . \\ \hline \mathrm{C} & 25 . & 20 . & \text { fifth } & 140 . & 175 . \\ \hline \mathrm{D} & 20 . & 35 . & \text { second } & 30 . & 70 . \\ \hline \mathrm{E} & 15 . & 10 . & \text { sixth } & 155 . & 185 . \\ \hline \text { F } & 10 . & 25 . & \text { first } & 10 . & 35 . \\ \hline \text { Makespan } & & && & 185 . \\ \hline \end{array} \text { Sequence: F, D, B, A, C, E } (c) The schedule appears in the chart below. (d) Job A is being processed at FR (Machine 1), while Job B is being processed at OS (e) Total flow time for the schedule is 185. (Machine 2)$ (Machine 2)

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