<p> Practice Problem: Chapter 15, Short Term Scheduling</p><p>Problem 1:</p><p>Assume that Susan is a sorority pledge coordinator with four jobs and only three pledges. The table below gives the expected time for each pledge to do each job.</p><p>Job 1 Job 2 Job 3 Job 4</p><p>Alice 4 9 3 8</p><p>Barbara 7 8 2 6</p><p>Jennifer 3 4 5 7</p><p>If she wishes to minimize the time taken, to whom should she assign which job?</p><p>1 Problem 2: Five jobs are to be done at custom furniture shop:</p><p>Job Days Date Promised to Finish (in Days from Today)</p><p>A 2 5</p><p>B 8 8</p><p>C 6 12</p><p>D 4 10</p><p>E 1 4</p><p>Compare the effect of the scheduling methods (A) FCFS (first come, first served), (B) EDD (earliest due date), and (C) SPT (smallest processing time).</p><p>2 Problem 3: The following six jobs are waiting to be processed:</p><p>Job Hours Time to Due Process</p><p>#407 2 7</p><p>#281 8 16</p><p>#306 4 4</p><p>#429 10 17</p><p>#038 5 15</p><p>#998 12 18</p><p>Develop the appropriate sequencing for these jobs using the Critical Ratio criteria.</p><p>3 Problem 4: Five jobs go through two work centers, as shown below:</p><p>Job Hours Required </p><p>Varnishing Painting (Center 1) (Center 2)</p><p>R 4 5</p><p>S 17 7</p><p>T 14 12</p><p>U 9 2</p><p>V 11 6</p><p>What is the appropriate sequence for these jobs?</p><p>4 ANSWERS</p><p>Problem 1: First, begin with the following assignment table:</p><p>Job 1 Job 2 Job 3 Job 4</p><p>Alice 4 9 3 8</p><p>Barbara 7 8 2 6</p><p>Jennifer 3 4 5 7</p><p>Dummy 0 0 0 0</p><p>Note: The “dummy” must be added because we have four jobs and only three people.</p><p>Solve this table for the set of assignments giving the minimum total job time.</p><p>Your final table should look like:</p><p>Job 1 Job 2 Job 3 Job 4</p><p>Alice 0 4 0 3</p><p>Barbara 4 4 0 2</p><p>Jennifer 0 0 3 3</p><p>Dummy 1 0 2 0</p><p>5 The set of optimal assignments would then be: Alice - Job 1 Barbara - Job 3 Jennifer - Job 2 Dummy - Job 4 Note that Job 4 does not get done since it is assigned to the “Dummy.”</p><p>Problem 2: (A)</p><p>FCFS</p><p>Sequence Process Flow Due Lateness Time Time Date</p><p>A 2 2 5 0</p><p>B 8 10 8 2</p><p>C 6 16 12 4</p><p>D 4 20 10 10</p><p>E 1 21 4 17</p><p>TOTALS 21 69 33</p><p>Average completion time  69 / 5  13.8 days</p><p>Average number of jobs in the system  69 / 21  3.28 jobs Average lateness  33 / 5  6.6 days</p><p>Utilization  21/ 69  30.4%</p><p>6 (B)</p><p>EDD</p><p>Sequence Process Flow Due Lateness Time Time Date</p><p>E 1 1 4 0</p><p>A 2 3 5 0</p><p>B 8 11 8 3</p><p>D 4 15 10 5</p><p>C 6 21 12 9</p><p>TOTALS 21 51 17</p><p>Utilization  21/ 51  41.2%</p><p>(C)</p><p>SPT</p><p>Sequence Process Flow Due Lateness Time Time Date</p><p>E 1 1 4 0</p><p>A 2 3 5 0</p><p>D 4 7 10 0</p><p>C 6 13 12 1</p><p>B 8 21 8 13</p><p>TOTALS 21 45 14</p><p>7 Average completion time  45 / 5  9 days</p><p>Average number of jobs in the system  45 / 21  2.14 jobs Average lateness  14 / 5  2.8 days</p><p>Utilization  21/ 45  46.7%</p><p>Problem 3:</p><p>Job Hours to Time Computed Process Due Critical Ratio</p><p>#407 2 7 7/2 = 3.5</p><p>#281 8 16 16/8 = 2.0</p><p>#306 4 4 4/4 = 1.0</p><p>#429 10 17 17/10 = 1.7</p><p>#038 5 15 15/5 = 3.0</p><p>#998 12 18 18/12 = 1.5</p><p>8 Critical Critical Ratio Ratio Sequence</p><p>#306 1.0</p><p>#998 1.5</p><p>#429 1.7</p><p>#281 2.0</p><p>#038 3.0</p><p>#407 3.5</p><p>Problem 4:</p><p>9</p>