Practice Problem: Chapter 15, Short Term Scheduling Problem 1: 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. Job 1 Job 2 Job 3 Job 4 Alice 4 9 3 8 Barbara 7 8 2 6 Jennifer 3 4 5 7 If she wishes to minimize the time taken, to whom should she assign which job? Problem 2: A custom furniture shop has the five jobs below to be done and they are unsure how to sequence them through the shop. Job Days to Finish Date Promised (in Days from Today) A 2 5 B 8 8 C 6 12 D 4 10 E 1 4 Compare the effect of the scheduling methods (a) FCFS (first come, first served), (b) EDD (earliest due date), and (c) SPT (smallest processing time). 1 Problem 3: A firm has the following six jobs waiting to be processed: Job Hours to Process Time Due #407 2 7 #281 8 16 #306 4 4 #429 10 17 #038 5 15 #998 12 18 Develop the appropriate sequencing for these jobs using the Critical Ratio criteria. Problem 4: Our furniture manufacturer has the following five jobs that must go through the two work centers in the table below: Job Hours Required Varnishing (Center 1) Painting (Center 2) R 4 5 S 17 7 T 14 12 U 9 2 V 11 6 What is the appropriate sequence for these jobs? 2 ANSWERS Problem 1: First, begin with the following assignment table: Job 1 Job 2 Job 3 Job 4 Alice 4 9 3 8 Barbara 7 8 2 6 Jennifer 3 4 5 7 Dummy 0 0 0 0 Note: The “dummy” must be added because we have four jobs and only three people. Solve this table for the set of assignments giving the minimum total job time. Your final table should look like: Job 1 Job 2 Job 3 Job 4 Alice 0 4 0 3 Barbara 4 4 0 2 Jennifer 0 0 3 3 Dummy 1 0 2 0 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.” 3 Problem 2: (a) FCFS Sequence Process Time Flow Time Due Date Lateness A 2 2 5 0 B 8 10 8 2 C 6 16 12 4 D 4 20 10 10 E 1 21 4 17 TOTALS 21 69 Average completion time = 69/5 = 13.8 days Average number of jobs in the system = 69/21 = 3.29 jobs Average lateness = 33/5 = 6.6 days Utilization = 21/69 = 30.4% 4 33 (b) EDD Sequence Process Time Flow Time Due Date Lateness E 1 1 4 0 A 2 3 5 0 B 8 11 8 3 D 4 15 10 5 C 6 21 12 9 TOTALS 21 51 17 Average completion time = 51/5 = 10.2 days Average number of jobs in the system = 51/21 = 2.43 jobs Average lateness = 17/5 = 3.4 days Utilization = 21/51 = 41.2% (c) SPT Sequence Process Time Flow Time Due Date Lateness E 1 1 4 0 A 2 3 5 0 D 4 7 10 0 C 6 13 12 1 B 8 21 8 13 TOTALS 21 45 5 14 Average completion time = 45/5 = 9 days Average number of jobs in the system = 45/21 = 2.14 jobs Average lateness = 14/5 = 2.8 days Utilization = 21/45 = 46.7% Problem 3: Job Hours to Process Time Due Computed Critical Ratio #407 2 7 7/2 = 3.5 #281 8 16 16/8 = 2.0 #306 4 4 4/4 = 1.0 #429 10 17 17/10 = 1.7 #038 5 15 15/5 = 3.0 #998 12 18 18/12 = 1.5 Critical Ratio Sequence Critical Ratio #306 1.0 #998 1.5 #429 1.7 #281 2.0 #038 3.0 #407 3.5 6 Problem 4: 7