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EPT 432 Operation Management Lab 7 – Short Term Scheduling PPK Pembuatan 2008/2009 Lab 7 Short Term Scheduling Objectives of this laboratory: 1. Student is able to define loading jobs, assignment method, and sequencing jobs. 2. Student is able to apply the assignment method for loading jobs. 3. Student is able to define and describe each of the priority sequencing rules. 4. Student is able to apply the priority rules and the critical ratio methods for sequencing jobs. Before we start this laboratory exercise, let familiarize our self with several terms that are commonly used in Short Term Scheduling realm. What is Loading Jobs? • Loading Jobs means the assignment of jobs to work or processing centers so that costs, idle time or completion times are kept to a minimum. What is assignment method? • Assignment method is a special class of linear programming models that involves assigning tasks or jobs to resources so that (most often objectives) the total costs or time required can be minimized. What is sequencing Jobs? • Sequencing Jobs is the determination of the order in which jobs should be done at each work center. Assignment Method Let say that there are three printing jobs that need to be processed at three different types of printing machines. To print specific jobs at each printing machine (typesetter) will cost a certain amount of money as refer to the table below. Typesetter Job A B C R-34 $11 $14 $6 S-66 $8 $10 $11 T-55 $9 $12 $7 The question is which job to assign to which machine in order to minimize the total cost for all the printing processes? So, the assignment method involves adding and subtracting appropriate numbers in the table to find the lowest opportunity cost for each assignment. There are four steps in the assignment method. Page 1 of 9 EPT 432 Operation Management Lab 7 – Short Term Scheduling PPK Pembuatan 2008/2009 Step 1a: Subtract the smallest number in each row from every numbers in the row. Typesetter Job A B C R-34 $11 - $6 $14 - $6 $6 - $6 S-66 $8 - $8 $10 - $8 $11 - $8 T-55 $9 - $7 $12 - $7 $7 - $7 Typesetter Job A B C R-34 5 8 0 S-66 0 2 3 T-55 2 5 0 Step 1b: Than, subtract the smallest number in each column from every numbers in the column. Typesetter Job A B C R-34 5-0 8-2 0-0 S-66 0-0 2-2 3-0 T-55 2-0 5-2 0-0 Typesetter Job A B C R-34 5 6 0 S-66 0 0 3 T-55 2 3 0 Page 2 of 9 EPT 432 Operation Management Lab 7 – Short Term Scheduling PPK Pembuatan 2008/2009 Step 2: Draw the minimum number of vertical and horizontal straight lines needed to cover all zeros. Because two lines suffice, the solution is not optimal. Typesetter Job A B C R-34 5 6 0 S-66 0 0 3 T-55 2 3 0 Smallest uncovered number Step 3: Subtract the smallest uncovered number from every other uncovered number and add it to numbers at the intersection of two lines. Typesetter Job A B C R-34 5 -2 6-2 0 S-66 0 0 3+2 T-55 2-2 3-2 0 Typesetter Job A B C R-34 3 4 0 S-66 0 0 5 T-55 0 1 0 Than return to step 2 Page 3 of 9 EPT 432 Operation Management Lab 7 – Short Term Scheduling PPK Pembuatan 2008/2009 Typesetter Job A B C R-34 3 4 0 S-66 0 0 5 T-55 0 1 0 Because three lines are necessary, an optimal assignment can be made. Assign R-34 to C Assign S-66 to B Assign T-50 to A The total cost is = $6 + $10 + $9 = $25 Sequencing Jobs a) Priority Rules Rules used to determine the sequence of jobs in process oriented facilities. There are four priority rules for dispatching jobs: • First come, first served (FCFS) o Jobs are completed in the order they arrived. • Shortest processing time (SPT) o Jobs with the shortest processing times are assigned first. • Earliest due date (EDD) o Earliest due date jobs are performed first. • Longest processing time (LPT) o Jobs with the longest processing time are completed first. There are four types of result in measuring the effectiveness of the priority rules • Average completion time = Sum of total flow time Number of jobs o The lower the better Page 4 of 9 EPT 432 Operation Management Lab 7 – Short Term Scheduling • Utilization = PPK Pembuatan 2008/2009 Total job work ( proces sin g ) time Sum of total flow time o The higher the better • Average number on jobs in the system = Sum of total flow time Total job work ( proces sin g ) time o The lower the better • Average job lateness = Total late days Number of jobs o The lower the better Example: Let say we have five jobs that need to be set prioritize which one run first and which is next and so on.(Refer to table below) A Job Work (Processing) Time (Days) 6 B 2 6 C 8 18 D 3 15 E 9 23 Job Job Due Date (Days) 8 Let choose the first come, first served priority rule (FCFS). Sort the job sequence based on FCFS. A Job Work (Processing) Time 6 B 2 6+2=8 6 8–6=2 C 8 8 + 8 = 16 18 16 – 18 = 0 D 3 16 + 3 = 19 15 19 – 15 = 4 E 9 19 + 9 = 28 23 28 – 23 = 0 Total 28 77 Job Sequence Flow Time Job Due Date Job Lateness 6 8 6–8=0 Page 5 of 9 11 EPT 432 Operation Management Lab 7 – Short Term Scheduling • • • PPK Pembuatan 2008/2009 Average completion time = Sum of total flow time Number of jobs Average completion time = 77 days = 15.4 days 5 Utilization = Total job work ( proces sin g ) time Sum of total flow time Utilization = 28 = 36.4% 77 Average number on jobs in the system = • Sum of total flow time Average number on jobs in the system = Total job work ( proces sin g ) time 77 days = 2.75 jobs 28 days Average job lateness = Total late days Number of jobs Average job lateness = 11 = 2.2 days 5 The results of these four rules are summarized in the following table: FCFS Average Completion Time (Days) 15.4 36.4 Average Number of Jobs in System 2.75 SPT 13.0 43.1 2.32 1.8 EDD 13.6 41.2 2.43 1.2 LPT 20.6 27.2 3.68 9.6 Rule Utilization (%) Average lateness (Says) 2.2 For this example the shortage processing time (SPT) is superior in 3 measures of effectiveness. Page 6 of 9 EPT 432 Operation Management Lab 7 – Short Term Scheduling PPK Pembuatan 2008/2009 Critical Ratio A sequencing rule that is an index number computed by dividing the time remaining until due date by the work time remaining. Critical ratio is dynamics and easy to update and it tends to perform better than FCFS, SPT, EDD or LPT on the average job lateness criterion. Critical Ratio = Time remaining Due date − Today ' s date = Workdays remaining Work (lead ) time remaining If the critical ratio is exactly 1.0 meaning the job is on schedule, if the value of critical ratio is greater than 1.0 means the job is ahead and if the value of critical ratio is glower than 1.0 means the job is falling behind schedule. Example: Today is day 25 on Zyco Medical Testing laboratories’ production schedule. Three jobs are on order, as shown in table below: Job Due Date Workdays Remaining A 30 4 B 28 5 C 27 2 Job Critical Ratio Priority Order Solution: A B C 30 − 25 = 1.25 4 28 − 25 = 0.60 5 27 − 25 = 1.00 2 Page 7 of 9 3 1 2 EPT 432 Operation Management Lab 7 – Short Term Scheduling PPK Pembuatan 2008/2009 Exercises: 1) The Orange Top Cab Company has a taxi waiting at each of four cabstands in Evanston, Illinois. Four customers have called and requested service. The distances, in miles, from the waiting taxis to the customers are given in the following table. Find the optimal assignment of taxis to customers so as to minimize total driving distance to the customers. [5 marks] Customer Cab Site A B C D Stand 1 7 3 4 8 Stand 2 5 4 6 5 Stand 3 6 7 9 6 Stand 4 8 6 7 4 Note: All the solutions / calculations must be constructed using Microsoft Excel program. 2) The following jobs are waiting to be processes at the same machine center. Jobs are logged as they arrive: Job Due Date Duration (days) A 313 7 B 312 15 C 325 30 D 314 10 E 314 6 In what sequence would the jobs be ranked according to the following decision rules: a) FCFS b) EDD c) SPT d) LPT All dates are specified as manufacturing planning calendar days. Assume that all jobs arrive on day 275. Which decision is best and why? [10 marks] Note: All the solutions / calculations must be constructed using Microsoft Excel program. Page 8 of 9 EPT 432 Operation Management Lab 7 – Short Term Scheduling PPK Pembuatan 2008/2009 3) The following 5 overhaul jobs are waiting to be processed at Avianic’s Engine Repair Inc. These jobs were logged as they arrived. All dates are specified as planning calendar days. Assume that all jobs arrived on day 180; today’s date is 200. Job Due date Duration (days) 103 214 10 205 223 7 309 217 11 412 219 5 517 217 15 Using the critical ratio scheduling rule, in what sequence would the jobs be processed? [5 marks] Note: All the solutions / calculations must be constructed using Microsoft Excel program. Total marks = _______ / 20 marks GOOD LUCK Page 9 of 9