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- 1. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />J<br />Operations Scheduling<br />For Operations Management, 9e by Krajewski/Ritzman/Malhotra © 2010 Pearson Education<br />PowerPoint Slides by Jeff Heyl<br />
- 2. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />The scheduling techniques cut across the various process types found in services and manufacturing<br />Front-office process with high customer contact, divergent work flows, customization, and a complex scheduling environment<br />Back-office process has low customer involvement, uses more line work flows, and provides standardized services<br />Scheduling Service and Manufacturing Processes <br />
- 3. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Performance Measures<br />Flow time is the amount of time a job spends in the service or manufacturing system<br />Past due (tardiness) is the amount of time by which a job missed its due date<br />Makespan is the total amount of time required to complete a group of jobs<br />
- 4. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Performance Measures<br />Total inventory is used to measure the effectiveness of schedules for manufacturing processes.<br /><ul><li>Utilization is the percentage of work time that is productively spent by an employee or a machine</li></li></ul><li>Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Sequencing Jobs<br />Operations schedules are short-term plans designed to implement the sales and operations plan<br />An operation with divergent flows is often called a job shop<br />Low-to medium-volume production<br />Utilizes job or batch processes<br />The front office would be the equivalent for a service provider<br />Difficult to schedule because of the variability in job routings and the continual introduction of new jobs to be processed<br />
- 5. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Sequencing Jobs<br />An operation with line flow is often called a flow shop<br />Medium- to high-volume production<br />Utilizes line or continuous flow processes<br />The back office would be the equivalent for a service provider <br />Tasks are easier to schedule because the jobs have a common flow pattern through the system<br />
- 6. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Shipping Department<br />Raw Materials<br />Legend:<br />Batch of parts<br />Workstation<br />Job Shop Sequencing<br />Figure J.1 – Diagram of a Manufacturing Job Shop Process<br />
- 7. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />First-come, first-served (FCFS) <br />Earliest due date (EDD)<br />Critical ratio (CR)<br />Priority Sequencing Rules<br />(Due date) – (Today’s date)<br />Total shop time remaining<br />CR =<br /><ul><li>A ratio less than 1.0 implies that the job is behind schedule
- 8. A ratio greater than 1.0 implies the job is ahead of schedule
- 9. The job with the lowest CR is scheduled next</li></li></ul><li>Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Priority Sequencing Rules<br />Duedate<br />Today’sdate<br />Total shop time remaining<br />– –<br />S/RO =<br />Number of operations remaining<br />Shortest processing time (SPT)<br />Slack per remaining operations (S/RO)<br /><ul><li>The job with the lowest S/RO is scheduled next</li></li></ul><li>Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Single-dimension rules<br />A job’s priority assignment based only on information waiting for processing at the individual workstation (e.g., FCFS, EDD, and SPT)<br />Sequencing One Workstation<br />
- 10. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Comparing EDD and SPT Rules<br />EXAMPLE J.1<br />The Taylor Machine Shop rebores engine blocks. Currently, five engine blocks are waiting for processing. At any time, the company has only one engine expert on duty who can do this type of work. The engine problems have been diagnosed, and the processing times for the jobs have been estimated. Expected completion times have been agreed upon with the shop’s customers. The accompanying table shows the current situation. Because the Taylor Machine Shop is open from 8:00 A.M. until 5:00 P.M. each weekday, plus weekend hours as needed, the customer pickup times are measured in business hours from the current time. Determine the schedule for the engine expert by using (a) the EDD rule and (b) the SPT rule. For each rule, calculate the average flow time, average hours early, and average hours past due. If average past due is most important, which rule should be chosen?<br />
- 11. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Comparing EDD and SPT Rules<br />
- 12. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Comparing EDD and SPT Rules<br />SOLUTION<br />a. The EDD rule states that the first engine block in the sequence is the one with the closest due date. Consequently, the Ranger engine block is processed first. The Thunderbird engine block, with its due date furthest in the future, is processed last. The sequence is shown in the following table, along with the flow times, the hours early, and the hours past due.<br />
- 13. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Comparing EDD and SPT Rules<br />The flow time for each job is its finish time, plus the time since the job arrived.1 For example, the Explorer engine block’s finish time will be 14 hours from now (8 hours waiting time before the engine expert started to work on it plus 6 hours processing). Adding the 10 hours since the order arrived at this workstation (before the processing of this group of orders began) results in a flow time of 24 hours. You might think of the sum of flow times as the total job hours spent by the engine blocks since their orders arrived at the workstation until they were processed.<br />
- 14. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Comparing EDD and SPT Rules<br />20 + 24 + 20 + 33 + 44<br />5<br />= 28.2 hrs<br />2 + 0 + 1 + 0 + 0<br />5<br />= 0.6 hrs<br />0 + 2 + 0 + 12 + 22<br />5<br />= 7.2 hrs<br />The performance measures for the EDD schedule for the five engine blocks are<br />Average flow time =<br />Average hours early =<br />Average hours past due =<br />
- 15. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Comparing EDD and SPT Rules<br />b. Under the SPT rule, the sequence starts with the engine block that has the shortest processing time, the Econoline 150, and it ends with the engine block that has the longest processing time, the Bronco. The sequence, along with the flow times, early hours, and past due hours, is contained in the following table:<br />
- 16. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Comparing EDD and SPT Rules<br />6 + 19 + 29 + 29 + 45<br />5<br />= 25.6 hrs<br />15 + 3 + 0 + 0 + 0<br />5<br />= 3.6 hrs<br />0 + 0 + 7 + 7 + 24<br />5<br />= 7.6 hrs<br />The performance measures are<br />Average flow time =<br />Average hours early =<br />Average hours past due =<br />
- 17. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Comparing Sequencing Rules<br />EDD rule<br />Performs well with respect to the percentage of jobs past due and the variance of hours past due<br />Popular with firms that are sensitive to achieving due dates<br /><ul><li>SPT rule
- 18. Tends to minimize the mean flow and maximize shop utilization
- 19. For single-workstations will always provide the lowest mean finish time
- 20. Could increase total inventory
- 21. Tends to produce a large variance in past due hours
- 22. FCFS rule
- 23. Considered fair
- 24. It performs poorly with respect to all performance measures</li></li></ul><li>Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Application J.1<br />Given the following information, devise an SPT schedule for the automatic routing machine.<br />
- 25. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Application J.1<br />
- 26. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Multiple-Dimension Rules<br />The priority rules CR and S/RO incorporate information about the remaining workstations<br /><ul><li>S/RO is better than EDD with respect to the percentage of jobs past due but usually worse than SPT and EDD with respect to average job flow times
- 27. CR results in longer job flow times than SPT, but CR also results in less variance in the distribution of past due hours
- 28. No choice is clearly best; each rule should be tested in the environment for which it is intended</li></li></ul><li>Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Sequencing with the CR and S/RO Rules<br />EXAMPLE J.2<br />The first five columns of the following table contain information about a set of four jobs that just arrived (end of hour 0 or beginning of hour 1) at an engine lathe. They are the only ones now waiting to be processed. Several operations, including the one at the engine lathe, remain to be done on each job. Determine the schedule by using (a) the CR rule and (b) the S/RO rule. Compare these schedules to those generated by FCFS, SPT, and EDD.<br />
- 29. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />CR =<br />= = 2.46<br />Time remaining until the due date<br />Shop time remaining<br />15<br />6.1<br />Sequencing with the CR and S/RO Rules<br />SOLUTION<br />a. Using CR to schedule the machine, we divide the time remaining until the due date by the shop time remaining to get the priority index for each job. For job 1,<br />By arranging the jobs in sequence with the lowest critical ratio first, we determine that the sequence of jobs to be processed by the engine lathe is 4, 2, 3, and finally 1, assuming that no other jobs arrive in the meantime.<br />
- 30. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />S/RO =<br />= = 0.89<br />Time remaining<br />until the due date<br />Shop time<br />remaining<br />–<br />15 – 6.1<br />10<br />Number of operations remaining <br />Sequencing with the CR and S/RO Rules<br />b. Using S/RO, we divide the difference between the time remaining until the due date and the shop time remaining by the number of remaining operations. For job 1,<br />Arranging the jobs by starting with the lowest S/RO yields a 4, 3, 1, 2 sequence of jobs.<br />
- 31. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Sequencing with the CR and S/RO Rules<br />
- 32. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Application J.2<br />The following four jobs have just arrived at an idle drill process and must be scheduled.<br />* including drill press<br />Create the sequences for two schedules, one using the Critical Ratio rule and one using the S/RO rule. <br />
- 33. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Application J.2<br />
- 34. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Identifying the best priority rule to use at a particular operation in a process is a complex problem because the output from one operation becomes the input to another<br />Computer simulation models are effective tools to determine which priority rules work best in a given situation<br />Multiple Workstations<br />
- 35. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />In single-workstation scheduling, the makespan is the same regardless of the priority rule chosen<br />In the scheduling of two or more workstations in a flow shop, the makespan varies according to the sequence chosen<br />Determining a production sequence for a group of jobs to minimize the makespan has two advantages<br />The group of jobs is completed in minimum time<br />The utilization of the two-station flow shop is maximized<br />Scheduling a Two-Station Flow Shop<br />
- 36. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Johnson’s Rule<br />Minimizes makespan when scheduling a group of jobs on two workstations<br />Step 1: Scan the processing time at each workstation and find the shortest processing time among the jobs not yet scheduled. If two or more jobs are tied, choose one job arbitrarily.<br />Step 2: If the shortest processing time is on workstation 1, schedule the corresponding job as early as possible. If the shortest processing time is on workstation 2, schedule the corresponding job as late as possible.<br />Step 3: Eliminate the last job scheduled from further consideration. Repeat steps 1 and 2 until all jobs have been scheduled.<br />
- 37. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Scheduling Jobs on Two Workstations<br />EXAMPLE J.3<br />The Morris Machine Company just received an order to refurbish five motors for materials handling equipment that were damaged in a fire. The motors have been delivered and are available for processing. The motors will be repaired at two workstations in the following manner.<br />Workstation 1: Dismantle the motor and clean the parts.<br />Workstation 2: Replace the parts as necessary, test the motor, and make adjustments.<br />
- 38. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Scheduling Jobs on Two Workstations<br />The customer’s shop will be inoperable until all the motors have been repaired, so the plant manager is interested in developing a schedule that minimizes the makespan and has authorized around-the-clock operations until the motors have been repaired. The estimated time to repair each motor is shown in the following table:<br />
- 39. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Scheduling Jobs on Two Workstations<br />SOLUTION<br />The logic for the optimal sequence is shown in the following table:<br />
- 40. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Workstation<br />M2 <br />M1 <br />M4 <br />M5 <br />M3 <br />Idle—available <br />1<br />(4)<br />(12)<br />(15)<br />(10)<br />(5)<br />for further work<br />M2 <br />M1 <br />M4 <br />M5 <br />M3 <br />Idle<br />Idle<br />2<br />(5)<br />(22)<br />(16)<br />(8)<br />(3)<br />0<br />5<br />10<br />15<br />20<br />25<br />30<br />35<br />40<br />45<br />50<br />55<br />60<br />65<br />Hour<br />Scheduling Jobs on Two Workstations<br />Figure J.2 – Gantt Chart for the Morris Machine Company Repair Schedule<br />
- 41. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Application J.3<br />Use the following data to schedule two workstations arranged as a flow shop<br />C<br />B<br />E<br />D<br />A<br />
- 42. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Application J.3<br />
- 43. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />The resource constraint is the amount of labor available, not the number of machines or workstations<br />The scheduler must also assign workers to their next workstations<br />Labor-Limited Environment<br /><ul><li>Some possible labor assignment rules
- 44. Assign personnel to the workstation with the job that has been in the system longest
- 45. Assign personnel to the workstation with the most jobs waiting for processing
- 46. Assign personnel to the workstation with the largest standard work content
- 47. Assign personnel to the workstation with the job that has the earliest due date</li></li></ul><li>Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />The Neptune’s Den Machine Shop specializes in overhauling outboard marine engines. Some engines require replacement of broken parts, whereas others need a complete overhaul. Currently, five engines with varying problems are awaiting service. The best estimates for the labor times involved and the promise dates (in number of days from today) are shown in the following table. Customers usually do not pick up their engines early.<br />Solved Problem 1<br />
- 48. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Solved Problem 1<br />a. Develop separate schedules by using the SPT and EDD rules<br />b. Compare the two schedules on the basis of average flow time, percentage of past due jobs, and maximum past due days for any engine<br />
- 49. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Solved Problem 1<br />SOLUTION<br />a. Using the SPT rule, we obtain the following schedule:<br />
- 50. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Solved Problem 1<br />Using the EDD rule we obtain this schedule:<br />
- 51. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Solved Problem 1<br />b. Performance measures are as follows:<br />Average flow time is 16.6 (or 83/5) days for SPT and 22.0 (or 110/5) days for EDD. The percentage of past due jobs is 40 percent (2/5) for SPT and 60 percent (3/5) for EDD. For this set of jobs, the EDD schedule minimizes the maximum days past due but has a greater flow time and causes more jobs to be past due.<br />
- 52. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Solved Problem 2<br />The following data were reported by the shop floor control system for order processing at the edge grinder. The current date is day 150. The number of remaining operations and the total work remaining include the operation at the edge grinder. All orders are available for processing, and none have been started yet. Assume the jobs were available for processing at the same time.<br />
- 53. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Solved Problem 2<br />a. Specify the priorities for each job if the shop floor control system uses slack per remaining operations (S/RO) or critical ratio (CR).<br />b. For each priority rule, calculate the average flow time per job at the edge grinder.<br />
- 54. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Solved Problem 2<br />SOLUTION<br />a. We specify the priorities for each job using the two sequencing rules. The sequence for S/RO is shown in the brackets.<br />
- 55. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Solved Problem 2<br />The sequence of production for CR is shown in the brackets.<br />
- 56. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Solved Problem 2<br />b. We are sequencing a set of jobs at a single machine, so each job’s finish time equals the finish time of the job just prior to it in sequence plus its own processing time. Further, all jobs were available for processing at the same time, so each job’s finish time equals its flow time. Consequently, the average flow times at this single machine are<br />In this example, the average flow time per job is lower for the CR rule, which is not always the case. For example, the critical ratios for B272 and A101 are tied at 1.33. If we arbitrarily assigned A101 before B272, the average flow time would increase to (8 + 12 + 22 + 29 + 44)/5 = 23.0 hours.<br />
- 57. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Solved Problem 3<br />The Rocky Mountain Arsenal, formerly a chemical warfare manufacturing site, is said to be one of the most polluted locations in the United States. Cleanup of chemical waste storage basins will involve two operations.<br />Operation 1: Drain and dredge basin.<br />Operation 2: Incinerate materials.<br />Management estimates that each operation will require the following amounts of time (in days):<br />
- 58. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Solved Problem 3<br />Management’s objective is to minimize the makespan of the cleanup operations. All storage basins are available for processing right now. First, find a schedule that minimizes the makespan. Then calculate the average flow time of a storage basin through the two operations. What is the total elapsed time for cleaning all 10 basins? Display the schedule in a Gantt machine chart.<br />SOLUTION<br />We can use Johnson’s rule to find the schedule that minimizes the total makespan. Four jobs are tied for the shortest process time: A, D, E, and H. E and H are tied for first place, while A and D are tied for last place. We arbitrarily choose to start with basin E, the first on the list for the drain and dredge operation. The 10 steps used to arrive at a sequence are as follows:<br />
- 59. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Solved Problem 3<br />
- 60. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />Solved Problem 3<br />Several optimal solutions are available to this problem because of the ties at the start of the scheduling procedure. However, all have the same makespan. The schedule would be as follows:<br />
- 61. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />E<br />H<br />G<br />F<br />B<br />J<br />I<br />C<br />D<br />A<br />Dredge<br />E<br />H<br />G<br />F<br />B<br />J<br />I<br />C<br />D<br />A<br />Solved Problem 3<br />Incinerate<br />The makespan is 36 days. The average flow time is the sum of incineration finish times divided by 10, or 200/10 = 20 days. The Gantt machine chart for this schedule is given in Figure J.3.<br />Storage Basin<br />Figure J.3<br />
- 62. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.<br />

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