1. Operations Scheduling Supplement J Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 01

2. Operations Scheduling Operations scheduling – A type of scheduling in which jobs are assigned to workstations or employees are assigned to jobs for specified time periods. Additional performance measures Priority sequencing rules Scheduling multiple workstations Scheduling a two-station flow shop Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 02

3. The scheduling techniques cut across the various process types found in services and manufacturing – Front-office process has high customer contact, divergent work flows, customization, and a complex scheduling environment. – Back-office process has low customer involvement, uses more line work flows, and provides standardized services. Scheduling Service and Manufacturing Processes Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J -03

4. Performance Measures Flow time – The time a job spends in the service or manufacturing system Past due (tardiness) – The amount of time by which a job missed its due date Makespan – The total amount of time required to complete a group of jobs Makespan= Time of completion of last job – Starting time of first job Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 04

5. Performance Measures Total inventory – A term used to measure the effectiveness of schedules for manufacturing processes. Utilization – The degree to which equipment, space, or the workforce is currently being used – The ratio of average output rate to maximum capacity (%) Total Inventory = Scheduled receipts for all items + On-hand inventories of all items Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 05

6. Sequencing Jobs An operation with divergent flows is often called a job shop – Low-to medium-volume production – Utilizes job or batch processes – The front office would be the equivalent for a service provider. – It is difficult to schedule because of the variability in job routings and the continual introduction of new jobs to be processed. Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 06

7. Sequencing Jobs An operation with line flow is often called a flow shop – Medium- to high-volume production – Utilizes line or continuous flow processes – The back office would be the equivalent for a service provider. – Tasks are easier to schedule because the jobs have a common flow pattern through the system. Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 07

8. Shipping Department Raw Materials Legend: Batch of parts Workstation Job Shop Sequencing Copyright ©2013 Pearson Education, Inc. publishing as Prentice HallJ- 08

9. First-come, first-served (FCFS) Earliest due date (EDD) Critical ratio (CR) Priority Sequencing Rules A ratio less than 1.0 implies that the job is behind schedule. A ratio greater than 1.0 implies the job is ahead of schedule. The job with the lowest CR is scheduled next. CR = (Due date) – (Today’s date) Total shop time remaining Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 09

10. Shortest processing time (SPT) Slack per remaining operations (S/RO) Priority Sequencing Rules The job with the lowest S/RO is scheduled next S/RO = Due date Today’s date Total shop time remaining – Number of operations remaining Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 10

11. Single-dimension rules – A set of rules that bases the priority of a job on a single aspect of the job, such as arrival time at the workstation, the due date, or the processing time. Sequencing Jobs for One Workstation Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 11

12. Example J.1 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. Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 12

13. Example J.1 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? Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 13

14. Example J.1 Engine Block Business Hours Since Order Arrived Processing Time, Including Setup (hours) Business Hours Until Due Date (customer pickup time) Ranger12810 Explorer10612 Bronco11520 Econoline 1503318 Thunderbird01222 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 14

15. Engine Block Sequence Hours Since Order Arrived Begin Work Processing Time, (hr) Finish Time (hr) Flow Time (hr) Scheduled Customer Pickup Time Actual Customer Pickup Time Hours Early Hours Past Due Ranger Explorer Econoline 150 Bronco Thunderbird 120+8=82010 2— 8+6=14241213—2 Example J.1 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. 314+3=172018 1— 117+15=32332032—12 032+12=44 2244—22 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 15

16. The flow time for each job is its finish time, plus the time since the job arrived. 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. Sum of flow times is the total job hours spent by the engine blocks since their orders arrived at the workstation until they were processed. Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 16 Example J.1

17. The performance measures for the EDD schedule for the five engine blocks are: Average flow time = Average hours early = Average hours past due = 20 + 24 + 20 + 33 + 44 5 = 28.2 hours 2 + 0 + 1 + 0 + 0 5 = 0.6 hour 0 + 2 + 0 + 12 + 22 5 = 7.2 hours Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 17

18. Engine Block Sequence Hours Since Order Arrived Begin Work Processing Time, (hr) Finish Time (hr) Flow Time (hr) Scheduled Customer Pickup Time Actual Customer Pickup Time Hours Early Hours Past Due Econoline 150 Explorer Ranger Thunderbird Bronco 30+3=36191815— 103+6=91912 3— Example J.1 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. 129+8=17291017—7 0 +12=29 2229—7 1 +15=44452044—24 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 18

19. Example J.1 The performance measures are: Average flow time = Average hours early = Average hours past due = 6 + 19 + 29 + 29 + 45 5 = 25.6 hours 15 + 3 + 0 + 0 + 0 5 = 3.6 hours 0 + 0 + 7 + 7 + 24 5 = 7.6 hours Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 19

20. Example J.1 EDD rule – Performs well with respect to the percentage of jobs past due and the variance of hours past due – Is popular with firms that are sensitive to achieving due dates SPT rule – Tends to minimize the mean flow and maximize shop utilization – For single-workstations will always provide the lowest mean finish time – Could increase total inventory – Tends to produce a large variance in past due hours FCFS rule – Is considered fair – Performs poorly with respect to all performance measures Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 20

21. Application J.1 Given the following information, devise an SPT schedule for the automatic routing machine: Order Standard Time, Including Setup (hour) Due Date (hrs from now) AZ13514 DM246820 SX435106 PC088318 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 21

22. Order Sequence Begin Work Finish Time (hr) Flow Time (hr) Scheduled Customer Pickup Time Actual Pickup Time Hours Early Hours Past Due 1. 2. 3. 4. Total Average PC088 DM246 SX435 AZ135 03318 15 311 20 9 1121 6 15 2135 143521 70942436 17.523.569 Application J.1 Copyright ©2013 Pearson Education, Inc. publishing as Prentice HallJ- 22

23. Sequencing Jobs for One Workstation Multiple-dimension rules – A set of rules that apply to more than one aspect of a job. Choosing a rule – 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. – CR results in longer job flow times than SPT, but CR also results in less variance in the distribution of past due hours. – No choice is clearly best; each rule should be tested in the environment for which it is intended. Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 23

24. 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. Job Processing Time at Engine Lathe (hours) Time Remaining Until Due Date (days) Number of Operations Remaining Shop Time Remaining (days)CRS/RO 12.315106.12.460.89 210.51027.81.281.10 36.2201214.51.380.46 415.68510.20.78–0.44 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 24 Example J.2

25. 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. CR = Time remaining until the due date Shop time remaining = = 2.46 15 6.1 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. Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 25 Job 1 Example J.2

26. 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. S/RO = Time remaining until the due date Shop time remaining – Number of operations remaining = = 0.89 15 – 6.1 10 Arranging the jobs by starting with the lowest S/RO yields a 4, 3, 1, 2 sequence of jobs. Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 26 Job 1 Example J.2

27. Priority Rule Summary FCFSSPTEDDCRS/RO Average flow time17.17516.10026.17527.15024.025 Average early time3.4256.050000 Average past due7.3508.90012.92513.90010.775 Copyright ©2013 Pearson Education, Inc. publishing as Prentice HallJ- 27 Example J.2

28. Application J.2 The following four jobs have just arrived at an idle drill process and must be scheduled. Job Processing Time at Drill Press (wk) Time Remaining to Due Date (wks) Number of Operations Remaining* Shop Time Remaining* (wks) AA4534 BB81146 CC1316109 DD618312 EE2753 * including drill press Create the sequences for two schedules, one using the Critical Ratio rule and one using the S/RO rule. Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 28

29. Critical RatioSlack/Remaining Operation JobPriority Index Sequence on Drill Press JobPriority Index Sequence on Drill Press Application J.2 AA BB CC DD EE 1.25 1.83 1.77 1.50 2.33 First Fourth Third Second Fifth AA BB CC DD EE 0.33 1.25 0.70 2.00 0.80 First Fourth Second Fifth Third Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 29

30. 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. Computer simulation models are effective tools to determine which priority rules work best in a given situation. Scheduling Jobs for Multiple Workstations Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 30

31. In the scheduling of two or more workstations in a flow shop, the makespan varies according to the sequence chosen. Determining a production sequence for a group of jobs to minimize the makespan has two advantages: – The group of jobs is completed in minimum time. – The utilization of the two-station flow shop is maximized. Scheduling Jobs for a Two-Station Flow Shop Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 31

32. Johnson’s Rule Minimizes makespan when scheduling a group of jobs on two workstations 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. 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. 3.Eliminate the last job scheduled from further consideration. Repeat steps 1 and 2 until all jobs have been scheduled. Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 32

33. Example J.3 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: Workstation 1:Dismantle the motor and clean the parts. Workstation 2:Replace the parts as necessary, test the motor, and make adjustments. Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 33

34. Example J.3 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: Time (hr) MotorWorkstation 1Workstation 2 M11222 M245 M363 M41516 M5108 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 34

35. Example J.3 Establishing a Job Sequence Iterati on Job SequenceComments 1 M3 The shortest processing time is 3 hours for M3 at workstation 2. Therefore, M3 is scheduled as late as possible. 2 M2M3 Eliminate M3 from the table of estimated times. The next shortest processing time is 4 hours for M2 at workstation 1. M2 is therefore scheduled first. 3 M2M5M3 Eliminate M2 from the table. The next shortest processing time is 8 hours for M5 at workstation 2. Therefore, M5 is scheduled as late as possible. 4 M2M1M5M3 Eliminate M5 from the table. The next shortest processing time is 12 hours for M1 at workstation 1. M1 is scheduled as early as possible. 5 M2M1M4M5M3 The last motor to be scheduled is M4. It is placed in the last remaining position, in the middle of the schedule. Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 35

36. Example J.3 M2 (4) M1 (12) M4 (15) M5 (10) M3 (5) Idle—available for further work Idle M2 (5) M1 (22) M4 (16) M5 (8) Idle (3) M3 Workstation 051015202530 Hour 35404550556065 1 2 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 36

37. Application J.3 Use the following data to schedule two workstations arranged as a flow shop using Johnson’s Rule: Time (hr) JobWorkstation 1Workstation 2 A43 B1020 C215 D87 E1413 Sequence:CBEDA Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 37

38. Application J.3 Workstation 1Workstation 2 StartFinishStartFinish C B E D A 02 212 26 34 38 217 37 50 57 60 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 38

39. Labor-Limited Environment – An environment in which the resource constraint is the amount of labor available, not the number of machines or workstations Some possible labor assignment rules: – Assign personnel to the workstation with the job that has been in the system longest. – Assign personnel to the workstation with the most jobs waiting for processing. – Assign personnel to the workstation with the largest standard work content. – Assign personnel to the workstation with the job that has the earliest due date. Labor-Limited Environment Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 39

40. 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. Customers usually do not pick up their engines early. Solved Problem 1 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 40

41. Solved Problem 1 Using the table below: a.Develop separate schedules by using the SPT and EDD rules. 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. Engine Time Since Order Arrived (days) Processing Time, Including Setup (days) Promise Date (days from now) 50-hp Evinrude458 7-hp Johnson6415 100-hp Mercury81012 50-hp Honda1120 75-hp Nautique15310 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 41

42. Solved Problem 1 a.Using the SPT rule, we obtain the following schedule: Repair Sequence Days Since Order Arrived Processing Time Finish Time Flow Time Promise Date Actual Pickup Date Days Early Days Past Due 50-hp Honda111220 19— 75-hp Nautique 15341910 6— 7-hp Johnson6481415 7— 50-hp Evinrude451317813—5 100-hp Mercury 81023311223—11 Total83 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 42

43. Solved Problem 1 Using the EDD rule we obtain this schedule: Repair Sequence Days Since Order Arrived Processing Time Finish Time Flow Time Promise Date Actual Pickup Date Days Early Days Past Due 50-hp Evinrude4559883— 75-hp Nautique 15382310 2— 100-hp Mercury 81018261218—6 7-hp Johnson6422281522—7 50-hp Honda1123242023—3 Total110 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 43

44. Solved Problem 1 b.Performance measures are as follows: 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. Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 44

45. Solved Problem 2 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. Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 45

46. Solved Problem 2 Using the Table below: a.Specify the priorities for each job if the shop floor control system uses slack per remaining operations (S/RO) or critical ratio (CR). b.For each priority rule, calculate the average flow time per job at the edge grinder. Current Order Processing Time (hr) Due Date (day) Remaining Operations Shop Time Remaining (days) A10110162109 B272715896 C1061515211 D7074170818 E555815458 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 46

47. Solved Problem 2 a.We specify the priorities for each job using the two sequencing rules. The sequence for S/RO is shown in the brackets. Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 47

48. Solved Problem 2 The sequence of production for CR is shown in the brackets. Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 48

49. Solved Problem 2 b.The average flow times at this single machine are: In this example, the average flow time per job is lower for the CR rule, which is not always the case. If we arbitrarily assigned A101 before B272, the average flow time would increase to (8 + 12 + 22 + 29 + 44)/5 = 23.0 hours. Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 49

50. Solved Problem 3 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. Operation 1: Drain and dredge basin. Operation 2: Incinerate materials. Management estimates that each operation will require the following amounts of time (in days): Storage Basin ABCDEFGHIJ Dredge3436132184 Incinerate1421264128 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 50

51. Solved Problem 3 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. Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 51

52. Solved Problem 3 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: Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 52

53. Solved Problem 3 2.Select basin H next; put it toward the front. EH———————— 3.Select basin A next (tied with basin D); put it at the end. EH———————A 4.Put basin D toward the end.EH——————DA 5.Put basin G toward the front.EHG—————DA 7.Put basin I toward the end.EHG———ICDA 8.Put basin F toward the front. EHGF——ICDA 9.Put basin B toward the front. EHGFB—ICDA 10.Put basin J in the remaining space. EHGFBJICDA 1.Select basin E first (tied with basin H); put it at the front. E————————— 6.Put basin C toward the end.EHG————CDA Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 53

54. Solved Problem 3 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. Operation 1Operation 2 BasinStartFinishStartFinish E0113 H1234 G2448 F47814 B7111418 J11151826 I15232628 C23262830 D2632 33 A3235 36 Total200 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 54

55. EHGFBJICDA EHGFBJICDA Solved Problem 3 The makespan is 36 days. The average flow time is the sum of incineration finish times divided by 10, or 200/10 = 20 days. Dredge Incinerate Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall J - 55

56. Copyright ©2013 Pearson Education, Inc. publishing as Prentice HallJ - 56 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.