1. Chapter 16 Scheduling McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

2. Chapter 16: Learning Objectives Instructor Slides  You should be able to: 1. Explain what scheduling involves and the importance of good scheduling 2. Describe scheduling needs in high-volume and intermediate-volume systems 3. Describe scheduling needs in job shops 4. Use and interpret Gantt charts, and use the assignment method for loading 5. Give examples of commonly used priority rules 6. Summarize some of the unique problems encountered in service systems, and describe some of the approaches used for scheduling service systems 16-2

3. Scheduling  Scheduling:  Establishing the timing of the use of equipment, facilities and human activities in an organization  Effective scheduling can yield  Cost savings  Increases in productivity  Other benefits Instructor Slides 16-3

4. Scheduling Context Instructor Slides  Scheduling is constrained by multiple system design decisions  System capacity  Product and/or service design  Equipment selection  Worker selection and training  Aggregate planning and master scheduling 16-4

5. High Volume Systems Instructor Slides  Flow System  High-volume system in which all jobs follow the same sequence  Flow system scheduling  Scheduling for flow systems  The goal is to achieve a smooth rate of flow of goods or customers through the system in order to get high utilization of labor and equipment Workstation 1 Workstation 2 Output 16-5

6. High-Volume: Scheduling Difficulties Instructor Slides  Few flow systems are entirely dedicated to a single product or service  Each product change requires  Slightly different inputs of parts  Slightly different materials  Slightly different processing requirements that must be scheduled into the line  Need to avoid excessive inventory buildup  Disruptions may result in less-than-desired output 16-6

7. High-Volume Success Factors Instructor Slides  The following factors often dictate the success of high-volume systems: Process and product design Preventive maintenance Rapid repair when breakdowns occur Optimal product mixes Minimization of quality problems Reliability and timing of supplies 16-7

8. Intermediate-Volume Systems Instructor Slides Outputs fall between the standardized type of output of high-volume systems and the make-to-order output of job shops Output rates are insufficient to warrant continuous production Rather, it is more economical to produce intermittently Work centers periodically shift from one product to another 16-8

9. Intermediate-Volume Systems  Three basic issues:  Run size of jobs  The timing of jobs  The sequence in which jobs will be produced Instructor Slides 16-9 Q QpQp I max Production and usage Production and usage Production and usage Usage only Usage only Cumulative production Amount on hand Time

10. Intermediate-Volume Systems Instructor Slides  Important considerations  Setup cost  Usage is not always as smooth as assumed in the economic lot size model  Alternative scheduling approach  Base production on a master schedule developed from customer orders and forecasted demand 16-10

11. Low-Volume Systems Instructor Slides Job shop scheduling (Loading and Sequencing) Scheduling for low-volume systems with many variations in requirements Make-to-order products Processing requirements Material requirements Processing time Processing sequence and steps A complex scheduling environment It is impossible to establish firm schedules until actual job orders are received 16-11

12. Low-Volume Systems: Loading Instructor Slides  Loading  the assignment of jobs to processing centers  Gantt chart  Used as a visual aid for loading and scheduling purposes  Purpose of the Gantt chart is to organize and visually display the actual or intended use of resources in a time framework  Managers may use the charts for trial-and-error schedule development to get an idea of what different arrangements would involve 16-12

13. Gantt Charts  Load chart  A Gantt chart that shows the loading and idle times for a group of machines or list of departments Instructor Slides 16-13

14. Loading Approaches  Infinite loading  Jobs are assigned to workstations without regard to the capacity of the work center  Finite loading  Jobs are assigned to work centers taking into account the work center capacity and job processing times Instructor Slides 1 2 3 45 6 over Capacity Infinite loading 1 2 3 4 5 6 Capacity Finite loading 16-14

15. Scheduling Approaches Instructor Slides  Forward scheduling  Scheduling ahead from some point in time.  Used when the question is:  “How long will it take to complete this job?  Backward scheduling  Scheduling backwards from some due date  Used when the question is:  “When is the latest this job can be started and still be completed on time?” 16-15

16. Gantt Charts  Schedule chart  A Gantt chart that shows the orders or jobs in progress and whether they are on schedule Instructor Slides 16-16

17. Assignment Instructor Slides  Assignment model  A linear programming model for optimal assignment of tasks and resources  Hungarian method  Method of assigning jobs by a one-for-one matching to identify the lowest cost solution 16-17

18. Hungarian Method Instructor Slides 1. Row reduction: subtract the smallest number in each row from every number in the row a. Enter the result in a new table 2. Column reduction: subtract the smallest number in each column from every number in the column a. Enter the result in a new table 3. Test whether an optimum assignment can be made a. Determine the minimum number of lines needed to cross out all zeros b. If the number of lines equals the number of rows, an optimum assignment is possible. Go to step 6 c. Else, go to step 4 16-18

19. Hungarian Method (contd.) Instructor Slides 4. If the number of lines is less than the number of rows, modify the table: a. Subtract the smallest number from every uncovered number in the table b. Add the smallest uncovered number to the numbers at intersections of cross-out lines c. Numbers crossed out but not at intersections of cross-out lines carry over unchanged to the next table 5. Repeat steps 3 and 4 until an optimal table is obtained 6. Make the assignments a. Begin with rows or columns with only one zero b. Match items that have zeros, using only one match for each row and each column c. Eliminate both the row and the column after the match 16-19

20. Example CostWorkerRow minimum ABCD 186242 Job26711106 335763 45 1295 Instructor Slides 20 1. Row reduction: subtract the smallest number in each row from every number in the row

21. Example CostWorkerRow minimum ABCD 164022 Job201556 302433 405745 Instructor Slides 21 1. Row reduction: subtract the smallest number in each row from every number in the row

22. Example CostWorkerRow minimum ABCD 164022 Job 201556 302433 405745 Column Minimu m 0102 Instructor Slides 22 2. Column reduction: subtract the smallest number in each column from every number in the column

23. Example CostWorkerRow minimum ABCD 163002 Job 200536 301413 404725 Column Minimu m 0102 Instructor Slides 23 2. Column reduction: subtract the smallest number in each column from every number in the column

24. Example CostWorker ABCD 16300 Job 20053 30141 40472 Instructor Slides 24 3. Determine the minimum number of lines needed to cross out all zeros Because # of lines =3 < 4, optimal solution has not been found.

25. Example CostWorker ABCD 17300 Job 21053 30030 40361 Instructor Slides 25 a.Subtract the smallest number from every uncovered number in the table b.Add the smallest uncovered number to the numbers at intersections of cross-out lines

26. Example CostWorker ABCD 17300 Job 21053 30030 40361 Instructor Slides 26 Determine the minimum number of lines needed to cross out all zeros a.Now, no matter how you draw, a minimum of 4 lines is needed. So optimal solution can be found from the table.

27. Example CostWorker ABCD 17300 Job 21053 30030 40361 Instructor Slides 27 Pick out zeros so that each line and column has one and only one zero. The corresponding assignment is optimal: 1-C 2-B 3-D 4-A

28. Low-Volume Systems: Sequencing Instructor Slides  Sequencing  Determine the order in which jobs at a work center will be processed  Priority rules  Simple heuristics used to select the order in which jobs will be processed  The rules generally assume that job setup cost and time are independent of processing sequence  Job time  Time needed for setup and processing of a job 16-28

29. Priority Rules  FCFS - first come, first served: Jobs are processed in the order in which they arrive at a machine or work center.  SPT- shortest processing time: Jobs are processed according to processing time at a machine or work center, shortest job first.  EDD - earliest due date: Jobs are processed according to due date, earliest due date first.  CR - critical ratio: Jobs are processed according to smallest ratio of time remaining until due date to processing time remaining.  S/O* - slack per operation: Jobs are processed according to average slack time (time until due date minus remaining time to process). Compute by dividing slack time by number of remaining operations, including the current one.  Rush* - emergency or preferred customers first. Instructor Slides 16-29

30. Priority Rules: Assumptions Instructor Slides The set of jobs is known; no new orders arrive after processing begins and no jobs are canceled Setup time is independent of processing time Setup time is deterministic Processing times are deterministic There will be no interruptions in processing such as machine breakdowns or accidents 16-30

31. Priority Rules: Local v. Global  Local priority rules: FCFS, SPT, EDD  Focus on information pertaining to a single workstation when establishing a job sequence  Global priority rules: CR, S/O  Incorporate information from multiple workstations when establishing a job sequence Instructor Slides 16-31

32. Sequence: Performance Metrics Instructor Slides Common performance metrics: Job flow time This is the amount of time it takes from when a job arrives until it is complete It includes not only processing time but also any time waiting to be processed Job lateness This is the amount of time the job completion time is expected to exceed the date the job was due or promised to a customer Tardiness = max {0, lateness}, 0 if lateness<0 Makespan The total time needed to complete a group of jobs from the beginning of the first job to the completion of the last job Average number of jobs Jobs that are in a shop are considered to be WIP inventory 16-32

33. Example JobProcessing Time (days)Due Date (days from present time) A27 B816 C44 D1017 E515 F1218 Instructor Slides 33 *Jobs arrived in the order shown (A,B,C,D,E,F)

34. Example Sequenc e Processing Time (days) Due Date Flow TimeTardines s # of remaining jobs A27 B816 C44 D1017 E515 F1218 Average?? Instructor Slides 34

35. Example Sequenc e Processing Time (days) Due Date Flow TimeTardines s # of remaining jobs A27206 B8161005 C4414104 D 172473 E51529142 F121841231 Total4112054 Average2092.93 Instructor Slides 35

36. Example  Makespan =2+8+4+10+5+12=41 (days)  Average Flow Time= (2+10+14+24+29+41)/6 =20 (days)  Average Tardiness= (0+0+10+7+14+23)/6 = 9 (days)  Average # of remaining jobs= Total Flow Time/ Total Processing Time (e.g. 120/41 2.93) Instructor Slides 36 FCFS is simple to use. SPT minimizes average flow time. EDD minimizes average tardiness. CR is quite well in terms of minimizing average tardiness

37. Example: CR JobProcessing Time Due DateCritical Ratio A27(7-0)/2=3.5 B816(16-0)/8=2 C44(4-0)/4=1 D1017(17-0)/10=1.7 E515(15-0)/5=3 F1218(18-0)/12=1.5 Instructor Slides 37 Order: C

38. Example: CR JobProcessing TimeDue DateCritical Ratio A27(7-4)/2=1.5 B816(16-4)/8=1.5 D1017(17-4)/10=1.3 E515(15-4)/5=2.2 F1218(18-4)/12=1.17 Instructor Slides 38 Order: C->F

39. Example: CR JobProcessing TimeDue DateCritical Ratio A27(7-16)/2=-4.5 B816(16-16)/8=0.0 D1017(17-16)/10=0.1 E515(15-16)/5=-0.2 Instructor Slides 39 Order: C->F->A

40. Example: CR JobProcessing Time Due DateCritical Ratio B816(16-18)/8=-0.25 D1017(17-18)/10=-0.1 E515(15-18)/5=-0.6 Instructor Slides 40 Order: C->F->A->E

41. Example: CR JobProcessing Time Due DateCritical Ratio B816(16-23)/8=-0.875 D1017(17-23)/10=-0.60 Instructor Slides 41 Order: C->F->A->E->B->D

42. Scheduling Difficulties Instructor Slides  Variability in  Setup times  Processing times  Interruptions  Changes in the set of jobs  Except for small job sets, there is no method for identifying an optimal schedule  Scheduling is not an exact science (heuristics)  It is an ongoing task for a manager 16-42

43. Minimizing Scheduling Difficulties  Set realistic due dates  Focus on bottleneck operations  First, try to increase the capacity of the operations  If that is not possible  Schedule bottleneck operations first  Then, schedule non-bottleneck operations around the bottleneck operations  Consider lot splitting of large jobs (smaller lot size)  Often works best when there are large differences in job times Instructor Slides 16-43

44. Service Operation Problems Instructor Slides Service scheduling often presents challenges not found in manufacturing These are primarily related to: 1. The inability to store or inventory services 2. The random nature of service requests Service scheduling may involve scheduling: 1. Customers 2. Workforce 3. Equipment 16-44

45. Scheduling Service Operations* Instructor Slides  Scheduling customers: Demand Management  Appointment systems  Controls customer arrivals for service  Reservation systems  Enable service systems to formulate a fairly accurate estimate demand on the system for a given time period  Scheduling the workforce: Capacity Management  Cyclical Scheduling  Employees are assigned to work shifts or time slots, and have days off, on a repeating basis 16-45

46. Operations Strategy* Instructor Slides  If scheduling is done well:  Goods and services can be made or delivered in a timely manner  Resources can be used to best advantage  Customers will be satisfied  It is important to not overlook the importance of scheduling to strategy and competitive advantage 16-46