1. Scheduling Chapter 16

2. How Scheduling fits the Operations Management Philosophy Operations As a Competitive Weapon Operations Strategy Project Management Process Strategy Process Analysis Process Performance and Quality Constraint Management Process Layout Lean Systems Supply Chain Strategy Location Inventory Management Forecasting Sales and Operations Planning Resource Planning Scheduling

6. Gantt Progress Chart Gantt Progress Chart for an Auto Parts Company Plymouth Ford Pontiac Job 4/20 4/22 4/23 4/24 4/25 4/26 4/21 4/17 4/18 4/19 Current date Scheduled activity time Actual progress Start activity Finish activity Nonproductive time

7. Gantt Workstation Chart Gantt Workstation Chart for Hospital Operating Rooms

10. The Amalgamated Parcel Service is open 7 days a week. The schedule of requirements is: The manager needs a workforce schedule that provides two consecutive days off and minimizes the amount of total slack capacity. To break ties in the selection of off days, the scheduler gives preference to Saturday and Sunday if it is one of the tied pairs. If not, she selects one of the tied pairs arbitrarily. Workforce Scheduling Example 16.1 Day M T W Th F S Su Number of employees 6 4 8 9 10 3 2 Required employees

11. Required employees Workforce Scheduling Example 16.1 Steps 1 & 2 Step 1 . Find all the pairs of consecutive days that exclude the maximum daily requirements. Select the unique pair that has the lowest total requirements for the 2 days. Friday contains the maximum requirements (10), and the pair S–Su has the lowest total requirements. Therefore, Employee 1 is scheduled to work Monday through Friday. Step 2 . If a tie occurs, choose one of the tied pairs or ask the employee to make a choice. Day M T W Th F S Su Number of employees 6 4 8 9 10* 3 2 Employee 1 X X X X X

12. Required employees Step 3 . Subtract the requirements satisfied by the Employee 1 from the net requirements for each day the employee is to work and repeat step one. Again the pair S–Su has the lowest total requirements. Therefore, Employee 2 is scheduled to work Monday through Friday. Workforce Scheduling Example 16.1 Step 3 Day M T W Th F S Su Number of employees 6 4 8 9 10* 3 2 Employee 1 X X X X X Requirements 5 3 7 8 9* 3 2 Employee 2 X X X X X

13. Required employees Workforce Scheduling Example 16.1 Step 4 Step 4 . Repeat steps 1 through 3 until all the requirements have been satisfied. After Employees 1, 2, and 3 have reduced the requirements, the pair with the lowest requirements changes, and Employee 4 will be scheduled for Wednesday through Sunday. Day M T W Th F S Su Number of employees 6 4 8 9 10* 3 2 Employee 1 X X X X X Requirement 5 3 7 8 9* 3 2 Employee 2 X X X X X Requirement 4 2 6 7 8* 3 2 Employee 3 X X X X X Requirement 3 1 5 6 7* 3 2

14. Workforce Scheduling Example 16.1 Step 4 continued Day M T W Th F S Su Number of employees 6 4 8 9 10* 3 2 Employee 1 X X X X X Requirement 5 3 7 8 9* 3 2 Employee 2 X X X X X Requirement 4 2 6 7 8* 3 2 Employee 3 X X X X X Requirement 3 1 5 6 7* 3 2 Employee 4 X X X X X Requirement 3 1 4 5 6* 2 1 Employee 5 X X X X X Required employees

15. Workforce Scheduling Example 16.1 Step 4 continued Day M T W Th F S Su Requirement 2 0 3 4 5* 2 1 Employee 6 X X X X X Requirement 2 0 2 3 4* 1 0 Employee 7 X X X X X Requirement 1 0 1 2 3* 1 0 Employee 8 X X X X X Requirement 0 0 0 1 2* 1 0 Employee 9 X X X X X Requirement 0 0 0 0 1* 0 0 Employee 10 X X X X X Required employees

16. Workforce Scheduling Example 16.1 Day M T W Th F S Su Employee 1 X X X X X off off Employee 2 X X X X X off off Employee 3 X X X X X off off Employee 4 off off X X X X X Employee 5 X X X X X off off Employee 6 off off X X X X X Employee 7 X X X X X off off Employee 8 X X X X X off off Employee 9 off X X X X X off Employee 10 X X X X X off off Final Schedule

17. M T W Th F S Su Employee 1 X X X X X off off Employee 2 X X X X X off off Employee 3 X X X X X off off Employee 4 off off X X X X X Employee 5 X X X X X off off Employee 6 off off X X X X X Employee 7 X X X X X off off Employee 8 X X X X X off off Employee 9 off X X X X X off Employee 10 X X X X X off off Workforce Scheduling Example 16.1 Final Schedule Capacity, C 7 8 10 10 10 3 2 50 Requirements, R 6 4 8 9 10 3 2 42 Slack, C – R 1 4 2 1 0 0 0 8 Total Final Schedule

19. Manufacturing Process Shipping Department Raw Materials Legend: Batch of parts Workstation

25. Average hours early = 0.6 hour Example 16.2 Single-Dimension Rule – EDD Average job flow time = 23 hours Average hours past due = 7.2 hours Average WIP = 2.61 blocks Average total inventory = 2.68 engine blocks 8 + 14 + 17 + 32 + 44 44 Job Scheduled Actual Engine Processing Flow Customer Customer Hours Block Begin Time Time Pickup Pickup Hours Past Sequence Work (hr) (hr) Time Time Early Due Ranger 8 10 Explorer 6 12 Econoline 150 3 18 Bronco 15 20 Thunderbird 12 22 0 + = 8 10 2 17 + = 32 32 12 8 + = 14 14 2 14 + = 17 18 1 32 + = 44 44 22 Average total inventory = 10 + 14 + 18 + 32 + 44 44

26. Average hours early = 3.6 hour Example 16.2 Single-Dimension Rule – SPT Average job flow time = 20.4 hours Average hours past due = 7.6 hours Average WIP = 2.32 blocks Average total inventory = 2.73 engine blocks Econoline 150 Explorer Ranger Thunderbird Bronco 0 3 9 17 29 3 6 8 12 15 18 12 10 22 20 3 + 9 + 17 + 29 + 44 44 Job Scheduled Actual Engine Processing Flow Customer Customer Hours Block Begin Time Time Pickup Pickup Hours Past Sequence Work (hr) (hr) Time Time Early Due Ranger 8 10 Explorer 6 12 Econoline 150 3 18 Bronco 15 20 Thunderbird 12 22 0 + = 3 18 15 17 + = 29 29 7 8 + = 9 12 14 + = 17 17 3 7 29 + = 44 44 24 Average total inventory = 18 + 12 + 17 + 20 + 44 44

28. Example 16.3 Multiple-Dimension Rule – CR 1 2.3 15 10 6.1 2.46 2 10.5 10 2 7.8 1.28 3 6.2 20 12 14.5 1.38 4 15.6 8 5 10.2 .78 Operation Time Time at Remaining Number of Engine to Due Date Operations Shop Time Job Lathe (hr) (Days) Remaining Remaining CR S/RO CR = Time remaining to due date Shop time remaining

29. Example 16.3 Multiple-Dimension Rule – S/RO 1 2.3 15 10 6.1 2.46 0.89 2 10.5 10 2 7.8 1.28 1.10 3 6.2 20 12 14.5 1.38 0.46 4 15.6 8 5 10.2 .78 – 0.44 Operation Time Time at Remaining Number of Engine to Due Date Operations Shop Time Job Lathe (hr) (Days) Remaining Remaining CR S/RO S/RO = Time remaining to due date – Shop time remaining Number of operations remaining

30. Comparing the CR and S/RO Rules 1 2.3 15 10 6.1 2.46 0.89 2 10.5 10 2 7.8 1.28 1.10 3 6.2 20 12 14.5 1.38 0.46 4 15.6 8 5 10.2 .78 – 0.44 Operation Time Time at Remaining Number of Engine to Due Date Operations Shop Time Job Lathe (hr) (Days) Remaining Remaining CR S/RO CR Sequence = 4 – 2 – 3 – 1 S/RO Sequence = 4 – 3 – 1 – 2 CR Sequence =

34. Example 16.5 Johnson’s Rule at the Morris Machine Co. Sequence = M1 M2 M3 M4 M5 Eliminate M3 from consideration. The next shortest time is M2 at Workstation 1, so schedule M2 first. Eliminate M5 from consideration. The next shortest time is M1 at workstation #1, so schedule M1 next. Eliminate M1 and the only job remaining to be scheduled is M4. Time (hr) Motor Workstation 1 Workstation 2 M1 12 22 M2 4 5 M3 5 3 M4 15 16 M5 10 8 Shortest time is 3 hours at workstation 2, so schedule job M3 last. Eliminate M2 from consideration. The next shortest time is M5 at workstation #2, so schedule M5 next to last.

35. The schedule minimizes the idle time of workstation 2 and gives the fastest repair time for all five motors. No other sequence will produce a lower makespan. Example 16.5 Johnson’s Rule at the Morris Machine Co. Workstation M2 (4) M1 (12) M4 (15) M5 (10) M3 (5) Idle—available for further work 0 5 10 15 20 25 30 Day 35 40 45 50 55 60 65 Idle 2 M2 (5) M1 (22) M4 (16) M5 (8) M3 (3) Idle 1 Gantt Chart for the Morris Machine Company Repair Schedule