1. 5. Operations Scheduling

2. Scheduling Flow

3. Managers Must Schedule the Following
Scheduling Decisions
Organization
Managers Must Schedule the Following
Arnold Palmer Hospital
Operating room use
Patient admissions
Nursing, security, maintenance staffs
Outpatient treatments
University of Missouri
Classrooms and audiovisual equipment
Student and instructor schedules
Graduate and undergraduate courses
Lockheed Martin factory
Production of goods
Purchases of materials
Workers
Hard Rock Cafe
Chef, waiters, bartenders
Delivery of fresh foods
Entertainers
Opening of dining areas
Delta Air Lines
Maintenance of aircraft
Departure timetables
Flight crews, catering, gate, ticketing personnel

4. Operations Scheduling
Specify time-phased activities and control job-order progress
Jobs are activities to be done and machines (work centers) process jobs
Single machine problem
Parallel machine problem
Flow shop problem
Job shop problem

5. Gantt Chart Example Day Monday Tuesday Wednesday Thursday Friday
Work Center
Metalworks
Mechanical
Electronics
Painting
Job 349
Job 408
Processing
Unscheduled
Center not available
Job 350
Job 295

6. Scheduling Criteria Makespan Total (average) flow time Utilization
Time required to complete a production schedule, or time required to manufacture all jobs
Total (average) flow time
Total (average) amount of time jobs spend in the system
Utilization
Total processing time / Total flow time
Total (average) lateness
Total (average) amount of time jobs are completed beyond its promised delivery date

7. Scheduling Rules FCFS (First come, first served)
The first job arriving is processed first
SPT (Shortest processing time)
The job with the SPT is processed first
EDD (Earliest due date)
The job with the EDD is processed first
LPT (Longest processing time)
The job with the LPT is processed first
CR (Critical ratio) – can be dynamic
Jobs are scheduled in order of increasing ratio of time remaining to required work time remaining

8. An Example (Single Machine)
Job
Processing time in days
Job Due Date (day) A 6 8 B 2 C 18 D 3 15 E 9 23

9. An Example (continued)
FCFS: A-B-C-D-E
SPT: B-D-A-C-E
EDD: B-A-D-C-E
LPT: E-C-A-D-B
CR: A-B-C-D-E

10. An Example (continued)
Rule
Makespan
Total
Flow Time
Utilization
Total Lateness
FCFS 28 77
36.4% 11
SPT 65
43.1% 9
EDD 68
41.2% 6
LPT
103
27.2% 48 CR

11. Comparison of Scheduling Rules
No one scheduling rule excels on all criteria
SPT minimizes flow time, but moves long jobs to the end, which may result in dissatisfied customers
FCFS does not do especially well (or poorly) on any criteria but is perceived as fair by customers
EDD often minimizes lateness related criteria

12. Two Machine Flow Shop Johnson’s algorithm minimizes makespan
List all jobs and times for each work center
Choose the job with the shortest activity time. If that time is in the first work center, schedule the job first. If it is in the second work center, schedule the job last
Once a job is scheduled, it is eliminated from the list
Repeat above steps working toward the center of the sequence

13. An Example Job Work Center 1 (Drill Press) Work Center 2 (Lathe) A 5 23 6 C 8 4 D 10 9 E 7 12

14. An Example (continued)
Time
Time B A C D E
WC 1
WC 2

15. More Than Two Machine Flow Shop
Each job is processed by each machine (work center) exactly once
Very difficult to solve; a heuristic approach is necessary
Reduce multiple machines to two machines and apply Johnson’s algorithm
Solve m-1 sub-problems for an m machine shop by increasing number of ‘real’ machines for the 1st ‘artificial’ machine and decreasing it for the 2nd one.

16. An Example Job Work Center 1 Work Center 2 Work Center 3 Work Center 413 6 2 B 10 12 18 C 17 9 4 D E 11 3 5 16

17. WC1
WC2
WC3
WC4 A 1 13 6 2 B 10 12 18 C 17 9 4 D E 11 3 5 16

18. Job Shop (6 job 4 machine example)
Machine # (processing time) A
1(6) > 2(8) > 3(12) > 4(5) B
1(4) > 2(1) > 3(4) > 4(3) C
4(3) > 2(8) > 1(6) > 3(4) D
2(5) > 1(10) > 3(15) > 4(4) E
1(3) > 2(4) > 4(6) > 3(4) F
3(4) > 1(2) > 2(4) >4(5)

19. Machine # (time) A 1(6) > 2(8) > 3(12) > 4(5) B
1(4) > 2(1) > 3(4) > 4(3) C
4(3) > 2(8) > 1(6) > 3(4) D
2(5) > 1(10) > 3(15) > 4(4) E
1(3) > 2(4) > 4(6) > 3(4) F
3(4) > 1(2) > 2(4) >4(5)

20. Limitations of Rule-Based Dispatching
Rules do not look upstream or downstream; idle resources and bottleneck resources in other departments may not be recognized
Rules do not look beyond due dates
Scheduling is dynamic and rules need to be revised to adjust to changes in process, equipment, product mix, etc.

21. Scheduling Service Employees With Cyclical Scheduling
Objective is to meet staffing requirements with the minimum number of workers
Schedules need to be smooth and keep personnel happy
Many techniques exist from simple algorithms to complex linear programming solutions
Cyclical scheduling -- Identify two consecutive days with the lowest total requirements and assign these as days off

22. An Example M T W F S
Employee 1 5 6 4 3