Post on 20-Dec-2015
transcript
Scheduling DecisionsOrganization Managers Must Schedule the Following
Arnold Palmer Hospital
Operating room usePatient admissionsNursing, security, maintenance staffsOutpatient treatments
University of Missouri Classrooms and audiovisual equipmentStudent and instructor schedulesGraduate and undergraduate courses
Lockheed Martin factory
Production of goodsPurchases of materialsWorkers
Hard Rock Cafe Chef, waiters, bartendersDelivery of fresh foodsEntertainersOpening of dining areas
Delta Air Lines Maintenance of aircraftDeparture timetablesFlight crews, catering, gate, ticketing personnel
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
Gantt Chart Example
Day Monday Tuesday Wednesday Thursday FridayWork Center
Metalworks
Mechanical
Electronics
Painting
Job 349
Job 349
Job 349
Job 408
Job 408
Job 408
ProcessingProcessing UnscheduledUnscheduled Center not availableCenter not available
Job 350
Job 349
Job 295
Scheduling Criteria Makespan
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
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
An Example (Single Machine)
JobProcessing
time in daysJob Due Date
(day)
A 6 8
B 2 6
C 8 18
D 3 15
E 9 23
An Example (continued)
Rule MakespanTotal
Flow TimeUtilization
Total Lateness
FCFS 28 77 36.4% 11
SPT 28 65 43.1% 9
EDD 28 68 41.2% 6
LPT 28 103 27.2% 48
CR 28 77 36.4% 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
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
An Example (continued)TimeTime 00 33 1010 2020 2828 3333
TimeTime 0 0 11 33 55 77 99 1010 1111 1212 1313 1717 1919 21 22 2321 22 232525 2727 2929 3131 33333535
B ACDE
B ACDE
WC 1
WC 2
BB EE DD CC AA
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.
An Example
JobWork
Center 1Work
Center 2Work
Center 3Work
Center 4
A 1 13 6 2
B 10 12 18 18
C 17 9 13 4
D 12 17 2 6
E 11 3 5 16
Job Shop (6 job 4 machine example)
Job 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)
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)
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.
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