5. Operations Scheduling

Scheduling Flow

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) 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

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

Job Work Center 1(Drill Press)

Work Center 2(Lathe)

A 5 2

B 3 6

C 8 4

D 10 9

E 7 12

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

WC1 WC2 WC3 WC4A 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

An ExampleM T W T F S S

Employee 1 5 5 6 5 4 3 3