5. Operations Scheduling

Scheduling Flow

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

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 Friday Work Center Metalworks Mechanical Electronics Painting Job 349 Job 408 Processing Unscheduled Center not available Job 350 Job 295

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

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) Job Processing time in days Job Due Date (day) A 6 8 B 2 C 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 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

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 3 6 C 8 4 D 10 9 E 7 12

An Example (continued) Time 0 3 10 20 28 33 Time 0 1 3 5 7 9 10 11 12 13 17 19 21 22 23 25 27 29 31 33 35 B A C D E WC 1 WC 2

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 Job Work Center 1 Work Center 2 Work Center 3 Work Center 4 13 6 2 B 10 12 18 C 17 9 4 D E 11 3 5 16

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

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)

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