3 Managers Must Schedule the Following Scheduling DecisionsOrganizationManagers Must Schedule the FollowingArnold Palmer HospitalOperating room usePatient admissionsNursing, security, maintenance staffsOutpatient treatmentsUniversity of MissouriClassrooms and audiovisual equipmentStudent and instructor schedulesGraduate and undergraduate coursesLockheed Martin factoryProduction of goodsPurchases of materialsWorkersHard Rock CafeChef, waiters, bartendersDelivery of fresh foodsEntertainersOpening of dining areasDelta Air LinesMaintenance of aircraftDeparture timetablesFlight crews, catering, gate, ticketing personnel
4 Operations Scheduling Specify time-phased activities and control job-order progressJobs are activities to be done and machines (work centers) process jobsSingle machine problemParallel machine problemFlow shop problemJob shop problem
5 Gantt Chart Example Day Monday Tuesday Wednesday Thursday Friday Work CenterMetalworksMechanicalElectronicsPaintingJob 349Job 408ProcessingUnscheduledCenter not availableJob 350Job 295
6 Scheduling Criteria Makespan Total (average) flow time Utilization Time required to complete a production schedule, or time required to manufacture all jobsTotal (average) flow timeTotal (average) amount of time jobs spend in the systemUtilizationTotal processing time / Total flow timeTotal (average) latenessTotal (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 firstSPT (Shortest processing time)The job with the SPT is processed firstEDD (Earliest due date)The job with the EDD is processed firstLPT (Longest processing time)The job with the LPT is processed firstCR (Critical ratio) – can be dynamicJobs are scheduled in order of increasing ratio of time remaining to required work time remaining
8 An Example (Single Machine) JobProcessing time in daysJob Due Date (day)A68B2C18D315E923
9 An Example (continued) FCFS: A-B-C-D-ESPT: B-D-A-C-EEDD: B-A-D-C-ELPT: E-C-A-D-BCR: A-B-C-D-E
10 An Example (continued) RuleMakespanTotalFlow TimeUtilizationTotal LatenessFCFS287736.4%11SPT6543.1%9EDD6841.2%6LPT10327.2%48CR
11 Comparison of Scheduling Rules No one scheduling rule excels on all criteriaSPT minimizes flow time, but moves long jobs to the end, which may result in dissatisfied customersFCFS does not do especially well (or poorly) on any criteria but is perceived as fair by customersEDD often minimizes lateness related criteria
12 Two Machine Flow Shop Johnson’s algorithm minimizes makespan List all jobs and times for each work centerChoose 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 lastOnce a job is scheduled, it is eliminated from the listRepeat above steps working toward the center of the sequence
13 An Example Job Work Center 1 (Drill Press) Work Center 2 (Lathe) A 5 2 36C84D109E712
15 More Than Two Machine Flow Shop Each job is processed by each machine (work center) exactly onceVery difficult to solve; a heuristic approach is necessaryReduce multiple machines to two machines and apply Johnson’s algorithmSolve 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 4 1362B101218C1794DE113516
20 Limitations of Rule-Based Dispatching Rules do not look upstream or downstream; idle resources and bottleneck resources in other departments may not be recognizedRules do not look beyond due datesScheduling 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 workersSchedules need to be smooth and keep personnel happyMany techniques exist from simple algorithms to complex linear programming solutionsCyclical scheduling -- Identify two consecutive days with the lowest total requirements and assign these as days off