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## Scheduling Seminar exercises

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**SchedulingSeminar exercises**2010.10.14 Process and Production Management**Scheduling**• Estabilishing the timing of the use of equipment, facilities and human activities in an organization. • High volume systems (characterized by standardized equipment and activities that provide identical or highly similar operations on products – autos, personnal computers, radios, TVs) • Intermediate – volume systems (ouput fall between the standardized type of output of the high volume systems and made-to-order output of job shops. Work centers periodically shift from one product to another, but lot size relatively high. • Low-volume systems (products are made to order, and orders differ in terms of processing requirements, materials needed, processing time.)**Priority rules**• Select the order in which job will be processed • First come first served (FCFS) – jobs are processed in the order which they arrive at a machine or work center • Shortest processing time (SPD) – according to processing time, shortest job first • Earliest due date (EDD) – according to due date, earliest due date first. • Critical ratio (CR) – smallest ratio of time remaining until due date to processing time remaining.**Assumptions**• The set of jobs is known • Setup time is independent of processing sequence • Setup time is deterministic • Process time are deterministic • There will be no interruptions in processing such as machine breakdowns, accidents, or workes illness.**Example 1**• Determine the sequence of jobs/products • Determine average flow time • Determine average tardiness • Determine average number of jobs at the workcenter**Job flow time – the length of time a job is at a**particular workstation or work center. (it includes not only procesing time, but waiting time, transportation time) • Average flow time = total flow time /number of jobs • Job lateness – length of time the job completion date is exceed the date the job was due to promised to the customer • Average tardiness=total lateness/number of products • Makespan – is the total time needed to complete a group of jobs (time between start the first and completion of the last one) • Average number of jobs=total flow time/makespan (it reflects the average work-in-process inventory if the jobs represent equal amount of inventory)**ABCDEF**FCFS • Aft=120/6=20 days • At=54/6=9 days • M=41 Aj=120/41=2,93 pieces** ACEBDF**SPT • Aft=108/6=18 days • At=40/6=6,67 days • Aj=108/41=2,63 pieces**CAEBDF**EDD • Aft=110/6=18,33 days • At=38/6=6,33 days • Aj=110/41=2,68 pieces**CR**??? Remaining time untill due to dat (on the 0th day) 1. 2.**3.**4. 1. 5. 4. 2.**CRCFAEBD**• Aft=133/6=22,16 days • At=58/6=9,66 days • Aj=133/41=3,24 pieces**Sequencing Jobs through two Work Center**• Job time is known and constant • Job time is independent of job sequence • All job must follow the same two-step job sequence • Job priorities cannot be used • All units must be completed at the first work center before moving on to the second work center**Example 2**• Select the job with the shortest time. • If the shortest time at first wc, schedule that job first. • If the time at the 2nd wc, schedule the work last. • Eliminate the job and its time from further consideration • Repeat steps E C F A B D**Chart**2 8 16 28 33 37 #1 #2 2 9 17 26 28 43 48 51 Idle time Flow time: 51 hours