Sequencing Sequencing: Determine the order in which jobs at a work center will be processed. Workstation: An area where one person works, usually with.

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Presentation transcript:

Sequencing Sequencing: Determine the order in which jobs at a work center will be processed. Workstation: An area where one person works, usually with special equipment, on a specialized job.

Sequencing Job time: Time needed for setup and processing of a job.

Priority Rules FCFS - first come, first served Jobs are processed in the order in which they arrive at a machine or work center. SPT - shortest processing time Jobs are processed according to processing time at a machine or work center, shortest job first. DD - due date Jobs are processed according to due date, earliest due date first.

Priority Rules CR - critical ratio S/O - slack per operation Jobs are processed according to smallest ratio of time remaining until due date to processing time remaining. S/O - slack per operation Jobs are processed according to average slack time (time until due date minus remaining time to process). Compute by dividing slack time by dividing slac time by number of remaining operations including the current one. Rush – emergency Emergency or Preferred Customers first.

Assumptions to Priority Rules Setup time is deterministic. The set of jobs is known, no new jobs arrive after processing begins and no jobs are canceled. Processing times are deterministic rather than variables. There will be no interruptions in processing such as machine breakdowns , accidents or worker illnesses.

Definitions Job Flow Time Job Lateness The length of time a job is in the shop at a particular workstation or work center. Job Lateness This is the length of time the job completion date is expected to exceed the date the job was due or promised to a customer.

Definitions Makespan Average Number of Jobs This is the total time needed to complete a group of jobs. It is the length of time between the start of the first job in the group and the completion of the last job in the group. Average Number of Jobs Jobs that are considered in a shop are considered to be work in process inventory. Mathematically Average Number of Jobs= Total Flow Time / Makespan

Example Determine the sequence of jobs, average time flow, average days late and average number of jobs at the work center, for each of these rules: FCFS SPT DD CR

Example Data JOB Processing Time Due Date A 2 7 B 8 16 C 4 D 10 17 E 5 15 F 12 18

FCFS Assume Jobs arrived in the following order: A-B-C-D-E-F JOB Sequences Processing Time (1) Flow Time ( cumulative processing time) (2) Due Date (3) 2-3 A 2 7 B 8 10 16 C 4 14 D 24 17 E 5 29 15 F 12 41 18 22 120 54

FCFS Average Flow time= Total Flow Time/Number of Jobs=120/6=20 days Average Tardiness=54/6=9 The makespan =41 days Average Number of Jobs at workstation= 120/41=2.93 jobs per workstation

SPT rule SPT, the sequence is A-C-E-B-D-F JOB Sequences Processing Time (1) Flow Time ( cumulative processing time) (2) Due Date (3) 2-3 A 2 7 C 4 6 E 5 11 15 B 8 19 16 3 D 10 29 17 12 F 41 18 23 108 40

SPT rule Average Number of Jobs at workstation= 108/41=2.63 jobs per workstation The makespan =41 days Average Tardiness=40/6=6.67days Average Flow time= Total Flow Time/Number of Jobs=108/6=18 days

Summary Part A,B,C and D JOB Sequences Rule Average Flow Time (Days) Average Lateness Average Number of Jobs of the Work Center FCFS 20.00 9.00 2.93 SPT 18.00 6.67 2.63 DD 18.33 6.33 2.68 CR 26.67 14.17 3.9

Two Work Center Sequencing Johnson’s Rule: Technique for minimizing completion time for a group of jobs to be processed on two machines or at two work centers. Minimizes total idle time Several conditions must be satisfied

Johnson’s Rule Conditions Job time must be known and constant. Job times must be independent of sequence. Jobs must follow same two-step sequence. Job priorities cannot be used. All units must be completed at the first work center before moving to second.