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Production lecture 5
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- 1(machine) scheduling-scheduling is the final stage of production planning
- scheduling can be defined as: prescribing of when and where each operation necessary to produce a product is to performed, fixing up starting and finishing times of each operation comprising a procedure - 2Goal- making a feasible production schedule
- making an optimal production schedule - 3scheduling = optimisation problem- given: machine(s), operations/jobs
- decisions: for every operation/job: on what machine, start times of the operations
- objective: several choices, depending on the production strategy
- constraints: capacity constraints of the machines, operations cannot overlap, operations cannot be interrupted - 4Input scheduling processFor job j:
- Pj (processing time)
- Rj (release date): time at which job j is available for processing
- Dj (due date): time at which the processing of job j is due to be completed - 5output scheduling process- Wj (waiting of job j): time that job j has to wait in the system before its processing starts
- Cj (completion time of job j): time at which job j finishes
- Fj (flow time of job j): time time that job j spends in the system
- Lj (lateness of job j) = Cj - Dj
- Tj (tardiness of job j): Tj = Lj if Lj > 0, 0 otherwise
M (makespan): moment at which the last job is finished - 6Objectives- minimize total time to run the entire set of jobs (sequence does not matter); makespan = sum of setup and run times for any sequence jobs
- minimize the average time each job spend at the machine (sequencing jobs in ascending order according to their total processing time, setup + run time)
- shortest processing time SPT: average time in the system will always be minimized by selecting the next job processing that has the shortest processing time at the current operation. - 7Priority rules (sequencing rules)use of logic rules that guide the prioritizing of job at a work station:
- random: often used as a benchmark for other rules
- FIFO/FCFS: 'fair' in that jobs are processed in the order they arrive at the work center
SPT: shortest processing time first: reduce work in process inventory, average job completion time, average job lateness
- LPT: longest processing time first
- EDD: earliest due date: work well for criteria associated with job lateness - 8SPTfor the basic single-machine scheduling problem, the SPT-priority rule minimizes the;
- average flow time
- average number of jobs in system
- average waiting time
- average lateness
- Max. waiting time - 9EDD- for the basic single-machine scheduling problem the EDD-priority rule minimizes; maximum lateness Lmax and maximum tardiness Tmax
- if the objective is to minimize the number of tardy jobs: if EDD leads to a schedule with no tardy jobs, the schedule is an optimal schedule otherwise, you can use (Moore-)Hodgson's algorithm to make an optimal schedule - 10(Moore-)Hodgson's algorithmminimizes the number of tardy jobs in the single machines environment with ready time equal to zero
- 112 machine flow shop; johnson's ruleJohnson's rule minimizes the makespan
- 12complexity of scheduling problems- for some scheduling problems simple methods exist to calculate an optimal schedule, but many scheduling problems are very complex
- for a lot of scheduling problems no simple method exists to determine an optimal schedule
- these problems are frequently modeled as (mixed) integer linear program (M)ILP
- often binary variables are used that indicate; wether a job is assigned to a machine, wether an employee is assignment to a machine
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- Fichas sobre Production lecture 5, creado por Elisa Vink el 11/10/2020.
- Creado por
- Elisa Vink
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