Flow Shop Scheduling 1 Flexible Flow Shop 2
Flow Shop Scheduling 1. Flexible Flow Shop 2. Flexible Assembly Systems (unpaced) 3. Paced Assembly Systems 4. Flexible Flow Systems Operational Research & Management Operations Scheduling
Topic 1 Special Case of Job Shops: Flexible Flow Shops Operational Research & Management Operations Scheduling
A Flexible Flow Shop with Setups Stage 1 Operational Research & Management Stage 2 Stage 3 Stage 4 Operations Scheduling 3
Applications Ø Very common in applications: – Paper mills – Steel lines – Bottling lines – Food processing lines Operational Research & Management Operations Scheduling 4
Objectives Ø Multiple objectives usual – Meet due dates – Maximize throughput – Minimize work-in-process (WIP) Operational Research & Management Setting for job j on Machine i Operations Scheduling 5
Generating Schedules 1. Identify bottlenecks 2. Compute time windows at bottleneck stage (release / due dates) 3. Compute machine capacity at bottleneck 4. Schedule bottleneck stage 5. Schedule non-bottlenecks Operational Research & Management Operations Scheduling 6
1: Identifying Bottlenecks Ø In practice usually known Ø Schedule downstream bottleneck first Ø Determining the bottleneck Ø – loading – number of shifts – downtime due to setups Bottleneck assumed fixed Operational Research & Management Operations Scheduling 7
2: Identifying Time Window Ø Ø Local Due date – Shipping day – Multiply remaining processing times with a safety factor Local Release date – Status sj of job j (# completed stages) – Release date if sj = l Decreasing function determined empirically Operational Research & Management Operations Scheduling 8
3: Computing Capacity Ø Ø Capacity of each machine at bottleneck – Speed – Number of shifts – Setups Two cases: – Identical machines – Non-identical machines Operational Research & Management Operations Scheduling 9
4: Scheduling Bottleneck Ø Ø Jobs selected one at a time – Setup time – Due date – Capacity For example ATCS rule Operational Research & Management Operations Scheduling 10
5: Schedule Remaining Jobs Ø Determined by sequence at bottleneck stage Ø Minor adjustments – Adjacent pairwise interchanges to reduce setup Operational Research & Management Operations Scheduling 11
Topic 2 Flexible Assembly Systems Operational Research & Management Operations Scheduling
Classical Literature Ø Ø Exact solutions – Simple flow shop with makespan criterion – Two machine case (Johnson’s rule) Realistic problems require heuristic approaches Operational Research & Management Operations Scheduling 13
Job Shops Flexible Assembly Ø Each job has an unique identity Ø Limited number of product types Ø Make to order, low volume environment Ø Given quantity of each type Ø Mass production Ø Possibly complicated route through system Ø High degree of automation Ø Very difficult Ø Even more difficult! Operational Research & Management Operations Scheduling 14
Flexible Assembly Systems Ø Ø Ø Sequencing Unpaced Assembly Systems – Simple flow line with finite buffers – Application: assembly of copiers Sequencing Paced Assembly Systems – Conveyor belt moves at a fixed speed – Application: automobile assembly Scheduling Flexible Flow Systems – Flow lines with finite buffers and bypass – Application: producing printed circuit board Operational Research & Management Operations Scheduling 15
Sequencing Unpaced Assembly Systems Ø Number of machines in series Ø No buffers Ø Material handling system Ø – When a job finishes moves to next station – No bypassing – Blocking Can model any finite buffer situation (pij = 0) Operational Research & Management Operations Scheduling 16
Cyclic Schedules Ø Schedules often cyclic or periodic: – – Ø Given set of jobs scheduled in certain order Ø Contains all product types Ø May contain multiple jobs of same type Second identical set scheduled, etc. Practical if insignificant setup time – Low inventory cost – Easy to implement Operational Research & Management Operations Scheduling 17
Minimum Part Set Ø Suppose L product types Ø Let Nk be target number of jobs of type k Ø Let z be the greatest common divisor Ø Then is the smallest set with ‘correct’ proportions Ø Called the minimum part set (MPS) Operational Research & Management Operations Scheduling 18
Defining a Cyclic Schedule Ø Consider the jobs in the MPS as n jobs Ø Let pij be as before Ø A cyclic schedule is determined by sequencing the job in the MPS Ø Maximizing TP = Minimizing cycle time Operational Research & Management Operations Scheduling 19
Minimizing Cycle Time Ø Profile Fitting (PF) heuristic: – Select first job j 1 Ø Arbitrarily Ø Largest amount of processing – Generate profile: – Determine which job goes next Operational Research & Management Operations Scheduling 20
PF: Next Job Ø Compute for each candidate job – Time machines are idle – Time job is blocked – Start with departure times: Operational Research & Management Operations Scheduling 21
Nonproductive Time Ø Calculate sum of idle and blocked time Ø Repeat for all remaining jobs in the MPS Ø Select job with smallest number Ø Calculate new profile and repeat Operational Research & Management Operations Scheduling 22
Discussion: PF Heuristic Ø PF heuristic performs well in practice Ø Refinement: – Nonproductive time is not equally bad on all machines – Bottleneck machine are more important (OPT philosophy) – Use weight in the sum (see example) Operational Research & Management Operations Scheduling 23
Discussion: PF Heuristic Ø Basic assumptions – Setup is not important – Low WIP is important Cyclic schedules good Ø Want to maximize throughput Minimize cycle time PF heuristic performs well Operational Research & Management Operations Scheduling 24
Additional Complications Ø The material handling system does not wait for a job to complete Paced assembly systems Ø There may be multiple machines at each station and/or there may be bypass Flexible flow systems with bypass Operational Research & Management Operations Scheduling 25
Topic 3 Paced Assembly Systems Operational Research & Management Operations Scheduling
Paced Assembly Systems Ø Conveyor moves jobs at fixed speeds Ø Fixed distance between jobs – Spacing proportional to processing time Ø No bypass Ø Unit cycle time – time between two successive jobs – linebalancing Operational Research & Management Operations Scheduling 27
Grouping and Spacing Ø Attributes and characteristics of each job – Ø Changeover cost – Ø Color, options, destination of cars Group operations with high changeover Certain long operations – Space evenly over the sequence – Capacity constrained operations (criticality index) Operational Research & Management Operations Scheduling 28
Objectives Ø Minimize total setup cost Ø Meet due dates for make-to-order jobs – Ø Spacing of capacity constrained operations – Ø Total weighted tardiness Pi(L) = penalty for working on two jobs L positions apart in ith workstation Regular rate of material consumption Operational Research & Management Operations Scheduling 29
Grouping and Spacing Heuristic Ø Determine the total number of jobs to be scheduled Ø Group jobs with high setup cost operations Ø Order each subgroup accounting for shipping dates Ø Space jobs within subgroups accounting for capacity constrained operations Operational Research & Management Operations Scheduling 30
Example Ø Single machine with 10 jobs Ø Each job has a unit processing time Ø Setup cost Ø If (with 2 attributes) (color) there is a penalty cost Operational Research & Management (sunroof) Operations Scheduling 31
Example Data Operational Research & Management Operations Scheduling 32
Grouping Ø Group A: Jobs 1, 2, and 3 Ø Group B: Jobs 4, 5, and 6 Ø Group C: Jobs 7, 8, 9, and 10 Ø Best order: A B C (according to setup cost) Operational Research & Management Operations Scheduling 33
Grouped Jobs A B C Due date Order A C B Operational Research & Management Operations Scheduling 34
Capacity Constrained Operations A Operational Research & Management C B Operations Scheduling 35
Topic 4 Flexible Flow Systems Operational Research & Management Operations Scheduling
Flexible Flow System with Bypass Operational Research & Management Operations Scheduling 37
Flexible Flow Line Loading Algorithm Ø Ø Objectives – Maximize throughput – Minimize work-in-process (WIP) Minimizes the makespan of a day’s mix – Ø Actually minimization of cycle time for MPS Reduces blocking probabilities Operational Research & Management Operations Scheduling 38
Flexible Flow Line Loading Algorithm Ø Three phases: – Machine allocation phase Ø – – assigns each job to a specific machine at station Sequencing phase Ø orders in which jobs are released Ø dynamic balancing heuristic Time release phase Ø minimize MPS cycle time on bottlenecks Operational Research & Management Operations Scheduling 39
1: Machine Allocation Ø Bank of machines Ø Which machine for which job? Ø Basic idea: workload balancing Ø Use LPT dispatching rule Operational Research & Management Operations Scheduling 40
2: Sequencing Ø Basic idea: spread out jobs sent to the same machine Ø Dynamic balancing heuristic Ø For a given station, let pij be processing time of job j on ith machine Ø Let Operational Research & Management and (the total workload) Operations Scheduling 41
Dynamic Balancing Heuristic Ø Let Sj be the jobs released before and including job j Ø Define Ø Target Operational Research & Management Operations Scheduling 42
Minimizing Overload Ø Define the overload of the ith machine Ø The cumulative overload is Ø Minimize Operational Research & Management Operations Scheduling 43
3: Release Timing Ø Ø MPS workload of each machine known – Highest workload = bottleneck – MPS cycle time Bottleneck cycle time Algorithm – Step 1: Release all jobs as soon as possible, then modify according to – Step 2: Delay all jobs upstream from bottleneck as much as possible – Step 3: Move up all jobs downstream from the bottleneck as much as possible Operational Research & Management Operations Scheduling 44
Example Operational Research & Management Operations Scheduling 45
Data Operational Research & Management Operations Scheduling 46
Machine Allocation Operational Research & Management Operations Scheduling 47
Workload Ø From this table we obtain each row Operational Research & Management each column Operations Scheduling 48
Overload With job 1 as first job of sequence Operational Research & Management Operations Scheduling 49
Overload Matrix With job 1 to 5 as first job of sequence Operational Research & Management Operations Scheduling 50
Dynamic Balancing First Job Operational Research & Management Operations Scheduling 51
Selecting the Second Job Ø Calculate the cumulative overload where Operational Research & Management Operations Scheduling 52
Cumulative Overload Selected next Operational Research & Management Operations Scheduling 53
Final Cycle Ø Schedule jobs 4, 5, 1, 3, 2 Ø Release timing phase – Machine 4 is the bottleneck – Delay jobs on Machine 1, 2, and 3 – Expedite jobs on Machine 5 Operational Research & Management Operations Scheduling 54
Final Sheet Ø Ø Ø Flexible Manufacturing Systems (FMS) – Numerically Controlled machines – Automated Material Handling system – Produces a variety of product/part types Scheduling – Routing of jobs – Sequencing on machines – Setup of tools Similar features but more complicated Operational Research & Management Operations Scheduling 55
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