IE450 Models Relating Cycle-time, Throughput, WIP and Batch Sizes Planning manufacturing capacity Dr. R. A. Wysk Learning Objectives To be able to name the most important factors that contribute to the increase in the cycle time of a production system. To be able to explain the Littles Law and its application to the operations of a production system. To be able to explain the fundamental relationship between resource utilization, cycle time and process and arrival variability in a production system. Any Production System Input Resources
WIP Output Any Production System Output Input WIP Input = Output [ defects] (1st Law of Factory Physics) WIP - Work-In-Process Idle time - % of time a resource is not working Any Production System Output Input Throughput the average output per unit time (a rate) Lead time the time needed to process a part through a facility Cycle time, flow time or sojourn time the average time from release of a job to
completion Relating Throughput and WIP One unit in WIP Lead time ? Idle time ? Throughput? Assuming each process takes 1 minute. More WIP (everything else the same) ... Lead time ? Idle time ? Throughput? More WIP - keep all machines busy ... Lead time ? Idle time ? Throughput? More WIP - diminishing returns ...
Lead time ? Idle time ? Throughput? Active Exercise: Diminishing return? At some point more WIP does not achieve anything except for longer lead times Take 3 minutes to complete the following task. Draw graphs relating WIP to throughput. Throughput Relating WIP and Throughput 100% What is the limiting throughput? WIP A very useful relationship Littles Law: WIP = (Throughput) x (Lead Time) Littles Law is a fundamental law of system dynamics Gives good results for a variety of scenarios
Throughput (Units/time). Example: A facility can produce 200 units per week, and the average lead time is 2 weeks. According to Littles law the average WIP = 200 x 2 = 400 units. Scenario 1: No Variability (Ideal World) Data and Calculations Planning Horizon 30 hours Processing time 8 hour/unit Inter-arrival time 10 hours Utilization 80% Average queue time 0 hours Average lead time 8 hours 1st part arrives 2nd part arrives
1st part processing 0 3rd part arrives 2nd part processing 8 10 1st part departs 3rd part processing 18 20 2nd part departs 28 30 3rd part departs
Scenario 2: Processing Variability SCENARIO Planning Horizon Processing time Inter-arrival time Utilization Average queue time Average lead time 1st part arrives 2nd part arrives Parts waiting in queue 2 same 12, 9, 3 Same average !!! same same 1 hour 9 hours
3rd part arrives 10 12 1st part departs 20 Same utilization but . . . More queue time 2nd part processing 1st part processing 0 1 30 hours 8 hour/unit 10 hours
80% 0 hours 8 hours 3 More lead time 21 24 2nd part departs 3rd part departs 30 Scenario 3: Arrival Variability SCENARIO Planning Horizon Processing time Inter-arrival time Utilization Average queue time
Average lead time 1st part arrives 1 30 hours 8 hour/unit 10 hours 80% 0 hours 8 hours 13.5 hours 2 same as 1 12, 9, 3 same same as 1 1 hours 9 hours 2nd part arrives 3
same as 1 same as 1 13.5, 6.5 Same average !!! same as 1 Again, same 0.5 hours 8.5 hours but . . . 6.5 hours utilization More queue time 3rd part arrives More lead time Part 3 waiting in queue 1st part processing
0 2nd part processing 8 10 1st part departs 13.5 20 2nd part departs 3rd part processing 21.5 29.5 3rd part departs
Scenario 4: Increased utilization SCENARIO Planning Horizon Processing time Inter-arrival time Utilization Average queue time Average lead time 1st part arrives 2nd part arrives 1 30 hours 8 hour/unit 10 hours 80% 0 hours 8 hours Parts waiting in queue 2
same as 1 12, 9, 3 same as 1 same as 1 1 hours 9 hours 3 same as 1 same as 1 13.5, 6.5 same as 1 0.5 hours 8.5 hours 3rd part arrives 4 same as 1 Larger (2) + 1 hour Batch Sizes same as 1 90%
2 hours 11 hours Increased utilization but more queue time 1st part processing 0 10 3 2nd part processing 13 1st part departs 20 23 2nd part
departs longer lead times 27 30 3rd part departs What would happen if the processing time variability is eliminated? Example Summary SCENARIO Planning Horizon Processing time Inter-arrival time Utilization Average queue time Average lead time 1 30 hours 8 hour/unit
10 hours 80% 0 hours 8 hours 2 same as 1 12, 9, 3 same as 1 same as 1 1 hours 9 hours 3 same as 1 same as 1 13.5, 6.5 same as 1 0.5 hours 8.5 hours 4 same as 1 (2) + 1 hour same as 1
90% 2 hours 11 hours Utilization alone is not sufficient to estimate the lead-time performance One must also consider the products arrival and processing variability. A mathematical model is needed to study the system. Questions??
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