IE450 Models Relating Cycle-time, Throughput, WIP and Batch Sizes

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Presentation transcript:

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 Little’s 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 Resources Output Input WIP

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.

Relating WIP and Throughput 100% Throughput What is the limiting throughput? WIP

A very useful relationship Little’s Law: WIP = (Throughput) x (Lead Time) Little’s 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 Little’s law the average WIP = 200 x 2 = 400 units.

Scenario 1: No Variability (Ideal World) 1st part arrives 2nd part arrives 3rd part arrives 1st part processing 2nd part processing 3rd part processing 10 20 30 8 18 28 1st part departs 2nd part departs 3rd part departs

Scenario 2: Processing Variability Same average !!! 1st part arrives 2nd part arrives 3rd part arrives Same utilization but . . . More queue time More lead time Parts waiting in queue 1st part processing 2nd part processing 3 10 30 12 21 24 20 1st part departs 2nd part departs 3rd part departs

Scenario 3: Arrival Variability Same average !!! Again, same utilization but . . . More queue time More lead time 1st part arrives 2nd part arrives 3rd part arrives 13.5 hours 6.5 hours Part 3 waiting in queue 1st part processing 2nd part processing 3rd part processing 21.5 8 29.5 10 13.5 20 1st part departs 2nd part departs 3rd part departs

Scenario 4: Increased utilization Larger Batch Sizes 1st part arrives 2nd part arrives 3rd part arrives Increased utilization but … more queue time longer lead times Parts waiting in queue 1st part processing 2nd part processing 3 10 13 23 27 20 30 1st part departs What would happen if the processing time variability is eliminated? 2nd part departs 3rd part departs

Example Summary 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??