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Dependent Events and Statistical Fluctuations - Jonah: What is the combine...


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Dependent Events and Statistical Fluctuations

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Dependent Events and Statistical Fluctuations

Jonah: What is the combined effect of dependent events and statistical fluctuations?

Paul A. Jensen

Operations Research Models and Methods

Copyright 2004 - All rights reserved


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Topics

  • Dependent Events

  • Statistical Fluctuations

  • Drum, Buffer, Rope Scheduling


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Dependent Events


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What are dependent events?


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What happens if we ask everyone to be efficient?


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How can we control a system with dependent events?

  • Step 1: Identify the system’s bottleneck

  • Step 2: Exploit the system’s bottleneck

  • Step 3: Subordinate everything else to the bottleneck


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How can we improve a system with dependent events?

  • Step 4: Elevate the system’s constraint.


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Focus on the bottleneck

  • What is time worth on the bottleneck?

  • What is time worth on the non-bottlenecks?


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What are the benefits of this process?

  • Better process control

  • Reduced inventories

  • Reduced operating expenses

  • Increased throughput


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Concepts: Dependent Events

  • Can we have bottlenecks in systems with independent events?

  • What is a bottleneck?

  • How do we control with a bottleneck?

  • What are the benefits of this control?

  • Where should we focus improvement efforts?

  • Should we have a bottleneck?


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Statistical Fluctuations


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Should we balance the capacities in the line?


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What is the effect of statistical fluctuation?

  • Where is the bottleneck?

  • How do we improve?


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Jonah: Balance flow not capacity

  • It is good to have a bottleneck?

  • Control production through the bottleneck.

  • Subordinate the production in nonbottlenecks to assure that the bottleneck is never delayed.


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Concepts: Statistical Fluctuations

  • What is the effect of statistical fluctuation?

  • Is it good to balance the capacities in the line?

  • Why is it helpful to have a bottleneck in the line?


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Drum, Buffer, Rope Scheduling


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What happens if Herbie cannot be put at the front of the line?


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We need some way to control those who are in front of Herbie

  • How about a drum?

  • How about a rope?

  • Where is the buffer?


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What is the equivalent in the manufacturing system?


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Drum, Buffer, Rope Scheduling System

  • Drum: A schedule for the Constraint resource

  • Rope: The time interval between when material is required at the constraint and the release of the raw material to the first station

  • Buffer: The difference between the rope and the minimum time required in the stages preceding the constraint


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A Cycle in the Production System


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How does the rope affect the cycle time?

  • What happens when we increase the rope?

  • Do we want the rope large or small?


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How does the cycle time affect work in process (inventory)?

  • Work in Process = (cycle time)*(Flow Rate)

  • Time in machine C = 12 minutes.

  • Flow rate = (1/12) units per minute.

  • Cycle time = 1500 minutes.

  • Work in Process = (1/12) units per minute*1500 minutes

    • = 125 Units.


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How do we select the length (time) of the rope?

  • Why would we like to keep the rope relatively long?

  • Why would we like to keep the rope relatively short?

  • Which is the most important effect?


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Concepts (D, B, R)

  • What is the drum?

  • What is the rope?

  • What is the buffer

  • How do we select the length (time) of the rope?