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Understanding Flow, Inventory, Throughput, and Little’s Law in IE

Learn the core concepts of flow, inventory, and Little’s Law in IE, with examples and practical applications. Explore throughput rates, flowtimes, and how Little’s Law applies to systems. Understand bottlenecks and variability in processes.

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Understanding Flow, Inventory, Throughput, and Little’s Law in IE

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  1. Models in IE: Lecture 6 Flow, Inventory, Throughput, and Little’s Law

  2. Today’s Core Concepts • Flow, Flow Unit • Flowtime • Throughput • WIP, Inventory • Little’s Law • Bottleneck

  3. Georgia Tech as a flow process Georgia Tech 1 student = 1 flow unit

  4. IE 2030 Lecture 6 • Flow unit • Throughput: rate of flow units through a point per unit time • Input rate, output rate, and steady state • Flow time: on average, amount of time a flow unit spends within the system • WIP, inventory: number of units in system (within system boundaries).

  5. IE 2030 Flow Unit Examples • Kitchen in restaurant: flow unit=1food order • Gas station pump: flow unit = 1 gallon of gasoline • Gas station: flow unit = 1 customer (1 car) • Clothes store: flow unit = 1 article of clothing

  6. IE 2030 Lecture 6: Inventory • Inventory: number of flow units within system boundaries • At Tech: number of students who have matriculated but not graduated (ignoring dropouts) • Number of cars waiting for or getting gas • Number of food orders waiting or cooking • OR, # of food orders brought to kitchen, not cooked and taken by waiters (different system boundary)

  7. Flow unit, inventory • Input: many different materials and parts • Output: many different electronics components • What is a flow unit? • Filled order • One component • materials to make a component?? • $ of materials

  8. IE 2030 Lecture 6: Flowtime • Flowtime for a particular item in a system = time it leaves system - time it enters system • Flowtime usually means: on average, the amount of time a flow unit spends in system How long does a dollar remain in your checking account?

  9. Throughput: rate of flow unitsthrough a point • Kitchen in restaurant: # food orders arriving OR started cooking OR finished cooking... • Gas pump:# gallons pumped out/hour • Gas station: # customers served/hour • # clothes sold/week

  10. IE 2030: Little’s Law • Little’s Law is for a system in steady state • input rate = output rate • Similar to rate × time = distance • Applies to most systems, even those with variability • Uses AVERAGE values • throughput rate × flowtime = inventory

  11. Little’s Law at Georgia Tech Georgia Tech 12,500 Students 2500/year How long does it take to graduate?

  12. 1 3 5 2 4 6 7 8 Simple example: all students take 5 years

  13. 1 3 5 2 4 6 7 8 Better example: some take 4, some take 6 years

  14. IE 2030 Lecture 6 Little’s LawMeasurement • In the first example, if you ask students how long they will be at Tech, they say… • In the second example, some say 4, some say 6, but on average they say…. 5 years 5.2 years

  15. Little’s Law,Measurement, and Sampling • Visit a prison and ask inmates the lengths of their sentences until probation • Find the time served of inmates who died or were released on probation • Do you believe statistics reported in the news by honest, well-meaning reporters? • In general, should sample flow units passing a point in the system. More work!

  16. Steady State vs. Startup • Flow time defined for stable system • Input rate = Output rate • Inventory doesn’t   • Startup or transient behavior can be important, especially if change is frequent • Does the economy ever reach equilibrium?

  17. Little’s Law works even if System has Variability

  18. 1 3 5 2 4 6 7 8 P[4 years]=.4 P[5 years]=.2 P[6 years]=.4

  19. 1 3 5 2 4 6 7 8 Random number of students arriving/year

  20. Variability Little’s Law still works • Randomness in arrival rate • Randomness in arrival type • Randomness in service or production rates System must be stable Dependence can be a problem

  21. Bottlenecks • Definition: reduce rate, reduce throughput • Why not defined in terms of increase? • Semester conversion at Tech --- Chem labs a bottleneck • Flowlines usually have bottlenecks. Line balancing. • Jobshops are more complex; idea of bottleneck less easily applicable. • Bottlenecks are often unclear when there is variability

  22. Example: Insight from Little’s Law(L. McGinnis) • We put orders into the production system 1 month before their deadlines, but they are taking 1 month to be produced on average. More than half are late (why need it not be exactly half?) • Response: we put orders in 2 months before deadline. What happens?

  23. Example: Insight from Little’s Law (L. McGinnis) • We think we’ve changed rate, but output rate and future input rate are the same. • We’ve doubled inventory  doubled flowtime • Now orders take 2 months to produce, on average • In fact, orders now take more than 2 months on average! (Why?)

  24. Some Objectives for a System • Throughput (max.) • Cost per unit, including inventory (min) • flowtime (min) • total flowtime for a set of jobs (min) • makespan for a set of jobs (min) • example: 6 jobs time 2; 4 time 3; 3 time 4, 2 time 6. On 4 machines, minimizing makespan is not the same as minimizing total flowtime

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