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Models in IE: Lecture 6 Flow, Inventory, Throughput, and Littles Law.

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Presentation on theme: "Models in IE: Lecture 6 Flow, Inventory, Throughput, and Littles Law."— Presentation transcript:

1 Models in IE: Lecture 6 Flow, Inventory, Throughput, and Littles Law

2 Todays Core Concepts Flow, Flow Unit Flowtime Throughput WIP, Inventory Littles Law Bottleneck

3 Georgia Tech Georgia Tech as a flow process 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 2030Flow 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 units through 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: Littles Law Littles 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 Georgia Tech Littles Law at Georgia Tech How long does it take to graduate? 2500 /year 12, 500 Students

12 Simple example: all students take 5 years

13 Better example: some take 4, some take 6 years

14 IE 2030 Lecture 6Littles Law Measurement 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 Littles 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 doesnt Startup or transient behavior can be important, especially if change is frequent –Does the economy ever reach equilibrium?

17 Littles Law works even if System has Variability

18 P[4 years]=.4P[5 years]=.2P[6 years]=

19 Random number of students arriving/year

20 Variability Littles 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 Littles 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 Littles Law ( L. McGinnis) We think weve changed rate, but output rate and future input rate are the same. Weve 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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