1. Flow, Inventory, Throughput, and Little’s Law
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
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 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 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: 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. Georgia Tech Little’s Law at Georgia Tech
12,500 Students
2500/year
How long does it take to graduate?

12. Simple example: all students take 5 years1 2 3 4 5 6 7 8
Simple example: all students take 5 years

13. Better example: some take 4, some take 6 years1 2 3 4 5 6 7 8
Better example: some take 4, some take 6 years

14. IE 2030 Lecture 6 Little’s 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. 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. P[4 years]=.4 P[5 years]=.2 P[6 years]=.41 2 3 4 5 6 7 8
P[4 years]=.4 P[5 years]=.2 P[6 years]=.4

19. Random number of students arriving/year1 2 3 4 5 6 7 8
Random number of students arriving/year

20. Little’s Law still works
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