Models in IE: Lecture 6

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

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

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

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).

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

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)

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

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?

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

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

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

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

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

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

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!

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?

Little’s Law works even if System has Variability

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

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

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

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

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?

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?)

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

Models in IE: Lecture 6