3 Georgia Tech as a flow process 1 student = 1 flow unit
4 IE 2030 Lecture 6Flow unitThroughput: rate of flow units through a point per unit timeInput rate, output rate, and steady stateFlow time: on average, amount of time a flow unit spends within the systemWIP, inventory: number of units in system (within system boundaries).
5 IE Flow Unit ExamplesKitchen in restaurant: flow unit=1food orderGas station pump: flow unit = 1 gallon of gasolineGas station: flow unit = 1 customer (1 car)Clothes store: flow unit = 1 article of clothing
6 IE 2030 Lecture 6: InventoryInventory: number of flow units within system boundariesAt Tech: number of students who have matriculated but not graduated (ignoring dropouts)Number of cars waiting for or getting gasNumber of food orders waiting or cookingOR, # 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 componentsWhat is a flow unit?Filled orderOne componentmaterials to make a component??$ of materials
8 IE 2030 Lecture 6: FlowtimeFlowtime for a particular item in a system = time it leaves system - time it enters systemFlowtime usually means: on average, the amount of time a flow unit spends in systemHow long does a dollarremain 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/hourGas 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 rateSimilar to rate × time = distanceApplies to most systems, even those with variabilityUses AVERAGE valuesthroughput rate × flowtime = inventory
11 Georgia Tech Little’s Law at Georgia Tech 12,500 Students2500/yearHow long does it take to graduate?
12 Simple example: all students take 5 years 12345678Simple example: all students take 5 years
13 Better example: some take 4, some take 6 years 12345678Better 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 years5.2 years
15 Little’s Law,Measurement, and Sampling Visit a prison and ask inmates the lengths of their sentences until probationFind the time served of inmates who died or were released on probationDo 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 systemInput rate = Output rateInventory doesn’t Startup or transient behavior can be important, especially if change is frequentDoes the economy ever reach equilibrium?
17 Little’s Law works even if System hasVariability
19 Random number of students arriving/year 12345678Random number of students arriving/year
20 Little’s Law still works VariabilityLittle’s Law still worksRandomness in arrival rateRandomness in arrival typeRandomness in service or production ratesSystem must be stableDependence 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 bottleneckFlowlines 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 flowtimeNow orders take 2 months to produce, on averageIn 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