311 Session 5 1 Littles law

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Text of 311 Session 5 1 Littles law

  • Littles LawBUAD311 Operations ManagementSession 5

    *

    Operations Management

  • AnnouncementsThe first homework is due before the end of the class on Sep/17The first quiz is on Sep/19 and it covers process analysisRead The Goal (2-page paper is due on Sep/24)

  • *Objectives: Littles LawRelationship amongFlow (Throughput) TimeFlow (Throughput) RateWIPLittles LawA general rule that links various performance measures

  • *Littles LawFlow rate Now1 min later2 min laterYouFlow time 2 3 timespeeddistance

  • *Littles LawLittles Law holds for any stable systems.

  • *Littles LawExample: Bank Teller(Average) WIP: 6 customers(Average) Flow rate: 12 customers per hour(Average) Flow time: 6/12 = 0.5A customer spends (on average) 0.5 hours in the bank

    Does this mean each customer spends 0.5 hour in the bank?

  • *Implications of Littles LawWhich one is (usually) difficult to measure ?Flow RateWIPFlow time

  • *Implications of Littles Law: ExampleAverage number of customers in a restaurant: 50Average number of customers arriving (and leaving) per hour: 30What is the flow time?50/30 = 1.66 hrsA customer spends (on average) 1hr and 40 mins.How can we increase the revenue? Revenue is proportional to Flow Rate = WIP / Flow Time

    Increase WIP:Add more chairsReduce FT: Faster service

  • *Example: Admission FlowMarshall undergraduate program receives about 1000 applications per month.The evaluation starts with a preliminary classification with basic information (Stage 1) :Group A: Applicants with desired recommendations, extracurricular activities, etc. (50% of the applicants) Applicants in this group will advance to a secondary review.Group B: Other applicants. (50% of the applicants) Applicants in this group will be rejected.On average there are:200 applications in the preliminary stage (Stage 1) 50 applications in the advanced review stage (Stage 2)

  • How long:do Group B applications spend in the process?do Group A applications spend in the process?is the average process time?

    *Example: Admission Flow (contd)

  • Group B:FT = WIP/FR = 200 / 1000 = 0.2 mo. = 6 days

    *Example: Admission Flow (contd)

  • Group A:Stage 2: FT = WIP/FR=50/(1000*50%) = 0.1 mo. = 3 daysReceive answer in 6+3 = 9 days on average*Example: Admission Flow (contd)

  • What is the average processing time?6*0.5+9*0.5 = 7.5 daysIs there a simple way to calculate the average waiting time?

    *Example: Admission Flow (contd)

  • Simple way:System WIP=200 (stage 1) + 50 (Stage 2)= 250 applicationsSystem FR=1000 applications per monthSystem FT=250/1000=0.25 month=7.5 days*Example: Admission Flow (contd)Littles Law still holds.

  • Example: ClinicImagine a clinic in which a patient can be treated in exactly 15 minutes. Two patients arrive 15 minutes past the hour (every hour), and one patient arrives 45 minutes past the hour: FR of 3 per hour

  • Example: ClinicWhat is the average waiting time? By Littles law: Average WIP = (0 + 1 + 0 + 0) / 4= 0.25 patients Average waiting time = 0.25 patients/(3 patients/ hr) = (0.25/3)*60 mins/hr = 5 min

    Directly from the Chart:Average waiting time = (0 + 15 + 0)/3 = 5 min

  • Example: ClinicWhat is the average total time spent (waiting + service)? Directly from the Chart:Average total time = (15 + 30 + 15)/3 = 20 minBy Littles law: Average WIP = (0 + 2 + 1 + 1) / 4= 1 Average total time = 1 patient/(3 patients per hr) = (1/3)*60 mins/ hr = 20 min

    Littles Law holds for variable/random arrivals

  • *Example: ClinicDo we have enough capacity?Patient arrival rate=3 patients per hourClinic Capacity=60 min/(15 mins per patient)= 4 patients per hourWhat is the utilization rate? 3/4=0.75 or 75%Why do patients wait?Arrivals are bunched up--not evenly spread out over the hour

    Randomness/Variability forces resource idleness & longer waiting time.

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