03. lecture - little's law

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Operations Management

Little’s Law - Lecture 3(Chapters 3 and 4)

Dr. Ursula G. Kraus

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Review

• Shouldice Hospital (“Focused Factory”)• Process View of Operations• Product/Process Attributes

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Agenda

• Process Characterization - By Architecture- By Positioning Strategy- By Customer Interface

• Operational Measures: Time, Inventory and Throughput

• Little’s Law• Flow Time Analysis

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Process Types Examples .

Project Construction, Consulting

Job Shop Machine Shop, Beauty Shop

Batch Bakery, Classroom

Line Flow Assembly Line, Cafeteria Line

Continuous Flow Paper mill, Central heating

Classification of Processes by: I. Process Architecture

Job Shop

Flow Shop

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Characteristics of Processes:Job Shop vs. Flow Shop

Type of Process

Product Volume

Specialized Equipment

Product Variety

Setup Frequency

Labor Skills

Variable Cost

Job Shop

Flow Shop

Source: Managing Business Process Flows (1999)

lowmediumhigh

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ProcessFlexibility

Jumbled Flow.Process segmentsloosely linked.

Disconnected LineFlow/Jumbled Flowbut a dominant flowexists.

JOB SHOP

(Commercial Printer,Architecture firm)

BATCH

(Heavy Equipment,Auto Repair)

LINE FLOWS

(Auto Assembly,Car lubrication shop)

CONTINUOUSFLOW

(Oil Refinery)

ProductVariety

LowLow Standardization

One of a kindLow Volume

Many ProductsFew Major ProductsHigh volume

High StandardizationCommodity Products

Connected LineFlow (assembly line)

Continuous, automated,rigid line flow.Process segments tightlylinked.

Opport

unity

Costs

Out-of-

pock

et

Costs

High

Low

High

Product-Process Matrix

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Classification of Processes by: II. Positioning Strategy

Functional Focus:… grouping by resource type• Job shop• General purpose resources

Product Focus:… grouping by product• Flow shop• Specialized resources

A B

C D

Product 1

Product 2

A D B

C B A

Product 1

Product 2

= resource pool (e.g., X-ray dept, billing)Source: Managing Business Process Flows (1999)

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Classification of Processes by: III. Customer Interface

Make to Stock

Make to Order


For Mr. Foley

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Self-service groceriesAutomobile

Comparison of Goods and Services

100% 75% 50% 25% 0% 100%75%50%25%

Goods Services

Installed carpeting

HaircutConsulting services

Fast-food restaurantGourmet restaurant

Auto maintenance

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Characteristics of Services

Typically labor intensive - difficult to automate

Frequently individually processed - low scale economies

Often an intellectual task performed by professionals - expensive resources and variable output

Often difficult to evaluate for quality

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Agenda

• Process Characterization • Operational Measures:

Time, Inventory and Throughput• Little’s Law• Flow Time Analysis

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Business Process Flows

Movement of flow units through a network of activities where resources transform inputs into outputs.

Inputs Outputs

Information

Network ofActivities and Buffers

Resources

ProcessManagement

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Definition: Process Flow Measures Flow Time (T): The average time a job spends in

the process Inventory (I): The average number of jobs

accumulated in the process Throughput, or Flow Rate (R): The average rate

at which jobs flow through a process (units/time)

Turnover: The ratio of throughput to average inventory (inventory turn)

Capacity: The largest sustainable flow rate possible


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Agenda



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Little’s Law…relating process flow measures

Inventory = Throughput x Flow Time

I = R x T Turnover = Throughput / Inventory = R/I

= 1/ T

Inventory I[units]

Flow rate or Throughput R

[units/hr]... ...... ......

Flow i[hrs]


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Material Flow: Bakery We are a bakery that specializes in making bread. We bake our bread

in batches of 100 loaves at a time. The typical inventory of bread in our bakery is 9 batches and we produce an average of 100 loaves per hour.

What is the average flow time of a batch of bread?

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Process Flow Examples

(1) Material Flow: A fast-food restaurant processes an average of 5,000 lb. of hamburgers per week. The typical inventory of raw meat is 2,500 lb. What is the average hamburger’s flow time and the restaurant’s turnover?

(2) Customer Flow: The above fast-food restaurant processes on average 1,500 customers per day (15 hours). On average there are 75 customers in the restaurant (waiting to place the order, waiting for the order to arrive, eating etc.). How long does an average customer spend at the restaurant and what is the average customer turnover?

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(3) Job Flow: A branch office of an insurance company processes 10,000 claims per year. The average processing time is 3 weeks. Assuming 50 weeks in a year, what is the average number of claims “in process”.

(4) Cash Flow: A major manufacturer sells $300 million worth of cellular equipment per year. The average accounts receivable in the cellular group is $45 million. What is the average billing to collection process flow time?

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(5) Material Flow: A general manager at at a pharmaceutical company states that her inventory turns three times a year. She also states that everything that the company buys gets processed and leaves the docks within six weeks. Are these statements consistent?

(6) Shouldice Hospital: Shouldice performs 137 surgeries per week, and the average patient stays 4 days. There are 125 regular hospital beds, and 12 pressure sensitive beds for patients susceptible to bed sores. What is the average number of beds occupied at Shouldice?

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(7) AIMD: The AIMD (Aircraft Intermediate Maintenance Division) onboard USS Roosevelt has an average of 13 hydraulic actuators awaiting repair at any given time. Last year, they repaired 156 actuators.

a) What is the flow time for hydraulic actuators at AIMD?

b) If the AIMD could cut flow time by 10%, by how much would the average inventory go down?

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(8) NADEP: The F-18 Repair shop at NADEP JAX (Naval Aviation Depot, Jacksonville) repairs engines in an average 86 days. They receive (and ship) an average of 30 engines per month.

a) What is the average number of engines at the NADEP?

b) At $3 million per copy, what is the value of the inventory?

c) By how much would the value of inventory decrease if NADEP could cut T by 1 day? 2 days? 30 days?

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Little’s Law -- Caveats Applies to the long run average of a stable system

– In any given time period (sample) the average may be different (especially for small samples)

– In an unstable, or dynamic system, the average may not be very useful

In systems with variance, we often need to know about more than the average– Fast Food Example (2) (what does Little’s Law tell us? Is that enough?)– More in chapter 8

Source: Ken Doerr, NPS 2002

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Agenda



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Process Flow Measures Flow Time (T): The average time a job spends in the process Inventory (I): The average number of jobs accumulated in

the process Throughput, or Flow Rate (R): The average rate at which

jobs flow through a process

Little’s LawI = R x T


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Why Flow Time (T) Matters

Reduced manufacturing flow time means– short delivery response time– reduced inventory (Little's Law) which in turn lowers cost– production closer to time of sale which increases (demand)

predictability– fast feedback on quality problems

Reduced development flow time means– quicker time to market (resulting in larger market share)

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Example: ZARA (Inditex)

„… possibly the most innovative and devastating retailer in the world“ (Daniel Piette, Louis Vuitton - Fashion Director)

Source: Business Week, 4 April, 2006

Two weeks to develop a new product and get it to stores (9-month industry average)

10,000 new designs each year Only limited production in low-cost countries Zero advertising

World's fastest growing retailer (3,100 stores, 70 countries) 32,000 employees and 200 fashion designers

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0 10 20 30 40 50

GM

Ford

Honda

Toyota From concept approval to production

MonthsMonths

Company

46

37

36

27

Mean Development Time

Importance of Short Development Times

Source: Operations Management, NPS 2003

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Average Flow Time consists of …

Theoretical Flow Time (Processing Time)

+Waiting time

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Process Flow Chart …

… is the visual representation of a business process showing major activities and their inter-relationships.

Inputs Outputs

Information

Network ofActivities and Buffers

Resources

ProcessManagement

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Operational Measures – Flow Time Activity Time, or Cycle time: Is the time required by a

typical flow unit to complete an activity once (Theoretical) Flow Time: Min. time required for

processing a typical flow unit through the whole process – without any waiting

Critical Path: A sequence of activities that takes the longest total (flow) time for completion

Critical Activities: All activities on a critical path

Flow Time Efficiency =


TimeFlowAverageTimeFlowlTheoretica

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Agenda



- Critical Path Identification

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Critical Path Example: Pusan Port (Korea)

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Critical Path - Definitions

Critical path consists of all activities that have a slack time of zero

Slack Time = LST - EST = LFT - EFT

EST: Earliest Start Time EFT: Earliest Finish Time

LST: Latest Start TimeLFT: Latest Finish Time

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Critical Path - AlgorithmA. Visit all activities from “start to finish”1. EST(first activity) = 02. EFT = EST + activity time3. EST(max EFT of all predecessors)

B. Now visit all activities from “finish to start” LFT(final activity) = EFT (final activity) LST = LFT – activity time LFT = (min LST of all successors)

C. Calculate Slack Times = LST - EST = LFT - EFT

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Critical Path Example: Project Scheduling

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Complex Example …

03. lecture - little's law

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