03. lecture - little's law
DESCRIPTION
Little's LawTRANSCRIPT
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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
Source: Managing Business Process Flows (1999)
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
Source: Managing Business Process Flows (1999)
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Agenda
• Process Characterization • Operational Measures:
Time, Inventory and Throughput• Little’s Law• Flow Time Analysis
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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]
Source: Managing Business Process Flows (1999)
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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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Process Flow Examples
(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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Process Flow Examples
(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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Process Flow Examples
(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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Process Flow Examples
(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
• Process Characterization • Operational Measures:
Time, Inventory and Throughput• Little’s Law• Flow Time Analysis
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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
Source: Managing Business Process Flows (1999)
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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 =
Source: Managing Business Process Flows (1999)
TimeFlowAverageTimeFlowlTheoretica
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Agenda
• Process Characterization • Operational Measures:
Time, Inventory and Throughput• Little’s Law• Flow Time Analysis
- 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 …