Manufacturing System Flow Analysis

Ronald G. AskinSystems & Industrial Engineering

The University of ArizonaTucson, AZ 85721

ron@sie.arizona.edu

October 12, 2005

How Many IEs Does It Take to Change a Light Bulb?

n?

• One to Work Sample to Detect Burned out Bulbs• One to Flowchart the Process • One to Schedule the Maintenance• One to Supervise the Maintenance Task• One to Implement a Process Improvement Plan/Kaizen

Event• One to Determine Optimal Lumens for Replacement Bulb• One to do an Economic Analysis of Buying Longer Life

Bulbs• …

Overview of Session

• The Modern (Lean) Factory• WIP vs. Flowtime & Throughput (Little’s Law)• Transfer Batches vs. Process Batches (Lot-streaming)• Cross-Training (Balancing and Buckets)• Performance Evaluation – Open & Closed Cells

1. Factory Flow Thru Cell System

Gears Chassis

Shafts Cards Frame

Assembly

Flow in a Cell

J. T. Black, Design of the Factory with a Future, 1991

Cell Independence (Burbidge)

• Dedicated Team of (Compatible) Workers• Dedicated Set of Machines• Specified Set of Parts/Products• Dedicated Space for Operations• Common Goal and Evaluation• Independence of Success• Ideally 7-10 Members

2. Little’s Law: Defining Rule for Flow

L = λW (N = XT)

WIP = Prod. Rate x Flow Time

Theoretical Profile!

Capacity Deterministic

Production

Probabilistic (Exponential)

WIP

N = X T

Empirical ProfileLittle's Law and Chaos

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70 80 90

WIP

Thr

ou

ghp

ut

Deterministic

Exponential

Empirical

10 stages, µ = 1

RememberN = XT

Questions?

• What happens when we release jobs to a busy shop floor?

• What happens when we reduce variability?

Typical Scenario: High Utilization, So Jobs are Late, Therefore Release More Jobs Early

L=λW (or N=XT)1. λ high implies ∆λ small;2. Since L increases, W increases;3. As W (lead time) increases, tempted to release

jobs even earlier4. Congestion and interference reduce throughput

Reducing Variability

General Arrivals (λ) and Service (S)

( ) ( )[ ]

2 2 2 2 2

2 2

( ) ( ) ( )

1( )

2 (1 )1

q

s a s

q

s

E ThroughputTime E W E S

C C CE W

C

ρ ρλ ρρ

= +

+ +≈ ⋅

−� �+� �

( )E Sρ λ= ⋅(ρ = X ÷÷÷÷ Capacity)

Question: How Far Is the Blue (Random) Line from the Purple (Deterministic) Line?

• ρ = 0.8, • Exponential Arrivals vs. Fixed Interarrivals• Random Service vs. Standardized Service

What happens if we release jobs at fixed intervals?What happens with reliable processes & standard tasks?

3. Transfer vs. Process Batches

• Lot-Streaming – Dividing the process batch into multiple transfer batches for concurrent processing at successive stages

Simple Illustration

• Three stages• Batch size = 20• Unit proc. times = 1, 3, 2• No setup

a. One Transfer Batch

b. Two Transfer Batches

. . .

0 1 4 20 61 63

c. Single Unit Transfer Batches

Machine

1

2

3

Time 120 80 20

Machine

1

2

3

Time 10 40 70 90

Machine

1

2

3

Time

MH vs Thruput Time TradeoffMH Loads vs. Cycle Time

0

5

10

15

20

25

0 20 40 60 80 100 120 140

Cycle Time

MH Loads

Basic Rules (L Sublots, Q units)

1. Consistent, equal sublots good (not optimal)

(p2 qi = p1 qi+1 is optimal for adjacent WSs)

2. Decreasing marginal benefit:

2 sublots � 50% of max gain

3. Protect bottleneck (avoid sublot setup loss)

b ii b

QT Q p p

L ≠

= ⋅ + ⋅�

4. Cross-Training

• Ensure Redundancy• Consider Job Enrichment as Motivator• Task Frequency Sufficient for Proficiency• Lead Experts for Each Task• Cover all Responsibilities• Pay per Skill Breadth and Depth• Worker Flexibility vs. WIP Safety Stock

a. Dynamic Rebalancing

1

4 min 3 min

6 min

8 min 3 min

a. Two Workers

1

4 min 3 min

6 min

8 min 3 min

b. Three Workers

Part Flow

Worker Flow (Orbit)

Workstation

Total Time = 24

b. Bucket Brigades (TSS) & Variants

• BBAssumes Task ContinuityOrdered WorkersSlowest to FastestEffective in PickingBuffers can be added

•Champion Strategy

(For low machine ρ)

•Leapfrog Strategy

(Less worker movement)

5. Performance Evaluation

• Find X & T given N & Capacity• Find T and needed N for desired X given Capacity• Find T, X Tradeoff

N = X T

Open System (Receive and Release)

Random

Basic Poisson Process Estimate

2. Evaluate Each Workstation

(M/M/1)

P(0) = 1-ρρρρ

L = ρρρρ/(1-ρρρρ)

W = L/λλλλ

1. Compute Effective Arrival Rates at Workstations

' '

1

m

j j k kjk

pλ λ λ=

= + ⋅�

5/day

(A)

6/day (B)

2

6

4

4

5

5

System & Product Measures

3. Aggregate Across Workstations

1

m

j jj

W v W=

= ⋅�

WB= W + .67W + W

Closed System (CONWIP)External Demand

Basic Performance Evaluation - ClosedConsider a Closed System with N Jobs:

1

M

jj

C c=

=� Total Servers or Max Active Jobs

1

M

jj

P t=

=� Total Job Processing time

min( , ) so

C NT P N XT X

P≥ = → ≤

X = Production rate, T = Throughput time

Performance Evaluation Extension

• Assume WIP Evenly Spread Out

As Always, N=XT

11 , Exponential Processing Time

, Constant, Synchronous Processing with

NP

MT

NP N M

M

� −� �+ ⋅ �� ��= ��

� �� ⋅ ≥ � � �

Very Optimistic Model! No Starvation when N ≥ M

References and Extensions

1. Askin, R. & J. Goldberg, Design and Analysis of Lean Production Systems, Wiley& Sons, 2002

2. Askin, R. & C. Standridge, Modeling and Analysis of Manufacturing Systems, Wiley & Sons, 1993

3. Black, J. T., Design of the Factory with a Future, McGraw Hill, 1991

4. Harmon, R & L. Peterson, Reinventing the Factory, Free Press, 1989

5. Hopp, W. and M. Spearman, Factory Physics, McGraw Hill, 2000.