Presentation

Kristin Sahyouni joint work with R. Canan Savaskan and Mark S. Daskin

Northwestern University

Transportation Center

March 29, 2007

Logistic Network Design ForClosed – Loop Supply Chains

Logistic Network Design For Closed – Loop Supply Chains

Kristin SahyouniNorthwestern University Transportation Center

March 29, 20072 / 33

Overview

Research Framework

Motivation and Definitions

Customer Driven Network Design Product Lifecycle Influences

Value and Impact of Bidirectional Decision Frameworks

Firm Driven Network Design Modeling Distance Sensitivity

Profit-Driven and Compliance-Driven Models

Future Research



March 29, 20073 / 33

Returns

SourcesCustomer driven (commercial returns, quality issues)

Firm driven (value recovery, legislation, competition)

Operational Impact Many industries suffer from high return rates

Financial Impact Estimated U.S. value = $100B annually

0.5 – 1.0% U.S. GDP



March 29, 20074 / 33

Research Framework

Raw Materials

Parts Production

Assembly Distribution Consumer

Forward LogisticsForward Logistics

Reverse LogisticsReverse Logistics

Reuse

Refurbishing

Remanufacturing

RecyclingLandfill



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Research Framework

OperationalTacticalStrategic

Capacity planning

Inventory management

Consumer driven

Firm driven

Production planning / scheduling

Demand / Return forecasting

Distribution network design

Problem level

Return type

Integrated Bidirectional

Network Design

Customer Behavior Influenced CLSC Network Design

Lifetime Buys in Warranty Repair

Operations



March 29, 20076 / 33

Research Framework

Raw Materials

Parts Production

Assembly Distribution Consumer

Forward LogisticsForward Logistics

Reverse LogisticsReverse Logistics

Reuse

Refurbishing

Remanufacturing

RecyclingLandfill



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Research Questions

What is the VALUE and IMPACT of integrating forward and reverse network decisions

throughout the product lifecycle?

in various industries?



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Life Cycle Considerations

IntroductoryStage

Forward Dominant

Model

MaturityStage

DeclineStage

Product Demand

Commercial Returns

End of Life Returns

Co-LocationModel

Reverse Dominant

Model



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Integrated Bi-Directional Networks

Integrated by location constraints

Integrated by financial incentives

F FFR

Forward Dominant Model

R RFR

Reverse Dominant Model

Demand node

Forward flow

Reverse flow

Co-Location Model

FR

F R



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Model Development

Recall the Uncapacitated Fixed Charge Problem (UFC):



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Case: Retail Returns

Minimize

Subject to

∑∑∑∈∈∈

+Jj

Fijiji

IiJj

Fjj YchXf

∑∈

=Jj

Fij 1Y

Fj

Fij XY ≤

Ii ∈∀

JjI,i ∈∈∀

{0,1}XFj =

Jj∈∀

0YFij ≥

∑∑∑∈∈∈

γ++Jj

Rijijijii

IiJj

Rjjj YchαXfβ

∑∈

=Jj

Rij 1Y

Rj

Rij XY ≤

{0,1}XRj =

0YRij ≥ JjI,i ∈∈∀

Rj

Fj XX ≥

Jj∈∀

assignment

open facilities

binary

non-negativity

linking

Solve using Lagrangian Relaxation

Relax Assignment Constraints

F FFR




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Case: Recycling Networks

Minimize

Subject to

∑∑∑∈∈∈

+Jj

Fijiji

IiJj

Fjj YchXf ∑∑∑

∈∈∈

γ++Jj

Rijijijii

IiJj

Rjjj YchαXfβ

∑∈

=Jj

Fij 1Y ∑

∈

=Jj

Rij 1Y

Fj

Fij XY ≤ R

jRij XY ≤

Ii ∈∀

JjI,i ∈∈∀

{0,1}XFj = {0,1}XR

j =

Jj∈∀

0YFij ≥ 0YR

ij ≥ JjI,i ∈∈∀

Rj

Fj XX ≤

Jj∈∀

assignment

open facilities

binary

non-negativity

linking

R RFR




March 29, 200713 / 33

Co-location Incentive Model

Case: Combined Commercial & End of Life Returns Handling

Minimize

Subject to

∑∈

−Jj

Cj

Cj Xs∑∑∑

∈∈∈

+Jj

Fijiji

IiJj

Fjj YchXf ∑∑∑

∈∈∈

γ++Jj

Rijijijii

IiJj

Rjjj YchαXfβ

∑∈

=Jj

Fij 1Y ∑

∈

=Jj

Rij 1Y

Fj

Fij XY ≤ R

jRij XY ≤

Ii ∈∀

JjI,i ∈∈∀

Cj

Fj XX ≥ C

jRj XX ≥

{0,1}XFj = {0,1}XR

j =

Jj∈∀

{0,1}XCj = Jj∈∀

0YFij ≥ 0YR

ij ≥ JjI,i ∈∈∀

Jj∈∀

assignment

open facilities

binary

non-negativity

linkingCo-Location Model

FR

F R



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Non-Integrated Design

Forward Dominant ModelSequential Design

All candidate sites

Forward sites

Reverse sites



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All candidate sites

Reverse Dominant ModelSequential Design

Reverse sites

Forward sites



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Co - Location ModelIndependent Design

All candidate sites

Forward sites

Reverse sites




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Similarity Measure

Solution 1

Solution 2

Solution 3

3 out of 4 common locations

0 out of 4 common locations



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Similarity Measure

Solution 1 Solution 2

3 of 4 locations in common

Total difference between solutions (in miles) = 2153

New York 0 New York

Chicago 0 Chicago

Los Angeles 2153 Jacksonville

Houston 0 Houston



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Similarity Measure

Solution 1 Solution 3

0 of 4 locations in common

Total difference between solutions (in miles) = 190

New York 81 Allentown

Chicago 86 Milwaukee

Los Angeles 7 Burbank

Houston 16 Pasadena



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Similarity Measure

Minimal Distance Matching Formulation

Minimize

Subject to

Solution Method: Modified Out of Kilter Flow Algorithm

∑∑∈∈ nm Xj

ijijXi

Yc

1YmXi

ij ≥∑∈

1YnXj

ij ≥∑∈

0Yij ≥

nXj∈∀

mXi ∈∀

mXi ∈∀ nXj∈∀

ij)j,i(

Xjijij

Xi

cMax

Ycnm

∑∑∈∈normalize to get similarity ratio =



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Results



March 29, 200722 / 33

Extensions

Time Integrated Models

Multiple Products with Overlapping Lifecycles

Customer Behavior Based Networks



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Customer Behavior - Based Networks

Applicable to:

Single use cameras (Kodak) Copy Print cartridges (Cartridge World) Mobile Phones (Recellular) Hard Drives (3P Remanufacturers) Medical Equipment



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Distance-Sensitive Customers



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Demand decays exponentially with distance

Demand at node i served by facility j (hij):

hi = 100

λi = 0.25

dij = 8 hij = 13.5

dik = 3 hik = 47.2

dim = 15 him = 2.4

Total: 63.1

ijidiij ehh λ−=

hi = total demand at node i

dij = distance between node i and facility j

λi = decay factor (distance sensitivity) at node i

i

j

k

m



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Capturing “Lost Demand”

Define an “area of interest” / maximum area of consideration

critical distance = 10

hi = 100

λi = 0.25

dij = 8 sij = 1 hij = 13.5

dik = 3 sik = 1 hik = 47.2

dim = 15 sim = 0 him = 0

Total: 60.7

i

j

k

m



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Capturing “lost demand” in a discrete location model

Add “lost demand facility” at border

∑∈

λ−

λ−

∗∗∗∗

=

Jk

dikk

dijj

ijik

ij

esX

esXp



March 29, 200728 / 33

Profit Maximizing Model

Max

Subject to

∑ ∑∑ ∑∑∈ ∈∈ ∈∈

−−∗Ii }0\J{j

ijiijIi }0\J{j

jj}0\J{j

iji phcXfphr

Revenue from satisfied demand

Fixed location costs

Variable transportation costs

}1,0{X j ∈ Jj∈∀ Binary location variables

1X0 = “Lost Demand” Facility is Open

Non – Linear Integer Formulation

This model can be effectively solved using a genetic algorithm heuristic



March 29, 200729 / 33

Demand Maximizing Model

Max

Subject to

∑ ∑∈ ∈

∗Ii }0\J{j

ijiphr

1X0 =

Revenue from satisfied demand

}1,0{X j ∈ Jj∈∀ Binary location variables

“Lost Demand” Facility is Open

PXJj

j =∑∈

Locate P Facilities



March 29, 200730 / 33

Example

Maximize Satisfied Demand

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

# facilities

% c

overe

d d

em

an

d

N = 577.8%

N = 1094.5%

N = 1599.6%

N = 244.8%

Maximum distance 300 miles

Distance decay factor 0.005263 largest US cities



March 29, 200731 / 33

A CLSC Model with Distance-Sensitive Demand and Returns

∑ ∑∑ ∑∈ ∈∈ ∈

−−Ii }0\J{j

RR

Ii }0\J{j

FF

jjjjXfXf

∑ ∑∑ ∑∈ ∈∈ ∈

∗+∗Ii }0\J{j

RRR

Ii }0\J{j

FFF

ijiijiphrphr

1X ,X RF

00=

Revenue from satisfied demand &

collected returns

Fixed location costs

Variable transportation costs

}1,0{X ,X RF

jj∈ Jj∈∀ Binary location

variables

“Lost Demand” Facility is Open

Max

Subject to

∑ ∑∑ ∑∈ ∈∈ ∈

−−Ii }0\J{j

RRR

Ii }0\J{j

FFF

ijiijijiijphcphc

∑ ∑∑ ∑∈ ∈∈ ∈

α>Ii }0\J{j

Fij

Fi

Ii }0\J{j

Rij

Ri phph Collect at least α

% of sold items



March 29, 200732 / 33

Extensions

Other Mechanisms to Influence Customer Return Behavior:

Future purchase incentives (mobile phones)

Cash Redemption / Payments / Deposit-Refund

Future Research Bounding & exact solution methods Integrate other customer behavior models into

CLSC network design problems (MCI & MNL models)



March 29, 200733 / 33

Questions?

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