Logistic Network Design For Closed â€“ Loop Supply Chains

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

Northwestern UniversityTransportation 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



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Returns

SourcesCustomer driven (commercial returns, quality issues)

Firm driven (value recovery, legislation, competition)

Operational ImpactMany industries suffer from high return rates

Financial ImpactEstimated U.S. value = $100B annually0.5 – 1.0% U.S. GDP



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Research Framework

Raw Materials

Parts Production Assembly Distribution Consumer

Forward Logistics

Reverse Logistics

Reuse

Refurbishing

Remanufacturing

RecyclingLandfill



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Research Framework

Strategic Tactical Operational

Distribution network design

Capacity planning

Inventory management

Production planning / scheduling

Demand / Return forecasting

Firm driven

Consumer driven

Problem level

Return type

Integrated Bidirectional

Network Design

Customer Behavior Influenced CLSC Network Design

Lifetime Buys in Warranty Repair

Operations



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Research Framework

Raw Materials

Parts Production Assembly Distribution Consumer

Forward Logistics

Reverse 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 DemandCommercial 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

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

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




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Co-location Incentive Model

Case: Combined Commercial & End of Life Returns Handling

Minimize

Subject to

Jj

Cj

Cj Xs

Jj

Fijiji

IiJj

Fjj YchXf

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 23 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 30 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



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

hi = 100λi = 0.25

dij = 8 hij = 13.5dik = 3 hik = 47.2dim = 15 him = 2.4

Total: 63.1

ijidiij ehh

hi = total demand at node i

dij = distance between node i and facility jλi = 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 = 100λi = 0.25

dij = 8 sij = 1 hij = 13.5dik = 3 sik = 1 hik = 47.2dim = 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

Jk

dikk

dijj

ij ik

ij

esXesX

p



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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 FormulationThis model can be effectively solved using a genetic algorithm heuristic



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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



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ExampleMaximize 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

over

ed d

eman

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



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A CLSC Model with Distance-Sensitive Demand and Returns

Ii }0\J{j

RR

Ii }0\J{j

FFjjjj

XfXf

Ii }0\J{j

RRR

Ii }0\J{j

FFFijiiji

phrphr

1X ,X RF00

Revenue from satisfied demand &

collected returns

Fixed location costs

Variable transportatiocosts

}1,0{X ,X RFjj Jj Binary location

variables

“Lost Demand” Facility is Open

Max

Subject to

Ii }0\J{j

RRR

Ii }0\J{j

FFFijiijijiij

phcphc

Ii }0\J{j

Fij

Fi

Ii }0\J{j

Rij

Ri phph Collect at least

α% of sold items



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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)



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Questions?

Documents

Logistic Network Design For Closed â€“ Loop Supply Chains