Modeling a Scenario-based Distribution Network Design Problem in a Physical Internet-enabled open Logistics Web

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Helia Sohrabi

Laval University, CIRRELT, Canada

Walid Klibi

BEM- Bordeaux Management School, CIRRELT, France

Benoit Montreuil

4th_{International conference on Information} Systems, Logistics and Supply Chain

Quebec City August 26-29, 2012

Modeling a Scenario-based

Distribution Network Design Problem

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Helia Sohrabi, Walid Klibi and Benoit Montreuil

Presentation plan

 Current distribution context

 Physical Internet initiative: Introduction

 Research methodology

 Future business environment modeling

 Distribution network design generation

 Mathematical model

o Generic model

o Context-driven model

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Current distribution context

Closed distribution system

(Private Distribution Network; PDN)

Cost-service trade offs

Addressing changes in the business environment

(e.g. customer expectations, economic instability and energy crisis)

Collaborative distribution system (Shared Distribution web; SDW)

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Physical Internet Initiative:

An Introduction

What is Physical Internet?

An open global logistics system founded on physical and digital interconnectivity through encapsulation, protocols and interfaces

http://physicalinternetinitiative.org

What is Physical Internet goal?

To reduce by an order of magnitude the environmental, economic and social efficiency and sustainability of the way physical objects are moved, stored, realized, supplied and used

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Mobility Web Moving goods & people

Interconnected open unimodal & multimodal infrastructures,

vehicles, hubs and transits

Distribution Web Deploying, storing

products

Interconnected open warehouses & distribution centers

Realization Web Realizing products

Interconnected open production, personalising & retrofit centers

Supply Web Supplying goods

Interconnected open suppliers and subcontractors

Service Web Enabling and sharing

access and usage of services rendered

by goods & people

Interconnected open users and service providers

Logistics Web

Set of openly interconnected physical, digital, human, organizational and social agents and networks aiming to serve efficiently and sustainably

the logistics needs of people, organizations, territories and society

The Physical Internet aims to enable an efficient and sustainable Logistics Web

Research question:

How to design distribution networks exploiting the open distribution web? Research goal:

To investigate the performance improvement (both from economic and

environmental perspectives) achievable by switching from current distribution context to Physical Internet enabled context.

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Research methodology

Distribution Network performance investigation (simulation) Distribution Network design generation

at each distribution context Future business

scenario generation

(Monte Carlo approach)

Distribution Network

design generation

at each distribution context Distribution Network

design generation

at each distribution context

ODW SDW PDN Distribution Network performance investigation (simulation) Distribution Network performance investigation (simulation) For company 1 company m

A single final design in PDN context SDW ODW Kli bi , W . an d Ma rt el, A ( 2 0 1 2 )

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Future business environment modeling

• Applying a novel scenario planning approach based on evolutionary paths

(Klibi and Martel, 2011).

• An evolutionary path is a possible view of the future characterized by the future-shaping variables.

• Future-shaping variables defined:

Demand-market,

Available capacity, (including production , storage capacity)

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Future business environment modeling

Three

defined evolutionary paths

I. Sustainability-unconscious

II. Sustainability-prone

III. Sustainability-engaged

.

• A pessimistic view of the future world

• Based on the unstable situation of several economies in the world and the scramble energy scenario described by Shell (2009).

• A world that is conscious about the need to become more sustainable, yet is slow in moving towards sustainability.

• anticipated to emerge in the parts of the world, mostly in North American and Western European developed countries.

• Moderate improvement in economy and local actions addressing energy security, in line with the blueprint scenario elaborated by Shell (2009)

• A more optimistic view

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Sustainability-unconscious Sustainability-prone Sustainability-engaged

Future business environment modeling

future shaping variables evolution through each evolutionary path

Cost of investment Accessible capabilities

Planning

horizon Planning _horizon

Using a

Monte Carlo

procedure

For each evolutionary path

For each future-shaping variable

A set of scenarios will be generated

This procedure will be

repeated for each company

case with

different characteristics

independently

from each other.

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Distribution network design generation

Strategic reengineering process

Yearly/quarterly planning period 𝐭 ∈ 𝑻

Planning horizon

Weekly/Daily working period τ ∈ 𝒕(τ)

Transportation cost in a scenario

Demand cost in a scenario

Available capacity cost in a scenario

A reengineering cycle

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Schematic representation of three distribution

contexts

Planning horizon PDN ODW Planning horizon SDW

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Facilities fixed and usage costs in different contexts

Initial state Do not use the site Use the site

Decision Fixed cost Decision Fixed cost Usage cost

Current facility

Own (o)

Close Transfer and closing cost

Use during all

the horizon T Capital recovery

Operating cost Rent/Use service (r) Stop for a period Closing cost plus lease penalty Renew rental contract for a period

Lease cost Operating cost

Potential site

Purchase/

Build Do not use Zero

Open and use during all the

horizon T

Setup cost plus capital recovery

Operating cost

Rent Do not use Zero

Agree a rental contract for a

period

Setup cost plus lease cost Operating cost c lL o c l L L l a l a l a r c l L L _t__T , lt a t T tT , a t T a t, T p lL o p l L L l a l a r p l L L _t_T , lt a t T _{a t}_lt_, _T

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The generic mathematical model

Customer-DC assignment constraints:





 







 



 





, r o o t lt lt lt lt lt lt lt lt t T l L l L l l l l l L E NOP Max R x a x a x a x a x a x a x                                   



Subject to: lst lt

x



x

1 lt lt x x 

DC state constraints (for rented facilities):

(1) , l L s S  and t T (2) (3) , r l L t T

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The generic mathematical model

continued

DC opening/closing constraints:

Non negativity constraints:

( 1)

0

lt lt lt l t

x



x



x



x

_



1 l l x  x  DC state constraints : 0 0 lt t l l l x x x x T      



DC state constraints : , , , , , {0,1} lt lst lt lt l l x x x x x  x  (4) , r l L t T o

l



L

(5) o

l



L

(6) (7) , , l L sS t T

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The generic mathematical model

continued

Transportation cost

Inventory cost

Recourse capacity acquirement cost

Where for a given planning period





_{, ,} , , [( ( ) ( ) ( ( ) ( )) ( )) t l l t _T _{p l s S} ps pls e e ps ps ps p s S R Max u F u f F                  



x

 

   

' ' ' , , , , ( ) ,

)]

pvl pvl p v l pll pll p l l L S pl pl p l l l l

f

F

f

F

g

I

k

Z

       



 





Total income – external sourcing cost

t T

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The generic mathematical model

continued

Subject to:

Capacity constraints:

Customer assignment constraints:

Inventory/ product flow constraints:

( ) ( ( )) ( ) ( ) pl p pls l l pI    pc s S F    b   Z 



, t pls ( ) , t ps ( ) lst pT F    pT d   x



( 1) ₍ ₎ ₍ ₎ ( ) ( ) ( ) ( ) pl pl _l _{L V} pl l _l _{L S} pll I _   I __  



__{ } F __  



__{ } F __  , , lL sS



 (9) , t, lL  T  (10) , , t, pP lL  T  (11)

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The generic mathematical model

continued

Initial inventory constraints:

Demand satisfaction flow constraints:

Recourse capacity constraints:

0

( )

0

pl

I

__





( ) e ( ) ( ) ( ) ps ps _{l L} pls ps d _



 F _







_ F _



 d _



Production capacity constraints:

Integrality and non negativity constraints:

( ) ( ) pvl pv l L F    b  



( ), ( ), e ( ), ( ), ( ) 0 pvl pll ps l pl F _



F __



F _



Z_



I _



 1 , , , pP lL  T  (12) , , t, pP sS  T  (13) , t, lL  T  (14) , , t, pP vV  T  (15) ( ) ( ) l l l lt Z_







b_



x

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Context-driven design models

Current context(closed)

• Private distribution network

 The design model in PDN is similar to the generic model (1)-(16)

 The optimal design solution is denoted by and the value of this solution is denoted by .

*

x





 

*

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 Group of M partnering companies

 Each company designs a distribution web maximizing its own performance subject to joint capacity restrictions for each shared facility

 The sets of locations dedicated to each company

 The set of shared facilities

 The portfolio of available resources

 The optimal solution and its value

Context-driven design models

Current context(collaborative)

• Shared distribution web

* m x





 

* m E_ NOP x m m

L



L



V L S_m, _m, _m



  ' ' \ m _m _M _m m m

L





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Context-driven design models

Open distribution web context

• Companies mostly deploy their products independently from each other even though collaborative behavior such as in SDW is possible.

• Dynamic available capacity

• Two additional set of resources :

 All private facilities operated by other companies

 Public facilities whose storage capacity is completely open to the market,

denoted by

 Ultimately, the open distribution web includes both companies, and third-party logistics providers openly offering distribution storage capacity. ( ) l b_  m L w m L w m m m m L  L  L  L

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Final remarks and future work

Final remarks

:

• Sample Average Approximation (SAA)

(period sampling, scenario

sampling and/or aggregations)

• Exact approach

(OPL-CPLEX) / Tabu based

metaheuristics

Future work:

 To validate the model on a representative case

 Comparison between the three alternative designs in different distribution contexts studied using a large set of scenarios and a various set of criteria such as: delivery speed, eco-efficiency, resiliency, etc.

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Your questions

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