Hub-and-Spoke Liner Shipping Network Design with Demand ... · Hub-and-Spoke Liner Shipping Network...
Transcript of Hub-and-Spoke Liner Shipping Network Design with Demand ... · Hub-and-Spoke Liner Shipping Network...
Hub-and-Spoke Liner Shipping Network Design
with Demand Uncertainty
Speaker: Wang Tingsong
03/Jun/2013
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Introduction
Literature Review
Problem Statement
Model Development
Solution Algorithm
Numerical Example
Conclusion
Outline
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Introduction
Liner Shipping
Regular service
Fixed schedule
Fixed route
A liner container shipping company typically operates a fleet
of heterogeneous ships on a set of liner trade routes at a
regular schedule in order to pick up and delivery cargoes for
shippers
Liner Operator
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Introduction (cont’d)
Hub-and-Spoke (H&S)
Main line: hub ports allocation
Feeder line: feeder ports allocation
Fleet deployment: ship assignment to main line and feeder line
to provide pickup and delivery liner shipping service for shipper
Uncontrollable and unpredicted factors
Container shipment demand of a port pair
Uncertainty
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Introduction (cont’d)
Objectives
How to design main line and feeder line?
How to deal with uncertainty of container shipment demand?
Model and solution algorithm
Evaluation by implementing a numerical example
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Literature Review
Representative literature Author (s) Year Model Problem Statement
Maurao et al 2001 IP Assign ships with hub and spoke constraints
Aversa et al 2005 MIP Locate a hub port in the East coast of South America
Imai et al 2006 IP Analyze mega ship viability and propose a model to deploy mega ship onto H&S shipping network
Konings 2006 Analyze the cost, service and
geographical characteristics of H&S networks
Hsu and Hsieh 2007 MIP A two-objective model to design a shipping network by minimizing shipping cost and inventory cost
Takano and Arai 2008 MIP Containerized cargo transport problem with H&S network
Imai et al 2009 MIP Compare multi-ports liner shipping network and H&S
network
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Problem Statement
Given a set of ports which can be divided into two groups: hub
and spoke, and given a set of ships which can be divided into
two groups: mega ship and feeder ship, it intends to make an
optimal hub-and-spoke shipping network design to minimize the
total cost over a given short-term planning horizon while
satisfies a predetermined service-level.
How to design main line?
How to allocate the feeder ships to each feeder line?
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Problem Statement (cont’d)
Assumption
The planning horizon is 6 months
Containers are homogeneous, all refer to TEUs
The liner operators are required to maintain a weekly shipping
frequency only on main line
The time of ships travelling between any two pots are known and
fixed
No direct link between any two spokes
Containers can be transferred via at most two hub ports
Model Development
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A typical hub-and-spoke liner shipping network
hub main line
spoke
feeder line
mega ships
feeder ships
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Model Development(cont’d)
Decision Variables
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Model Development (cont’d)
Objective Function
,
intrinsic cost
,
transport
min
Feeder Mega
Feeder Mega
Feeder Feeder Mega Megakhs k vhj v
s h h jk v
Feeder Feeder Mega Megakhs khs vhj vhj
s h h jk v
Z c z c z
c x c x
∗ ∗
∈ ∈ ∈∈ ∈
∈ ∈ ∈∈ ∈
= + +
+
∑∑ ∑ ∑ ∑
∑∑ ∑ ∑ ∑
S H HV V
S H HV V
ing cost
transshiping cost
Feeder Mega
trans Feeder trans Megah khs h vhs
s h s hk v
c y c y∈ ∈ ∈ ∈∈ ∈
+
+∑∑ ∑ ∑∑ ∑
S H S HV V
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Model Development (cont’d)
Constraints
Ship constraints
Chance constraints
capacity constraints , , ,Feeder Feeder Feeder Feeder
khs k kx z C k h s≤ ∀ ∈ ∈ ∈V H S, , ,Mega Mega Mega Mega
vhj v vx z C v h j≤ ∀ ∈ ∈V H
, , ,Feeder Feeder Feederkhs khsy x k h s≤ ∀ ∈ ∈ ∈V H S
, , ,Mega Mega Megavhs vhj
sy x v h j
∈
≤ ∀ ∈ ∀ ∈∑S
V H
( ) maxˆ δ, , ,Feeder Feeder Feeder Feeder Feederk khs kh k khsz t t t k h s+ ≤ ∀ ∈ ∈ ∈V H S
( ) max
,
ˆ δ,Mega Mega Mega Mega Megav vhj vj vhj v
h jz t t t v
∈
+ ≤ ∀ ∈∑H
V
δ1, ,Feeder Feederkhs
sh k
∈
≤ ∀ ∈ ∈∑S
H V
δ1, ,Feeder
Feederkhs
k
h s∈
≥ ∀ ∈ ∈∑V
H S
,
δδ7, , ,Mega
Mega Mega Mega Megavhj vhj vhj
h jv
t v h j∈∈
≥ ∀ ∈ ∀ ∈∑ ∑HV
V H
Prξ, , 1Feeder
Feeder Feederk k hs
k
z C h s∈
≥ ∀ ∈ ∈ ≥ −α
∑V
H S
Prξ, , 1Mega
Mega Megav v hj
v
z C h j∈
≥ ∀ ∈ ≥ −α
∑V
H
Transshipment constraints
Time constraints
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Solution Algorithm
Difficulties of Solving the Model
Nonlinear
Probabilistic form
( ) max
,
ˆ δ,Mega Mega Mega Mega Megav vhj vj vhj v
h jz t t t v
∈
+ ≤ ∀ ∈∑H
V
Prξ, , 1Feeder
Feeder Feederk k hs
k
z C h s∈
≥ ∀ ∈ ∈ ≥ −α
∑V
H S
Prξ, , 1Mega
Mega Megav v hj
v
z C h j∈
≥ ∀ ∈ ≥ −α
∑V
H
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Solution Algorithm (cont’d)
Linearization It is noticed that if decision variables is removed, then
the problem is reduced to a mixed integer linear programming
(MILP) model with chance constraints.
If the mega ship v serves only two ports and does not visit any
other port enroute, it makes the maximum number of trips; if it
serves all ports enroute, it makes the minimum number of
trips
For example, if 2 ≤ ≤ 5, then has 4 values: 2,3,4,5.
For each problem with a corresponding value of , it is a
MILP model with chance constraints.
Megavz
Megavz Mega
vzMegavz
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Solution Algorithm (cont’d)
Sample Average Approximation (SAA)
Let
( ) ( )( ): Pr , 0Mega ML MegaMegap = ∆ >z zξ
( ),
, maxξFeeder
FL Feeder Feeder FeederFeeder hs k kh s
k
z C∈ ∈
∈
∆ = −
∑zξ
H SV
( ),
, maxξMega
ML Mega Mega MegaMega hj v vh j
v
z C∈
∈
∆ = −
∑zξ
HV
We then define ( ) ( )( ): Pr , 0Feeder FL FeederFeederp = ∆ >z zξ
Rewrite the chance constraints
Prξ, , 1Feeder
Feeder Feederk k hs
k
z C h s∈
≥ ∀ ∈ ∈ ≥ −α
∑V
H S
Prξ, , 1Mega
Mega Megav v hj
v
z C h j∈
≥ ∀ ∈ ≥ −α
∑V
H
( )Feederp ≤ αz
( )Megap ≤ αz
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Solution Algorithm (cont’d)
SAA(Atlason et al., 2008; Luedtke and Ahmed, 2008)
Let ( ) ( ) ( )( )0,1
,Feeder
NN Feeder FL Feeder n
np N∞
=
= ∆∑z zξ 11
( ) ( ) ( )( )0,1
,Mega
NN Mega FL Mega n
np N∞
=
= ∆∑z zξ 11
( ) ( )0,
1, if 0,:
0, if 0.y
yy∞
>= ≤
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Then ( )Feederp ≤ αz
( )Megap ≤ αz
( )N Feederp ≤ βz
( )N Megap ≤ βzβ can be different with α
Law of Large Number Theory
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Solution Algorithm (cont’d)
MILP
{ }β min intrinsic cost transporting cost transshiping costNZ = + +s.t.
Ship constraints + Chance constraints
capacity constraints + Transshipment constraints +
ξξ, 1, , ; ,Feeder
Feeder n Feeder Feeder nn hs k k hs
k
z C n N h s∈
ϑ + ≥ ∀ = ∀ ∈ ∈∑ V
H S
1
NFeedern
nN
=
ϑ ≤ β∑
ξξ, 1, , ; ,Mega
Mega n Mega Mega nn hj v v hj
v
z C n N h j∈
ϑ + ≥ ∀ = ∀ ∈∑ V
H
1
NMegan
nN
=
ϑ ≤ β∑ { }, 0,1 NFeeder Megan nϑ ϑ ∈
( )N Feederp ≤ βz
( )N Megap ≤ βz
equivalent
equivalent
Time constraints +
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Solution Algorithm (cont’d)
Solution quality(Luedtke and Ahemd, 2008)
Lower bound
Let , is a lower bound of Z with a significance level ε Lβα > LNZβ
Upper bound
Let , is a upper bound of Z with a significance level ε Uβα < UNZβ
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Numerical Example
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Results
Sensitivity Analysis of SAA Parameters
Results(cont’d)
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Shanghai
Hong Kong
Singapore Penang
Port Kelang
Shekou
Xingang Dalian
Qingdao
Results(cont’d)
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Conclusion
A H&S shipping network design problem
Demand uncertainty
Linearization
SAA
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