and-spoke routing on a maritime container network

Direct versus hub

Direct versus hub

-

_-

and

_and

-

_-

spoke routing

_{spoke routing}

on a maritime container network

on a maritime container network

Chaug-Ing Hsu and Yu-Ping Hsieh

Department of Transportation Technology & Management National Chiao Tung University, Taiwan

Introduction

Introduction

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-

Motivation

Motivation

Container carriers operate in an increasing

competitive and market-driven environment.

Most of them continuously provide their services

using hub-and-spoke networks.

Under a hub-and-spoke networks, economies of

flow can be realized by consolidating freight

through a hub and using large ships.

Routing all freight through a hub is not

appropriate in any situations.

Introduction

Introduction

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-

Motivation

Motivation

Although the average shipping cost per TEU decreases on main-line of hub-and-spoke networks,

Freight originated in feeder ports must be transshipped through a hub, and incur extra shipping distance, shipping time, port charges and loading/unloading charges.

Container carriers must decide whether to route a shipment through a hub or directly to its destination.

This study constructs an analytical model on exploring this issue.

Introduction

Introduction

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-

Literature Review

Literature Review

Previous studies were focused on general networks, while studies about hub-and-spoke networks were few.

Some proposed employing constraints to deal with the characteristic of transshipment.

Some introduced cost discount on main-line shipping to deal with flow economics.

Differing from previous studies, this study formulates flow-dependent cost functions and constructs a two-objective model to deal with this two characteristics, respectively.

Introduction

Introduction

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-

Methodology

Methodology

Based on that ocean carriers consider not only lowering their shipping costs, but also enhancing their service, thereby

attracting more shippers.

The inventory costs usually are the main considerations of shippers.

A two-objective model by individually minimizing shipping costs and inventory costs is constructed.

This model not only provides flexibility for ocean carriers in routing, ship size decision-making, but also provides a tool to analyze the trade-off between these two costs.

Introduction

Introduction

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-

Objective

Objective

Formulate both shipping and inventory cost

functions by analyzing a multi-port calling route.

Determine the Pareto optimal solutions of the

two-objective model.

Show the optimal routing, ship size and sailing

frequency with respect to each level of inventory

cost.

Present an example that demonstrates the

usefulness of the proposed model.

Cost Functions

Cost Functions

Shipping Cost Function, TC1m

Shipping costs can be divided into three main

categories: Capital and operating cost, fuel cost, and port charge. +         + + + =

∑

∑ ∑

(

)

∑

(

)

∑∑

∑

Capital and operating cost

Fuel cost

Cost Functions (Cont.)

Cost Functions (Cont.)

Inventory cost function, TC2m

Inventory costs represents opportunity cost or loss of value that cargo cannot be used or sold in the shipping process.

Only inventory costs related to container shipping process are taken into account, involving the waiting time cost and the shipping time cost.

(

)

∑∑∑∑

∑∑∑

∑∑

2 Waiting time cost

Ship Size and Sailings Frequency Decision

Ship Size and Sailings Frequency Decision

For any type of ship, there is a trade-off between shipping costs and inventory costs.

The relationship is a hyperbolic function:

A complete optimal solution does not exist due to these two costs conflict with each other.

TC2m

TC1m

(TC2m

t,TC1mt)

Shipping costs(TC1m_{) decrease as}

Ship Size and Sailings Frequency Decision

Ship Size and Sailings Frequency Decision

Instead of a complete optimal solution, the Pareto optimality concept introduced herein.

The Pareto optimality is the solution where no objective can be reached without simultaneously worsening at leasing one of the remaining objectives.

The hyperbolic function indicates not only trade-off

between two costs, but also solutions for the two-objective model.

Consider the capacity constraint, then the feasible solutions can be determined.

Routing Decision

Routing Decision

Whether shipping through a hub or directly to its

destination can be determined by comparing Pareto optimal solutions for the two types of shipping routes.

Since Pareto optimal solutions for one feeder line won’t be affected by all other feeder lines, only costs on three lines are considered.

Shipping through a hub Shipping directly to its

Feeder line, qs_-qd Direct line, qd Main line, qh_-qd spoke

hub hub Main line,_qh

spoke

hub hub

Feeder line,

Routing Decision

Routing Decision

Costs for shipping through a hub

The total shipping costs(TTC1t_{) and inventory} costs(TTC2t_{) for shipping through a hub can be} expressed as

Since a hub has the advantage of cargo-consolidation, the study assumes cargo flow in main line is very large. Then, the main line can be served with the minimum

( )

( )

_TC

_q

_TC

_q

TTC

1

=

1

+

1

( )

( )

_TC

_q

_TC

_q

TTC

2

=

2

+

2

Costs for the main line Constant

Costs for the feeder line Trade-off

Routing Decision

Routing Decision

Since there is a trade-off between shipping and

inventory costs of the feeder line.

The Pareto optimal solutions for the feeder line

can be determined.

Consequently, the Pareto optimal solutions for

shipping through a hub can be determined.

(

)

(

)

( )

(

)

(

)

( )

Routing Decision

Routing Decision

Costs for shipping directly to its destination

The total shipping costs(TTC1d_{) and inventory}

costs(TTC2d_{) for shipping directly to its destination can} be expressed as

Costs for the main line

Constant _Trade-off

Costs for the direct line Costs for the feeder line

Routing Decision

Routing Decision

Since there are trade-offs between shipping costs

and inventory costs of feeder line and directly line.

The Pareto optimal solutions for these two line can

be determined by the cost functions formulated.

Consequently, the Pareto optimal solutions for

shipping directly to its destination can be

Example

Example

A Transpacific containership service from Far East to US West Coast is considered herein to demonstrate the

application of the proposed models.

The objective of the example attempts to a make analysis about routing decision whether shipping container from Manila to US West Coast through hub port Kaohsiung or directly to US West Coast.

Busan Los Angeles

Malia Kaohsiung Hong Kong 908 5230 342 1410 1140 543

Busan Los Angeles

Malia Kaohsiung Hong Kong 908 5230 342 1140 543

Example

Example

Suppose five types of ships are used.

Port relative parameters are estimated from data of Kaohsiung Harbor.

Example

Example

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Shipping through a hub

Shipping through a hub

The Pareto optimal solutions for shipping through a hub are determined:

The optimal ship size of feeder line is T4, T2 and T1 for three cases.

Example

Example

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Shipping directly to its destination

Shipping directly to its destination

The Pareto optimal solution for shipping directly to its destination are shown:

The optimal ship size is shown in Table:

The inventory costs for direct shipping

TTC2d

Optimal ship size

Direct line Feeder line TTC2d_{< 7.36*10}7 _{T4 T4}

7.36*107_{< TTC2}d_{< 8.43*10}7 _{T4 T1}

8.43*107_{< TTC2}d_{< 8.66*10}7 _{T4 T2}

8.66*107_{< TTC2}d_{< 8.69*10}7 _{T5 T1}

Example

Example

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Routing

Routing

Decision

Decision

The figure shows both Pareto optimal solutions for

shipping through hub port and directly to its destination. For the range of inventory cost between 7.358*107 _and

8.015*107 _{USD, transshipment is preferred, while for others} direct shipping is preferred.

Example

Example

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Flow

Flow

increases

increases

This figure shows that as container flow between origin and destination port raises five times, no matter what the

inventory cost are, the shipping directly is always the optimal routing decision.

The result shows that the routing decision tends to shipping directly as container flow between origin and destination ports increases.

Conclusions

Conclusions

This study developed a two-objective model by

individually minimizing shipping costs and

inventory costs to decide ship size and routing

strategies for container carriers.

Shipping and inventory cost function are

formulated for a multi-port calling route.

Based on a trade-off between two costs for two

types of shipping routes, Pareto optimal

solutions of the two-objective model are

determined.

Conclusions(Cont.)

Conclusions(Cont.)

A routing decision can be illustrated and made in

objective value space.

The optimal routing, ship size and sailings

frequency with respect to each level of inventory

cost is shown.

The optimal decision tends to be direct shipping

as container flow between origin and destination

ports increases.

Thank

Thank

You!

You!

Chaug-Ing Hsu Yu-Ping Hsieh

cihsu@cc.nctu.edu.tw patty@mail.ihmt.gov.tw

Department of Transportation Technology and Management National Chiao Tung University

1001 Ta Hsueh Road, Hsinchu 300, Taiwan, R.O.C. Fax: +886-3-5720844, Tel: +886-3-5731672