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A genetic algorithm for the hub-and-spoke problem applied to containerized cargo transport

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Abstract

A genetic algorithm for the hub-and-spoke problem (GAHP) is proposed in this work. The GAHP configures a hub-and-spoke network with shuttle services for containerized cargo transport. For a fixed number of hubs, it determines the best network configuration of hub locations and spoke allocations that minimizes the total costs of the system. The GAHP has a simple individual structure with integer number representation, where spokes, their allocations, and hub locations are easily recognized. Due to the characteristics of the problem, which has fixed number of hubs, rearrangements should be performed after every process. The GAHP rearrangement process includes improvements of individual structures, resulting in an improved population. Before applying the GAHP to the container transport network problem, the algorithm is validated using the Civil Aeronautics Board data set, which is extensively used in the literature to benchmark heuristics of hub location problems. To illustrate an example of a hub-and-spoke network with shuttle services, a study case with 18 ports is analyzed.

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Abbreviations

TEU:

20-foot equivalent unit, unit of measurement equivalent to one 20-foot container

W ij :

flow from location i to location j

Z ik :

equals 1 if location i is allocated to hub k and 0 otherwise

Z kk :

equals 1 if location k is a hub and 0 otherwise

flowcollection,ik :

collection flow, amount of cargo from spoke i to hub k

flowdistribution,jm :

distribution flow, amount of cargo from hub m to spoke j

flowinterhub,km :

interhub flow, amount of cargo from hub k to hub m

shipI :

ship type I

shipII :

ship type II

capshipI :

capacity in TEUs of shipI; capshipII > capshipI

cshipI,ik :

shipping cost of shipI, from location i to k

c collection,ik :

collection costs, from spoke i to hub k

c distribution,jm :

distribution costs, from hub m to spoke j

c interhub,km :

interhub costs, from hub k to hub m

C&D:

collection and distribution

ceil:

ceil function, gives the smallest integer greater than or equal to a given value

floor:

floor function, gives the largest integer less than or equal to a given value

rem:

remainder of a given quotient

THC:

terminal handling charges

n :

number of nodes

p :

number of desired hubs in the network

i alt :

number of alternative individuals for the crossover rearrangement

p switch :

switch probability for the crossover rearrangement

α :

discount factor on the interhub link

costship :

shipping costs

costtime_port :

cost of time spent in port

costtime_sea :

cost of time at sea of a ship during a given voyage

chargesport_entry :

port entry charges

NTEU:

nominal capacity in TEU of a ship

TIMEport :

time spent in port

costdaily_fixed :

daily fixed costs of a ship

costper_mile :

cost per mile of a ship

distvoyage :

voyage distance

costdaily_capital :

daily capital costs

costdaily_operating :

daily operating costs

priceship :

new building contract price

costrepairs&maintenance :

repairs and maintenance costs

costinsurance&administration :

insurance and administration costs

costcrew :

crew costs

costdaily_fuel :

daily fuel costs

distdaily :

daily distance of ship

FOC:

daily fuel oil consumption

pricefuel :

price of fuel

BHPinstalled :

installed BHP of a ship

SFOC:

specific fuel oil consumption

υ :

utilization of power to achieve service speed

speed:

speed of a ship

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Authors and Affiliations

  1. Department of Systems Design for Ocean-Space, Yokohama National University, Yokohama, Japan

    Kelly Takano & Makoto Arai

Authors
  1. Kelly Takano
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  2. Makoto Arai
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Correspondence to Kelly Takano.

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Takano, K., Arai, M. A genetic algorithm for the hub-and-spoke problem applied to containerized cargo transport. J Mar Sci Technol 14, 256–274 (2009). https://doi.org/10.1007/s00773-008-0035-0

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  • DOI: https://doi.org/10.1007/s00773-008-0035-0

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