Ant Colony Optimization for vehicle routing in advanced
logistics systems
Luca Maria Gambardella
a,b
, Andrea E. Rizzoli
a,b
, Fabrizio Oliverio
b
,
Norman Casagrande
a
, Alberto V. Donati
a
, Roberto Montemanni
a
, Enzo Lucibello
b

a
IDSIA, Galleria 2, 6928 Manno, Switzerland
b
AntOptima, via Fusoni 4, 6900 Lugano, Switzerland
URL: http://www.idsia.ch, http://www.antoptima.com
Email: luca@idsia.ch

ABSTRACT
Many distribution companies service their customers
with non homogeneous fleets of trucks. Their problem is
to find a set of routes minimising the number of travelled
kilometres and the number of used vehicles, while
satisfying customer demand. There are three major
problems why traditional Operations Research
techniques are not enough to deal with this problem,
which is known as the Vehicle Routing Problem. First of
all, it is inherently combinatorial, and exact algorithms
fail when the dimension of the problem (number of
customers and orders) reaches a reasonable size.
Secondly, the problem can be extended and made more
complex in many ways, for instance, adding more than
one depot, considering more than one vehicle type,
accounting for stochastic customer demand (the exact
requested quantity is known only at delivery time),
considering time windows during which the customers
must be served, taking into account vehicle accessibility
restrictions (some customers cannot be served by some
vehicles). Finally, the problem can become very different
when we consider on-line distribution, that is, we accept
delivery orders for lorries which are en route. There,
geolocation of customers and vehicles, online data
transfer among lorries and the base station, have an
impact as great as the solution strategy.
In this paper we present DyvOil and AntRoute, two
software tools which assist the tour planner during the
different stages of goods distribution, from pre-planning
on the basis of reorder forecasts, to online planning,
through offline planning based on an advanced
metaheuristic such as Ant Colony System. We also
describe the case of Pina Petroli, a fuel oil distribution
company located in Canton Ticino, Switzerland, which
operates a fleet of 12 vehicles and serves customers using
DyvOil and Migros, the largest Swiss supermarket chain,
which uses AntRoute operates daily a fleet of hundreds
of trucks distributing goods to its shops.
Keywords: Supply chain optimisation, vehicle routing
problem, ant colony optimisation
INTRODUCTION
A traditional business model is articulated in three
stages: production, distribution, and sales. Each one of
these activities is usually managed by a different
company, or by a different branch of the same company.
Research has been trying to integrate these activities
since the 60s when multi-echelon inventory systems were
first investigated (Clark and Scarf, 1960), but, in the late
70s, the discipline which is now widely known as Supply
Chain Management was not delivering what was
expected, since the integration of data and management
procedures was too hard to achieve, given the lack of real
integration between the Enterprise Resource Planning
(ERP) and the Enterprise Data Processing (EDP) systems
(Sodhi, 2001). Only in the early 1990s did ERP vendors
start to deploy products able to exploit the pervasive
expansion of EDP systems at all levels of the supply
chain. The moment was ripe for a new breed of
companies, such as SAP, i2, Manugistics and others, to
put data to work and start to implement and
commercialise Advanced Logistics Systems (ALS),
whose aim is to optimise the supply chain seen as a
unique process from the start to the end.
The first ALSs were the preserve of big companies, who
could afford the investment in research and development
required to study their case and to customise the
application to interact with the existing EDP systems.
Moreover, the available optimisation algorithms required
massive computational resources, especially for
combinatorial problems such as Vehicle Routing.
While ALSs were first deployed, researchers in the field
of Operational Research were first investigating new
meta-heuristics , heuristic methods that can be applied
to a wide class of problems, such as Ant Colony
Optimisation ACO (Dorigo et al. 1996, Bonabeau et al.
2000). Algorithms based on ACO are multi-agent
systems that exploit artificial stigmergy for the solution
of combinatorial optimization problems: they draw their
inspiration from the behaviour of real ants, which always
find the shortest path between their nest and a food
source, thanks to local message exchange via the

deposition of pheromone trails. The
remarkable advantage of ACO based
algorithm over traditional optimisation
algorithms is the ability to produce a
good suboptimal solution in a very short
time. Moreover, for some problem
instances, ACO algorithms enhanced
with local optimisation capabilities, have
been proven to be the best overall
(Gambardella and Dorigo, 2000).
The integration of optimisation
algorithms based on innovative meta-
heuristics, such as Ant Colony
Optimisation, Tabu Search (Glover and
Laguna, 1997), Iterated Local Search
(St tzle and Hoos, 1999), Simulated
Annealing (Kirkpatrick et al., 1984),
with ALSs for Supply Chain
Management opens new perspectives of
OR applications in industry. Not only big companies can
afford ALSs, but also small and medium enterprises can
use state-of-the-art algorithms, which run quickly enough
to be adopted for online decision making.
In this paper we present a modular approach to ALS
design and implementation, driven by the user needs. We
show how different algorithms and modules can be
implemented in an ALS and how tailor-made solutions
can be integrated into traditional supply chain
management software.
In the next sections, first we detail the workflow in a
distribution centred company, then we introduce and
discuss the off-line and on-line vehicle routing problems,
which are common to most distribution companies. The
former is solved when the orders to be delivered are
known in advance, the latter when new orders arrive
while the distribution process is on. Finally, we briefly
report on how two pieces of software, DyvOil and
AntRoute, have been designed, implemented, and tested
in collaboration with Pina Petroli, a leading Swiss fuel
oil distribution company, and Migros, the largest
supermarket chain in Switzerland.
CLOSING THE LOOP BETWEEN SALES AND
DISTRIBUTION
Sales and distribution processes require the ability to
forecast customer demand and to optimally plan the fine
distribution of the products to the consumers. These two
strategic activities, forecast and optimisation, must be
tightly interconnected in order to improve the
performance of the system as a whole (Gambardella et
al., 2001).
In Figure 1 the workflow process of a distribution-
centred company is sketched.
The sales department generates new orders by contacting
the customers (old and new ones) to check whether they
need a new delivery. The effectiveness of this operation
can be increased thanks to the FORECAST module,
which estimates the consumption of every customer,
indicating the best re-order time for each of them.
New orders are then processed by the planning
department, which, according to the quantity requested,
the location of the customers, the time windows for the
delivery, decides how many vehicles to employ and
computes the best routes for the delivery, in order to
minimise the total travel time and space. This task is
assisted by ACO algorithms solving the Static Vehicle
Routing Problem (SVRP), embedded in the OPTIMISE
block in our schema.
The vehicle tours are then assigned to the fleet, which is
monitored by the fleet operational control station, which
monitors the evolution of deliveries in real time. This
process is assisted by the SIMULATE/MONITOR/RE-
PLAN module, which allows re-planning online in face
of new urgent orders, which were not yet available
during the previous off-line planning phase. This module
uses ACO algorithms designed to solve the Dynamic
Vehicle Routing Problem (DVRP)
Finally, after vehicles have returned to the depot,
delivery data are off-loaded and transferred back to the
company database.
THE STATIC VEHICLE ROUTING PROBLEM
The most elementary version of the vehicle routing
problem is the capacitated vehicle routing problem
(CVRP) where n customers must be served from a
unique depot, each customer asks for a quantity q, while
the vehicles have a capacity Q. Since the vehicles
capacities are limited, they must periodically return to the
depot for refilling. Therefore a CVRP solution is a
collection of tours, where each customer is visited only
DyvOil

Customers DB,
Orders DB
Sales Dept
FORECAST
New orders
Planning Dept
Vehicles'
Tours
Fleet operational
control station
SIMULATE/
MONITOR/
RE-PLAN
OPTIMISE
Delivered
orders

Figure 1. The workflow loop in a distribution-centred company.