4OR-Q J Oper Res (2011) 9:321–324
DOI 10.1007/s10288-010-0146-4
PHD THESIS
Solving real-world vehicle routing problems
in uncertain environments
Jorge E. Mendoza
Received: 24 June 2010 / Revised: 1 October 2010 / Published online: 26 October 2010
© Springer-Verlag 2010
Abstract This is a summary of the Ph.D. thesis defended by the author in December
2009 at École des Mines de Nantes and Universidad de los Andes in Bogotá. The thesis
was advised by Christelle Guéret and Andrés L. Medaglia and co-advised by Bruno
Castanier and Nubia Velasco. The manuscript is written in English and it is available
from the author upon request. The focus of the dissertation is to study real-world vehi-
cle routing problems (VRPs) in uncertain environments. First, the thesis proposes a
set of new methods for the VRP faced by a public utility and reports how these meth-
ods were embedded into a decision support system. Second, the thesis introduces a
stochastic VRP widely found in practice but never studied in the literature before: the
multi-compartment VRP with stochastic demands (MC-VRPSD). To solve the prob-
lem the dissertation proposes a set of solution methods that offer different tradeoffs
between accuracy, speed, simplicity and flexibility. Lastly, the thesis proposes two
multiobjective approaches to address the risk behavior of decision makers towards the
cost spread in stochastic routing problems and applies them to the MC-VRPSD.
Keywords Vehicle routing · Stochastic demands · Multi-compartment · Heuristics ·
Memetic algorithms · Pilot method · Multi-objective optimization
MSC classification (2000) 90B06 · 90B90 · 90C15
1 Introduction
The effective design of vehicle routes plays a major role in the efficiency and environ-
mental responsibility of enterprises. Although great effort has been devoted to solve
vehicle routing problems (VRPs), the gap between academic research and practical
J. E. Mendoza (
B
)
Équipe Optimisation des Systèmes de Production et Logistiques, LISA (EA CNRS 4094),
Université Catholique de l’Ouest, 3 Place André Leroy, 49008 Angers, France
e-mail: jorge.mendoza@uco.fr
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322 J. E. Mendoza
problem solving is still significant. The main focus of this thesis is to contribute to
bridge this gap by (i) studying real-world vehicle routing problems in uncertain envi-
ronments never addressed in the academic literature before, (ii) proposing solution
methods to tackle such problems, and (iii) transferring, when possible, the results to
industry. The remainder of this abstract summarizes the results of the dissertation.
2 Solving a real-world distance constraint VRP
Planning visits to audit processes such as meter replacements and service connections
at the water and sewer company of Bogotá implies solving a large-scale distance con-
strained VRP (DVRP). The first contribution of the thesis is to propose a decision
support system to effectively manage the planning of these visits. The system inte-
grates commercial systems such as SAP/R3 and ArcGIS with a custom-made routing
module. This module involves two main decision problems: designing efficient routes
and balancing the workload. Although all problem parameters are known with cer-
tainty when solving the underlying DVRP, unpredictable events (e.g., the customer is
not present) may result on failed visits. Thus, the routing module also addresses the
problem of replanning visits. To solve the routing problem, we propose a randomized
savings heuristic and two new memetic algorithms. For balancing the workload we
embedded in the system two clustering models based on integer programming and
for replanning visits we implemented a fast insertion heuristic. To support the routing
module we developed two independent software components, namely, Java Clarke and
Wright and RoutePlotter. The former is an object-oriented framework for the rapid
development of routing heuristics based on savings, while the latter is a visualization
and analysis tool that allows for manual manipulation of solutions provided by vehicle
routing algorithms. The two components can be used to solve other vehicle routing
problems both in academic and industrial environments. Therefore, we made them
publicly available at: http://copa.uniandes.edu.co.
To assess the benefits for the utility, we tested the system on real instances ranging
from 323 to 601 customers and compared the results with those achieved using the
routing strategy formerly used by the company. The results show potential savings
of nearly 50% (over 200 km per week) in the total distance traveled by the auditors
and improvements in the workload balance. The proposed routing algorithms and the
implementation of the system are thoroughly discussed in Mendoza et al. (2009b).
3 The multi-compartment vehicle routing problem with stochastic demands
The thesis also introduces the multi-compartment vehicle routing problem with
stochastic demands (MC-VRPSD). The problem consists of designing transportation
routes of minimal expected cost to satisfy the random demands of a set of customers
for several incompatible products that must be loaded in independent vehicle compart-
ments. The MC-VRPSD naturally arises in several practical situations. For instance,
petroleum companies deliver different types of fuel using multi-compartment tankers
and public utilities use trucks with compartments to perform selective waste collection.
In contrast to the problem solved for the utility, the uncertainty in the MC-VRPSD
does not come from random events occurred during the route execution phase, but
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