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Parallelization of the Vehicle Routing Problem with Time Windows
, 2001
"... Routing with time windows (VRPTW) has been an area of research that have
attracted many researchers within the last 10 { 15 years. In this period a number
of papers and technical reports have been published on the exact solution of the
VRPTW.
The VRPTW is a generalization of the wellknown capacitat ..."
Abstract

Cited by 24 (1 self)
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Routing with time windows (VRPTW) has been an area of research that have
attracted many researchers within the last 10 { 15 years. In this period a number
of papers and technical reports have been published on the exact solution of the
VRPTW.
The VRPTW is a generalization of the wellknown capacitated routing problem
(VRP or CVRP). In the VRP a
eet of vehicles must visit (service) a number
of customers. All vehicles start and end at the depot. For each pair of customers
or customer and depot there is a cost. The cost denotes how much is costs a
vehicle to drive from one customer to another. Every customer must be visited
exactly ones. Additionally each customer demands a certain quantity of goods
delivered (know as the customer demand). For the vehicles we have an upper
limit on the amount of goods that can be carried (known as the capacity). In
the most basic case all vehicles are of the same type and hence have the same
capacity. The problem is now for a given scenario to plan routes for the vehicles
in accordance with the mentioned constraints such that the cost accumulated
on the routes, the xed costs (how much does it cost to maintain a vehicle) or
a combination hereof is minimized.
In the more general VRPTW each customer has a time window, and between
all pairs of customers or a customer and the depot we have a travel time. The
vehicles now have to comply with the additional constraint that servicing of the
customers can only be started within the time windows of the customers. It
is legal to arrive before a time window \opens" but the vehicle must wait and
service will not start until the time window of the customer actually opens.
For solving the problem exactly 4 general types of solution methods have
evolved in the literature: dynamic programming, DantzigWolfe (column generation),
Lagrange decomposition and solving the classical model formulation
directly.
Presently the algorithms that uses DantzigWolfe given the best results
(Desrochers, Desrosiers and Solomon, and Kohl), but the Ph.D. thesis of Kontoravdis
shows promising results for using the classical model formulation directly.
In this Ph.D. project we have used the DantzigWolfe method. In the
DantzigWolfe method the problem is split into two problems: a \master problem"
and a \subproblem". The master problem is a relaxed set partitioning
v
vi
problem that guarantees that each customer is visited exactly ones, while the
subproblem is a shortest path problem with additional constraints (capacity and
time window). Using the master problem the reduced costs are computed for
each arc, and these costs are then used in the subproblem in order to generate
routes from the depot and back to the depot again. The best (improving) routes
are then returned to the master problem and entered into the relaxed set partitioning
problem. As the set partitioning problem is relaxed by removing the
integer constraints the solution is seldomly integral therefore the DantzigWolfe
method is embedded in a separationbased solutiontechnique.
In this Ph.D. project we have been trying to exploit structural properties in
order to speed up execution times, and we have been using parallel computers
to be able to solve problems faster or solve larger problems.
The thesis starts with a review of previous work within the eld of VRPTW
both with respect to heuristic solution methods and exact (optimal) methods.
Through a series of experimental tests we seek to dene and examine a number
of structural characteristics.
The rst series of tests examine the use of dividing time windows as the
branching principle in the separationbased solutiontechnique. Instead of using
the methods previously described in the literature for dividing a problem into
smaller problems we use a methods developed for a variant of the VRPTW. The
results are unfortunately not positive.
Instead of dividing a problem into two smaller problems and try to solve
these we can try to get an integer solution without having to branch. A cut is an
inequality that separates the (nonintegral) optimal solution from all the integer
solutions. By nding and inserting cuts we can try to avoid branching. For the
VRPTW Kohl has developed the 2path cuts. In the separationalgorithm for
detecting 2path cuts a number of test are made. By structuring the order in
which we try to generate cuts we achieved very positive results.
In the DantzigWolfe process a large number of columns may be generated,
but a signicant fraction of the columns introduced will not be interesting with
respect to the master problem. It is a priori not possible to determine which
columns are attractive and which are not, but if a column does not become part
of the basis of the relaxed set partitioning problem we consider it to be of no
benet for the solution process. These columns are subsequently removed from
the master problem. Experiments demonstrate a signicant cut of the running
time.
Positive results were also achieved by stopping the routegeneration process
prematurely in the case of timeconsuming shortest path computations. Often
this leads to stopping the shortest path subroutine in cases where the information
(from the dual variables) leads to \bad" routes. The premature exit
from the shortest path subroutine restricts the generation of \bad" routes signi
cantly. This produces very good results and has made it possible to solve
problem instances not solved to optimality before.
The parallel algorithm is based upon the sequential DantzigWolfe based
algorithm developed earlier in the project. In an initial (sequential) phase unsolved
problems are generated and when there are unsolved problems enough
vii
to start work on every processor the parallel solution phase is initiated. In the
parallel phase each processor runs the sequential algorithm. To get a good workload
a strategy based on balancing the load between neighbouring processors is
implemented. The resulting algorithm is eÆcient and capable of attaining good
speedup values. The loadbalancing strategy shows an even distribution of work
among the processors. Due to the large demand for using the IBM SP2 parallel
computer at UNIC it has unfortunately not be possible to run as many tests
as we would have liked. We have although managed to solve one problem not
solved before using our parallel algorithm.
Reverse Logistics: Managing Returns on a Delivery Route
, 2004
"... Designing pickup protocols for materials returning on a delivery route is the focus of this paper. Pickup strategies on a fixed route are influenced by variables such as the number of stops on the route, the variability of stop demand, delivery vehicle capacity, the use of outside carriers to supple ..."
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Designing pickup protocols for materials returning on a delivery route is the focus of this paper. Pickup strategies on a fixed route are influenced by variables such as the number of stops on the route, the variability of stop demand, delivery vehicle capacity, the use of outside carriers to supplement delivery vehicle capacity, the number of periods for planning, the penalty cost for not picking up returning materials promptly. Three special cases are identified where the problem is analytically tractable. For the general problem where customers have different penalty costs for materials not returned promptly, an efficient heuristic procedure is proposed. Several insightful rules for route management resulting from this analysis are offered. i 1
Mobile Medical Operation Route Planning
"... Abstract—Medical services are usually provided in hospitals; however, in developing country, some rural residences have fewer opportunities to access in healthcare services due to the limitation of transportation communication. Therefore, in Thailand, there are charitable organizations operating to ..."
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Abstract—Medical services are usually provided in hospitals; however, in developing country, some rural residences have fewer opportunities to access in healthcare services due to the limitation of transportation communication. Therefore, in Thailand, there are charitable organizations operating to provide medical treatments to these people by shifting the medical services to operation sites; this is commonly known as mobile medical service. Operation routing is important for the organization to reduce its transportation cost in order to focus more on other important activities; for instance, the development of medical apparatus. VRP is applied to solve the problem of high transportation cost of the studied organization with the searching techniques of saving algorithm to find the minimum total distance of operation route and satisfy available time constraints of voluntary medical staffs.
A Decision Support System for . . .
, 2001
"... The Vehicle Routing Problem is one of the most studied areas in literature, mainly because of the real world logistics and transportation problems related to it. In the present paper, a new twostage approach for solving a speci c real problem is shown, along with a decision making software. In the ..."
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The Vehicle Routing Problem is one of the most studied areas in literature, mainly because of the real world logistics and transportation problems related to it. In the present paper, a new twostage approach for solving a speci c real problem is shown, along with a decision making software. In the rst stage all the feasible routes are generated by means of an implicit enumeration algorithm, afterwards, all the information gathered is used by an integer programming model that determines the optimum set of routes for the given demand. The integer model uses a number of 01 variables ranging from 2,000 to 15,000 and gives optimum solutions in an average of 60 seconds. An interactive Decision Support System was also developed to help the user in the dierent aspects of the route scheduling process. In a worstcase scenario, the schedules obtained range from a 7% to 12% reduction in the distance travelled and from a 9% to 11% reduction in operational costs.
Constraint violation in vehicle routing
"... Nowadays, automated route planning models and algorithms are supporting decision makers in designing efficient delivery plans. Anyway, in practical applications the management of constraints is not as rigorous as in mathematical models. Human planners tend to evaluate solutions with a potential viol ..."
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Nowadays, automated route planning models and algorithms are supporting decision makers in designing efficient delivery plans. Anyway, in practical applications the management of constraints is not as rigorous as in mathematical models. Human planners tend to evaluate solutions with a potential violation of some constraints if they estimate to obtain some clear benefit from that. In this paper we propose an alternative model to deal with constraint violation inspired by practice. It overcomes strict management of constraints as done in classical mathematical models and does not overburden decision makers with an excessive number of parameters. The proposed model is formed of twolevels: the first level solves the nominal problem, i.e., without constraint violations. The second level minimizes the violation of constraints and imposes a minimal improvement on the primary objective with respect to the optimal solution of the nominal problem. To obtain an optimal solution of the presented model, we propose a nontrivial implementation of a branchandcutandprice procedure. Furthermore, we introduce and discuss a novel embedded relaxation procedure which is efficiently used to identify unfeasible nodes of the search tree. A computational experience over a set of 120 instances is presented and optimal results on all instances are reported. 1
unknown title
, 2013
"... A column generation based label correcting approach for the sensor management in an information collection process ..."
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A column generation based label correcting approach for the sensor management in an information collection process
Tuning the Parameters of a Memetic Algorithm to Solve Vehicle Routing Problem with Backhauls Using Design of Experiments
, 2006
"... AbstractVehicle Routing Problem with Backhauls (VRPB) is an extension of the general Vehicle Routing Problem (VRP). In contrast with general VRP, VRPB considers two types of linehaul and backhaul customers. VRPB tries to find optimal routes with minimum cost in which backhaul customers are visited a ..."
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AbstractVehicle Routing Problem with Backhauls (VRPB) is an extension of the general Vehicle Routing Problem (VRP). In contrast with general VRP, VRPB considers two types of linehaul and backhaul customers. VRPB tries to find optimal routes with minimum cost in which backhaul customers are visited after linehaul customers for a fleet of heterogeneous vehicles. In this paper, a Memetic Algorithm (MA) is developed to solve the VRPB. Similar to other metaheuristic algorithms, an important issue that affects the performance of MA is the selection of components employed in the algorithm along with their parameters ’ values. This work examines the effect of employing different combinations of MA components and parameter values on both the algorithm’s efficiency and the quality of solutions. Design of Experiments (DOE) is introduced as a systematic approach to find the best combination of these parameters ’ values. Analysis of variance (ANOVA) is used to analyze the main effect and interaction effects of the considered parameters. Results verified the efficacy of the proposed MA method and the systematic tuning approach for MA to solve VRPB. KeywordsMemetic algorithm, Design of experiments, Metaheuristics, Vehicle routing problem 1.