International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 4 – Sep 2014
A Review of Vehicle Routing Problem with
Simultaneous Pickup and Delivery
Aravind.P #1, Deepak Eldho Babu *2, Brijesh Paul #3
#1
P.G. Scholar, Mechanical, Mar Athanasius college of engineering kothamangalam, India
Associate professor, Mechanical, Mar Athanasius college of engineering kothamangalam, India
#3
Associate professor, Mechanical, Mar Athanasius college of engineering kothamangalam,India
*2
Abstract— This paper presents a review of vehicle routing
problem with simultaneous pickup and deliveries (VRPSPD).
VRPSPD is a variant of the VRP where both delivery and pickup
demands are fulfilled simultaneously. Due to computer
accessibility and increased capability in computing, algorithm
development has shown major advancements. These were
reflected in VRP researches also. The need to improve vehicle
routing, in turn, stimulates explosive developments in theory and
applications of supply chain management. So without any
surprise the VRP literature has grown exponentially. It is even
more important to regularly assess and evaluate where the field
is heading, and what should be done to improve that field’s
course. This indicates the need for some form of taxonomical
research.
Keywords— Put your keywords here, keywords are separated by
comma.
I. INTRODUCTION
Vehicle routing problem (VRP) is a widely studied
combinatorial optimisation problem in operations research and
computer science. This problem was first introduced by G.
Dantzig and J. Ramser (1954), which was about the routing of
a fleet of gasoline delivery trucks between a bulk terminal and
a number of service stations supplied by the terminal [1]. VRP
is a special case of travelling salesman problem where the
objective is to provide a minimum distance route thereby
minimizing the cost of providing the service.
Fig. (1)
Toth & Vino, 1998 represented VRP as the following graphtheoretic problem. Let G = (V, A) be a complete graph where
V = {0, 1, . . . ,n} is the vertex set and A is the arc set.
Vertices j = 1. . . n correspond to the customers, each with a
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known non-negative demand, dj, whereas vertex 0
corresponds to the depot. A non-negative cost, cij, is
associated with each arc (i, j)eA and represents the cost of
travelling from vertex i to vertex j. If the cost values satisfy cij
= cji for all i, jeV, then the problem is said to be a symmetric
VRP; otherwise, it is called an asymmetric VRP. In several
practical cases the cost matrix satisfies the triangle inequality,
such that cik + ckjPcij for any i, j, k eV [2]. Fig.1 shows a
typical vehicle route with three vehicles and one depot.
II .LITERATURE REVIEW.
A. Major literatures on vrp
After G. Dantzig and J.Ramser unveiled the VRP problem
in 1954, many other VRP literatures were published. Clarke
and Wright (1964) first incorporated more than one vehicle in
the problem formulation. Consequently, this study may be
considered as being first in the VRP literature as we know it
[3]. Different variants of VRP were also emerged due to
extensive research like VRP with pickup and delivery, VRP
with time windows etc. Solomon attempted to solve VRP with
time windows in his literature, M. Solomon, “Algorithms for
the Vehicle Routing and scheduling problem with time
window constraints” (1987) [4]. Min (1989), solved a
practical problem faced by a public library, with one depot,
two vehicles and 22 customers. This is considered as one of
the first attempt to solve Vehicle routing problem with
simultaneous pickup and delivery [5].
B. Major literatures on vrpspd
An extensive literature survey of the vehicle routing
problem is done. Various papers related to VRP problem,
different methodologies and solution techniques were
investigated. It is found that VRP is a very important
combinatorial optimization problem in operation research for
its practical application in routing of vehicles. During the last
few decades, the importance of reverse logistics has shown a
rapid increase due to the environmental and economical issues.
Routing of vehicles is one of the most critical issues that
affect the performance of the reverse logistics. The
importance of reverse logistics increased the importance of
Vehicle routing problem with simultaneous pick-up and
delivery (VRPSPD). So it is decided to focus on VRPSPD
and its related studies.
A general assumption in VRPSPD is that all delivered
goods must be originated from the depot, all pickup goods
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International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 4 – Sep 2014
must be transported back to the depot. Delivery and pickup
goods must be met simultaneously when each customer is
visited only once by a vehicle and unloading is carried out
before loading at the customers (Chen and Wu, 2006) [6].
Vehicle routing with simultaneous pickup and deliveries have
practical application in beverage industry, grocery stores etc.
The Vehicle Routing Problem with Simultaneous Delivery
and Pick-up was introduced in the literature by Min H (1989).
His study considered distribution problem of a public library
at Ohio with 22 branch libraries and 2 vehicles based on the
central library. Vehicles serve branch libraries everyday with
deliveries and pick-ups at each branch library. Vehicle routes
were determined by a solution approach that based on
clustering customers according to their demands and vehicle
capacities first, and then solving TSP for each cluster. While
determining routes for each cluster, an iterative procedure was
used in order to satisfy the feasibility of the route. VRPSPD
make this problem more difficult than VRPB to solve [5].
Dethloff (2001) remarked about the relationship between
reverse logistics in environmental protection and VRPSPD. In
this paper, the relation between this problem and other vehicle
routing problems is investigated. A heuristic construction
procedure is suggested. The proposed algorithm is
successfully applied to a real-life problem as well as test
instances introduced in the literature earlier. The heuristic
approach does not include an improvement routine [7]. Salhi
and Nagy (2005) proposed insertion heuristics, based on the
methodology which was proposed by Golden et al in order to
solve VRP-SPD. Problems with single and multiple depots
were considered. The basic steps of these heuristics are
constructing partial routes for a set of customers, and then
inserting the remaining customers to the existing route. They
introduced the concepts of weak and strong feasibility and
their proposed approach allowed infeasibilities to occur while
searching towards strong feasibility. In feasibilities to occur
while searching towards strong feasibility [8].
Meta-heuristic approaches have been also successfully
applied to solve the VRPSPD and VRPMPD. Crispim and
Brandao (2005) are the first authors who attempted a metaheuristic approach for the VRPSPD. The proposed approach
was a hybrid algorithm based on tabu search (TS) and variable
neighbourhood descent (VND). Initial solutions were obtained
by sweep method. If any route in the initial solution is
infeasible because of the overloading of some intermediate
arcs, the feasibility is established by exchanging the order of
customers on the route. The improvement phase implements
insert and swap as moves. Penalties were given to infeasible
solutions. [9].
Gajpal and Abad (2009) develop a heuristic approach
based on ant colony optimization (ACO). They introduced a
twostep heuristics: In the first step the trail intensities and
parameters are initialized using an initial solution obtained by
means of a nearest neighbourhood constructive heuristic and
an ant-solution [10].Fatma Pinar Goksal et. al (2012) proposed
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meta-heuristic approach to deal with the VRPSPD. The
approach is a hybridization of the particle swarm optimization
(PSO) and variable neighbourhood descent (VND). While
PSO is implemented to search good quality solutions in the
solution space, VND is used to improve solutions which are
randomly selected from the population in each iteration of the
PSO. Moreover, an annealing-like strategy was employed to
preserve the swarm diversity of the PSO [11].As per
knowledge the latest literature on VRPSPD is done by Serdan
Tasan and Mituo Gen (2012). Their study proposes a genetic
algorithm based approach to this problem [12]
C. Findings from literature survey
An extensive literature survey of the vehicle routing
problem is carried out. Various papers related to VRP problem,
different methodologies and solution techniques have
investigated. It is found that VRP is a very important
combinatorial optimization problem in operation research for
its practical application in routing of vehicles. During the last
few decades, the importance of reverse logistics has shown a
rapid increase due to the environmental and economical issues
as well as legal obligations. One of the most critical issues that
affect the performance of the reverse logistics is the routing of
vehicles. The importance of reverse logistics increased the
importance of Vehicle routing problem with simultaneous
pick-up and delivery (VRPSPD).
II. CONCLUSIONS
The VRP is a well known combinatorial optimization
problem. Customers require simultaneous pick-up of goods
from their location in addition to delivery of goods to their
location in some cases. The VRP-SPD is an extension of the
CVRP and considers simultaneous distribution and collection
of goods to/from customers. A fleet of vehicles originated in a
depot serves customers with pick-up and deliveries from/to
their locations. VRP-SPD has been receiving growing
attention due to the increasing importance of reverse logistics
activities.
References
[1]
G. Dantzig and J. Ramser, “The Truck Dispatching Problem,”
Management Science, Vol. 6, No. 1, 1959, pp. 80-91.
[2] Toth, P., & Vigo, D. (1998). Exact algorithms for vehicle routing. In T.
Crainic & G.Laporte (Eds.), Fleet management and logistics (pp. 1–31).
Boston, MA: Kluwer Academic Publishers.
[3] Clarke, G., & Wright, J. W. (1964). Scheduling of vehicles from a depot
to a number of delivery points. Operations Research, 12, 568–581.
[4] Solomon, M.(1983).Vehicle routing and scheduling with time window
constraints Models and algorithms. Technical report, College of Business
Admin., Northeastern University, No. 83-42.
[5] Min H (1989) The multiple vehicle routing problem with simultaneous
delivery and pickup points. Transportation Research-A 23A: 377–386
[6] Chen, J. F., Wu, T. H., Vehicle routing problem with simultaneous
deliveries and pickups (2006) Journal of the Operational Research Society, 57,
pp. 579-587.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 4 – Sep 2014
[7] Dethloff, J. (2001), “Vehicle routing and reverse logistics: The vehicle
routing problem with simultaneous delivery and pick-up”. OR Spektrum, 23,
79–96.
[8] Nagy, G., & Salhi, S. (2005), “Heuristic algorithms for single and
multiple depot vehicle routing problems with pickups and deliveries”.
European Journal of Operational Research, 162, 126–141.
[9] Crispim J., & Branda J. (2005), “Metaheuristics applied to mixed and
simultaneous extensions of vehicle routing problems with backhaul”, Journal
of the Operational Research Society, 56, 1296–1302.
[10] Gajpal, Y., & Abad, P. (2009), “An ant colony system for vehicle
routing problem with simultaneous delivery and pickup”. Computers &
Operations Research, 36, 3215–3223.
[11] Fatma Pinar Goksal, Ismail Karaoglan, Fulya Altiparmak, (2012), "A
hybrid discrete particle swarm optimization for vehicle routing problem with
simultaneous pickup and delivery", Computers & Industrial Engineering
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