RESEARCH ON THE ROUTE OPTIMIZATION OF BOOK
DISTRIBUTION BASED ON THE TABU SEARCH ALGORITHM
Pengfei Zhang and Zhenji Zhang
School of Enconomics and Management, Beijing Jiaotong University, District Haidian, Beijing, China
Keywords: Book Distribution, Path Optimization, Tabu Search.
Abstract: Currently, the research of distribution problems not only widens the area of distribution research, but also
makes distribution research content more concrete. What's more, it can solve distribution problem in the
actual industry. Distribution route optimization Problem, is the Vehicle Routing Problem （VRP）, and it is
a research hotspot of logistics industry. Based on the book distribution route optimization, mainly aiming at
all the sales network circumstance served by the distribution center, to optimize and analyze the distribution
path will be a new attempt.
1 INTRODUCTION
In recent years, the research of distribution problems
not only widens the problem of distribution areas of
research, but also makes distribution research
content more concrete. More still, it can solve
distribution problem in the actual industry.
Distribution route optimization problems, also called
Vehicle Routing Problem (VRP), are a hotspot of the
logistics industry research. VRP can improve the
efficiency of supply, reduce distribution costs on the
distribution vehicle and accomplish a specific
purpose; can deliver the goods to the hands of
customers on time and quickly, and improve
customer satisfaction greatly; it also can improve
efficiency for enterprises. In the case of society,
VRP saves transportation vehicles, alleviate traffic
emergencies, and reduce noise and emissions
transport pollution. Therefore, optimizing vehicle
distribution path is not only an important means of
traffic control, also is a key link of the realization of
green logistics.
2 INFLUENCING FACTORS
OF DISTRIBUTION ROUTE
OPTIMIZATION PROBLEMS
2.1 Influencing Factors of Distribution
Scheme Selection
The selection of distribution scheme targets can be
analyzed as follows:
(1) Distribution mileage
Distribution mileage has direct relation to the
distribution vehicle's fuel consumption, worn degree
and driver fatigue degree, etc. It directly determines
the costs of transportation, and has a great effect on
the economic benefit of distribution business. Also it
has indirect relationship with environmental
pollution.
(2) Distance of delivery vehicles.
The target is related to distribution distance and
vehicle loads. The goal is to minimum the sum of
the product between all the distribution vehicle the
tonnage number (maximum load number) and
driving distance
(3) Comprehensive cost
Reducing comprehensive cost is the basic
requirement of realizing distribution business
economic benefits. In distribution process, the fees
concern with taking and delivery include: vehicles
maintenance, driving expenses, team management
125
Zhang P. and Zhang Z..
RESEARCH ON THE ROUTE OPTIMIZATION OF BOOK DISTRIBUTION BASED ON THE TABU SEARCH ALGORITHM.
DOI: 10.5220/0003422701250130
In Proceedings of the 13th International Conference on Enterprise Information Systems (ICEIS-2011), pages 125-130
ISBN: 978-989-8425-54-6
Copyright
c
2011 SCITEPRESS (Science and Technology Publications, Lda.)
fees, goods stevedore charges and relevant personnel
salary expenses.
(4) Punctuality
Due to the customer has strict requirements for
the distribution time, in order to improve the quality
of distribution service, punctuality should be a goal
of distribution route selection.
(5) Distribution of labor consumption
That is the goal of minimization materialized
labor and narrow consumption. Something
happening on various occasions, such as supply
constraints of labor, fuel, vehicles and equipment,
limits ranges of options of distribution operation. In
this way we can consider distribution of labor,
vehicle required or other related resources as the
target.
(6) Reasonable capacity utilization
This goal requires use less vehicles to fulfill
distribution task, and make the vehicle efficiency.
To take full advantage of vehicle load ability, and
reduce the requirement of environmental pollution.
To satisfy the optimal distribution scheme, the
final results must meet the following conditions:
Highest punctuality; shortest distribution mileage;
least distance of delivery vehicles; lowest
comprehensive cost; least distribution of labor
consumption; most reasonable capacity utilization.
2.2 Constraint Factors of Distribution
Scheme Selection
Distribution plan to achieve the goal of process is
limited by many binding factors, therefore it must be
satisfying the constraint factors obtained under
limited lowest cost, shortest mileage, or
consumption least objectives, etc. common
constraint factors include:
(1)The consignee to goods varieties,
specifications and quantities of requirements;
(2)The consignee to goods distribution time or
time range of requirements;
(3)Road running conditions of distribution of
restricting (road line to urban roads of the freight
traffic, time, passage tonnage restrictions);
(4)Vehicles carrying capacity of maximum limit;
(5)Vehicles driving maximum mileage limit;
(6)The longest working time limit of drivers
The traditional VRP problem mostly only place
weight on the positive logistics distribution,
therefore, the reverse logistics is out of
consideration. In this paper, the reverse logistics is
also an important component of green logistics.
From a transportation perspective, positive
logistics distribution is similar to reverse logistics
recycling. With the realization of the logistics "the
third profits source" value creation, the environment
is caused by a certain degree of harm. Normally,
positive logistics and reverse logistics transport have
same routes, but opposite directions. For VRP
problem, if distribution and recycling are
organization by the distribution centre organization,
vehicles by the distribution canter set out, distribute
the book to various sales outlets, simultaneously get
the return books the sales outlets need to book
distribution centre. Distribution and recycling hand
in hand can save vehicles, reduce pollution and
reduce the cost.
Realizing seamless docking between positive
logistics and reverse logistics is a necessary
condition of structuring a green logistics system of
symbiotic type circulating. Therefore, in addition to
consider the distribution of each section of
optimization and improve, return books recycle
should be emphatically discussed.
3 DISTRIBUTION ROUTE
OPTIMIZATION MODEL
3.1 Definition of Distribution Route
Optimization Problem Type
Combined with specific situation of the distribution
center, we can definite the type of distribution route
optimization problem from the eight aspects: the
number of books distribution center, freight
condition, distribution task features, time required of
books store distribution, vehicle type, subordinate
relationship between vehicles and yard, optimized
objectives and the information is determined or not
(client, vehicle and so on).
(1)Number of books distribution center: single
distribution center and many distribution centers.
In this article there is only a distribution center
which we research, thus, books for each outlet are
distributed by the distribution center.
(2)Freight condition: full loaded, not full,
moderate problem between full loaded and not full
In this paper, the distribution of vehicle in daily
distribution cannot reach its load; this issue can be
treated as not full distribution problem.
(3)Distribution task features: Pure distribution
problems, pure pickup problems and mixed problem
for distribution and pickup.
When books distribution center carries on
forward distribution, books of reverse recovery
ICEIS 2011 - 13th International Conference on Enterprise Information Systems
126
should be more considered. Here what we research
is mixed problem for distribution and pickup.
(4)Time required of books store distribution: No
time limit problem and time limit problem
No time limit problem is a good choice and
reasonable for the realistic problems.
(5)Vehicle type. Here we choose single models
problem
(6)Subordinate relationship between vehicles and
yard.
Because of the particular case of distribution
centre, this problem can be seen as closed problem.
(7)Optimized objectives. Single objective
problem (only consider a distribution goal) and
multi-objective question (considering multiple
distribution targets)
(8)The information is determined or not. Static
problems and dynamic problems
In this case, since the client, vehicle attribute
information is all known and fixed, so it can be
regarded as static problem.
Through the above analysis, there are more
restrictions for path optimization problem of the
distribution center. In order to simplify the modeling
and operations, it is possible to simplify this problem
appropriately and do appropriate hypotheses for
non-key conditions. Therefore, the matter can be
treated as: No Duration and two-way Distribution
VRP.
3.2 The Distribution Centre Path
Optimization Model
No Duration and two-way Distribution VRP can be
described: use multiple distribution vehicles and
send the books outlets need to the outlets from the
distribution centre and get back the returned books
from the outlets to the centre. In the process, the
outlets position, cargo demand and supply, load
capacity per distribution vehicle and maximum
driving distance per distribution is all known. The
next Requests is how to arrange vehicles distribution
route reasonable and make the objective function
optimal.
Because there is no time constraint for
distribution and take the goods, in the process of
distribution, the distribution vehicle may give the
customer demand of books, and then loaded the
return books, namely vehicles finish the distribution
at the same time books returned task is done.
Supposed the number of distribution vehicles for
the centre is K, the full-load of the first k vehicle is
Q
(k=1, 2, …, K). Maximum driving distance per
distribution is D
, the number of outlets is L, the
demand amount of the first outlet i is q
,the return
amount is u
(i=1,2, …,L),the distance between the
first outlet i and j is d
, the distance between
distribution and outlet is d
(i 、 j=1,2, …,L),the
number of outlets which the first k vehicle severs is
n
,the first k route is aggregate R
,among them, the
factor r
means that the sequence that the client r
in the route k is i(the distribution centre is not
included),when r
=0,it means the distribution
centre. Making the number of total ton-km for the
distribution vehicle minimum, we can construct the
distribution centre path optimization model as
follows:
=
∑
∑
(
)
+
(
)
（3-1)
s.t. :
∑
≤
（3-2)
∑
+
∑
≤
( = 1,2,…,
−1 )
（3-3)
∑
u
≤Q
（3-4)
∑
(
)
+
(
)≤
（3-5)
0≤
≤
（3-6)
∑
n
=L
（3-7)
=
|
∈
1,2,…
，
,=1,2,…,
（3-8)
∩
=∅,∀
≠
(3-9)
(
)
=
1,
≥1
0,ℎ
(3-10)
From the model above, the formula (3-1) is
objective function, making the number of total ton-
km for the distribution vehicle minimum that is a
representation of lower cost; what is more, it is also
a reflection for decreasing pollution and reducing
environment hazards.
The formulas (3-2), (3-3), (3-4) are used to
ensure its distribution volume still cannot exceed its
load in the process of the vehicle distribution;
The formula (3-5) ensures the length of each
distribution path does not exceed the maximum
driving distance of distribution once;
RESEARCH ON THE ROUTE OPTIMIZATION OF BOOK DISTRIBUTION BASED ON THE TABU SEARCH
ALGORITHM
127
The formula (3-6) shows that the client of each
path should not exceed the total number of
customers;
The formula (3-7) ensures that each of our
customers gets distribution service;
The formula (3-8) shows the customers’
composition of each path;
The formula (3-9) restrains that each customer
can be supplied by only one distribution vehicle
once;
The formula (3-10) indicates that if the number
of the customer of the first k distribution vehicle is
not less than 1,that means the vehicle attends the
distribution, then sign
(
n
)
=1 ;else, sign
(
n
)
=0
4 SOLVING METHODS
OF DISTRIBUTION ROUTE
OPTIMIZATION MODEL
4.1 Common Methods of Distribution
Route Optimization
As a problem of NP, The research of distribution
route optimization has been a hot spot. Along with
the increase of the number of customers, optional
distribution path increase rapidly as an index number
scheme speed. Therefore, only when the number of
customer is less and the transportation network is
simple, can the distribution vehicle scheduling go
for precision optimal solution; as a more complex
path optimization problem, the process for the
accurate and optimal solution is relatively difficult.
At present, algorithms to solve the logistics
distribution path optimization are divided into two
categories: exact algorithm and heuristic algorithm.
Exact algorithm is generally used to solve the small-
scale path optimization problems, such as branch-
and-bound method, cutting plane method, network
flow algorithm, dynamic programming and so on.
Heuristic algorithm is mainly used for large-scale
path optimization problems. Unlike the exact
algorithm, Heuristic algorithm pays attention to the
satisfactory solution, not for the optimal solution.
Thus, heuristic algorithm can get satisfactory
solution in a short time when dealing with large-
scale vehicle scheduling problems, and the
generality of these algorithms is strong. There are
several common kinds of heuristic algorithm as
follows:
4.1.1 Tabu Search (TS) Algorithm
TS algorithm is also called List optimization method;
it is promotion of local search algorithm. Tabu
search algorithm is adopted taboo technology. In
order to avoid insufficiency that local field search
easily falls into local optimum, Tabu search
algorithm records local optimal points passed with a
taboo list record, at the next search, the use of the
information in the Tabu search form no longer or
selectively search for these points, so as to jump out
of the local optimum.
4.1.2 Simulated Annealing (SA) Algorithm
Simulated annealing (SA) algorithm is promotion of
local search algorithm. Its characteristic is to choose
poor conditions of area of the objective function
values by a certain probability. The algorithm was
originally proposed by Metropolis in 1953，Osman
used the method to solve the optimization problems
in 1993. The simulated annealing algorithm
combines optimization problem with solid annealing
simulation, it can simulate internal energy as the
objective function values, and can evolve
temperature evolution into control parameters. It
starts from the initial solution and initial control
parameters, iterates the current solution repeatedly
as “new solution→ Calculating different of target
function→ to accept or abandon” and gradual
attenuates the control parameter values. When
algorithm terminates, the current solution is
approximate optimal solution. This solution is used
for no time limit one-way distribution vehicle
routing optimization problems.
4.1.3 Genetic Algorithm (GA)
Using search technology and the survival of the
fittest rule, this method does some local search
improvement. It produces new generation by a series
of genetic operations which is selection, crossover
and mutation on the current groups, and gradually
make groups evolution to contain or close to the
state of optimal solution. When iteration times
achieve maximum number of limitation or the
individual of the group has no significant difference，
Iterative terminates. The theory of GA was first
applied to solve the vehicle path optimization
problems by J.L awrence .
There are other methods such as: the artificial neural
networks (anns), ant colony optimization, etc.
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4.2 Tabu Search Algorithm Realization
The current path optimization problem study, more
application Tabu search algorithm, simulated
annealing method, the genetic algorithm three
methods. With Tabu search algorithm in solving
without time limit two-way distribution vehicle
routing optimization problem is can achieve good
results and algorithm of settlement calculation
results more stable, computation efficiency is higher.
4.2.1 Tabu Search Algorithm
Implementation Steps
For solving path optimization problem with tabu
search algorithm, the implementation steps can be
elaborated as follows:
Step 1: Select an initial solution x
now
; Tabu list
H=
φ
Step 2: when meeting the termination criterion,
then it goes to step 4; Else, select the candidate set
which satisfies requirement of Tabu from the
domain of x
now
,which named N(x
now
),then goes to
Step 3.
Step 3: Choose the best solution: x
best
from
Can_N(x
now
), command x
now
=x
best
，then exchange
the new Tabu list, go to step 2.
Step 4: Input calculation results, and stop.
The structure of Tabu search algorithm program
realization is shown in figure 1. Based on figure 1,
make up the corresponding program of its
composition modules and obtain the required results
Figure 1: Structure of Tabu search algorithm module.
4.2.2 Determination of Tabu Search
Algorithm Strategy
According to the model construction of no time limit
two-way distribution route optimization problem,
using the following algorithm strategy, we can
realize the algorithm:
①Indicating method of solutions: By the way of
store direct arrangement
Directly produce L sets of natural array between
1~L, and the L sets mutually uncorrelated repeat,
then the store arrangement is a solution, and it
Corresponds to a distribution route scheme. We get
the satisfied solution when we substitute the solution
elements (store) to the vehicles of distribution path.
②The evaluation method of solution: Using the
formulas E=Z+M*P
w
After we solve the solution, we must evaluate the
solution to make sure the solution good or not. In the
process of iteration, more optimal solution is
constantly searched, and finally optimal solution or
approximate optimal solution comes out.
The specific evaluation method of solution of No
Duration and two-way Distribution VRP can be
described as: satisfy that the sum amount of each
store distribution of each strip distribution path shall
not exceed the maximum weight of the distribution
vehicles and the length of each distribution path
should not exceed the maximum driving distance.
As to some solution, if all the stores can be involved
into a distribution path, the number of no desirable
path of the distribution M=0, and it means the
solution is a feasible solution; if several store cannot
be involved into a distribution path, the number of
no desirable path of the distribution M=1, and it
means the solution is not a feasible solution. The
target value of Distribution route schemes is Z, then
we can get E from the formulas E=Z+M*P
w
, and the
value of E is the value of evaluation. Among the
formulas, P
w
is the punishment weight of no viable
path and the less the value of E is, the better quality
of solution is.
③ Neighborhood operation method ： By two-
exchange way
Two-exchange way is a method of selecting two
elements of solutions randomly and exchange their
neighborhood.
④Determination of Taboo object: Put the best
solution each iteration into taboo list
⑤Determination of the taboo length: Select a
constant according to the scale of the problem.
⑥ Determination of candidate set: Choose
several neighbors from the current adjacent domain
random.
⑦Stopping rule: Using iterative specified steps
RESEARCH ON THE ROUTE OPTIMIZATION OF BOOK DISTRIBUTION BASED ON THE TABU SEARCH
ALGORITHM
129
4.2.3 Structure of Tabu Search Algorithm
Its algorithm structure can be conveyed as follows:
{ Input the known condition of No
Duration and two-way Distribution VRP;
Input operation parameters of algorithm，
including the number of termination
iteration steps T ,the number of
adjacent domain each iteration N, the
length of taboo l and the punishment
weight of no viable path P
w
, and so on;
Initialization taboo list H;
Consider random generation an initial
solution S as the current solution,
iteration step t=0; evaluate the
solution S;
Then, S
best
=S;
The current best solution evaluation
value E
best
= the evaluation of S;
While (t<Termination iteration steps T)
do
{ The number of neighbors searched
this iteration n=0;
The evaluation value of the best
solution this iteration E
localbest
is a
large positive number;
While (n<N) do
{ S’ can be got from S by two-
exchange ways in the process of
adjacent domain operation;
If (S’ is not a factor of the
Tabu list H)
{ Calculate the evaluation
value of S’ by the solution
evaluation method;
If (the evaluation
value of S’<E
localbest
)
{ S
localbest
< S’;
E
localbest
= evaluation
value of S’;
}
n=n+1
}
}
If (E
localbest
<E
best
)
{ S
best
= S
localbest
;
E
best
= E
localbest
;
}
S= S
localbest
The first factor of the Tabu
list is lifted a ban, and put
S
localbest
into the Tabu list and
consider it as the list factor
of the list;
t=t+1;
}
Output the optimal distribution
path scheme and the objective function
values corresponding with S
best
}
5 CONCLUSIONS
The article optimizes the path of distribution by the
Tabu search algorithm and his path can be used as
the path of the daily distribution. The algorithm
makes an attempt to combine the positive logistics
and reverse logistics. Structure of Models and
implementation of algorithm provides certain
theoretical support for the selections of distribution
vehicle path and it is of great practical significance.
Construction of this model and algorithm
implementation provides a theoretical support for
the Vehicle Routing distribution problem.
The next step for the research is to focus on
improving the model based on single object and
establishing multi-objective model. Besides, the
influence of external environment should be
considered in the new model.
REFERENCES
Qian Zhang., 2006. The book, Logistics distribution route
optimization scheduling modelling and practice, China
materials press
Jun Li., Yaohuang Guo., 2001. The book, Logistics
distribution vehicle optimized scheduling theory and
methods, China materials press
Maoxiang Lang., 2009. The book, Optimize the
distribution vehicle scheduling model and algorithm,
Electronic Industry Press
Xueli Cui., 2004.04. Journal of Systems Engineering,
Tabu Search of VRP
Solomon,M., 2004. Operations Research, Algorithms for
the vehicle routing and scheduling problems with time
window constraints
Yuhui Zhuang., 2010. 08. China's publication. Analyzed
on logistics status of china book publishing industry.
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