RESEARCH ON LOGISTICS LOCATION OPTIMIZATION

MODEL BASED ON TIME DIMENSIONS

Jiuguo Zhao

School of Economics and Management, Beijing Jiaotong University

No.3 Shang Yuan Cun, Haidian District, Beijing, China

Keywords: Location model, Time-satisfaction, Time cost, Service facility.

Abstract: The classical logistics facility location models seldom lay emphasis on time, which is a critical issue for a

company to gain its competitive advantage nowadays. Some scholars study maximal covering location

problem based on time-satisfaction, but most of them have not taken the consumption of time cost into

account. This paper presents a new location model which incorporates time cost compared with previous

approaches of time satisfaction. The model is initially developed based on the integer programming, whose

objective function is subject to the maximization of total satisfaction and the minimization of total cost.

Finally, it makes precise analysis taking the case of a regional network layout optimization. The

computational result proves the feasibility and value of this model in its practical application.

1 INTRODUCTION

The competition advantage in Modern logistics is

focused on how to access to consumption with the

fastest speed, the shortest distance and lowest cost

under the premise of the satisfaction of individual

customer needs by distribution channels. So logistics

siting problem in logistic distribution centre is an

important part of the entire product supply chain

optimization.

The economic globalization and international

competition augment the frequency of location

decisions because of shortened product life cycles.

On the other hand, the decisions on the siting

problem have a growing impact on competitiveness

of enterprises. With the progress of information

technology and developing of logistics and supply

chain management in recent years, making location

decisions has become a corporate capacity trained

for business and part of changing tactical decisions.

Sometimes it is usually structured to support the

organization's daily scientific decision-making.

Therefore, the academics and managers pay close

attention to how to solve the location problem by

analysing, classifying, modelling and calculating

(Bo et al, 2008).

Nowadays, time is on the cutting edge. Time will

become the next competitive resource advantages.

Time-based competition can be a strategic tool to

gain success in many industries, especially in

logistics industry. Especially in delivery of

perishable goods and emergency services, time is

even more obvious. For the pursuit of zero-time

response to customer demand, siting problem of

various service facilities cannot be an overlooked

factor. The conventional location models of logistics

facilities have a time constraint or use time as the

main target elements, but it is still too simplified to

define time. Usually enterprises look on time of

customers demand from its own perspective, not

from the customer itself. It did not fully reflect the

importance and differentiation of time required by

people in the 2l century.

Based on the background hereinbefore, time is

even more obvious. Therefore, time effect should be

fully taken into account in the location decision-

making process of logistics distribution centre as the

key factors. Thus, this paper introduces time into

location model of logistics distribution centre. We

propose time is not considered in isolation and

shortening the time without condition is not

scientific. It should define and model time from the

perspective of the customer. In this model, we

consider not only maximizing total time satisfaction,

but also minimizing total cost of time. The time

satisfaction mentioned in this article means the

customer satisfaction of responding to the needs of

the time required. The time cost is the cost

consumed by logistics services for customers in

order to satisfy their needs.

656

Zhao J..

RESEARCH ON LOGISTICS LOCATION OPTIMIZATION MODEL BASED ON TIME DIMENSIONS.

DOI: 10.5220/0003580406560661

In Proceedings of the 13th International Conference on Enterprise Information Systems (MMLM-2011), pages 656-661

ISBN: 978-989-8425-56-0

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

2 LITERATURE OVERVIEW

With the growing attention on logistics industry,

more and more enterprises are starting to focus on

logistics facilities location problem. Logistics

facility Location is a very old and classic problem,

developing of the foreign research can be divided

into three stages with different focus (Brandeau and

Chui, 1989).

① Fragmented Research Stage

This stage was from 1909 to 1960. It focused on

solving a variety of practical problems in production

and daily life. The mainly representatives was the

German economist Alfred weber. He considered a

single warehouse location problem is to determine

the location, so that total transportation distance is

the shortest between warehouse and customers.

Hotelling proposed location of two competing

suppliers in a straight line and built related models in

1929. Then Smithies, Stevens studied this problem

in more depth. Regional economist Isard also

analysed the choice of industrial location from the

perspective of land use, input and output.

② Systemic Research Stage

Hakimi went into more theoretical issues of

research on the site in 1964. For selecting for the

network location of one or more facilities, he

considers it should make the total distance or the

distance between facilities minimum. Since then, the

location problem was introduced into a broader area.

After that, the location problem of Production

centre, the transport hub and substation was

researched in succession.

③ Uncertainty Research Stage

So far into the 80s of last century, along with

great changes in the market, the static and

deterministic location model cannot meet the

development of location method. Louveaux,

Mirchandani, Weaver, Church and other scholars let

the transport time and demands as random variables

on the issue of uncertainty median. Berman and

Odoni, Berman and Leblanc let the time or

transportation costs as uncertain system variables to

study the traffic problem in random networks

(Owen

and Daskin, 1998).

The existing literatures mainly consider the

location problem of logistics from the perspective of

minimizing the cost and the time, but research on

location model of logistics facilities and distribution

considered by satisfying customer needs is not too

much. Logistic is a typical service industry,

customer satisfaction must be put in the first place.

At the same time, it is an important factor to

determine customer satisfaction. The aim of

introducing the concept of time satisfaction to

location model of logistics distribution centre is to

ensure location of services and facilities is consistent

with strategic goals and business objectives and the

expectations of customers, but few studies take into

account the cost of time caused by satisfying

customer needs when time satisfaction is considered

in the model.

3 OPTIMIZATION MODEL

TO LOGISTICS LOCATION

PROBLEM

This siting model is formulated to solve location

problem of logistics distribution centre, so as to

maximize a range of benefits. In this model, we

employ the Ma Yun-feng TSBMCLP model to

calculate the time satisfaction and establish the

frame of the time cost. We formulated model as an

integer programming under the goal of maximizing

the total satisfaction of customers and minimizing

the total cost to the service facility’s response time,

which builds respectively from the points of cost and

benefit (Daskin, 1995). The above-mentioned model

is given as follows:

3.1 Notations

The shortest waiting time accepted by customers

between the service demand point i and the primary

service point j.

Transportation cost per unit between service

demand point i and the primary service point j. It is

proportional to the shortest distance between two

points.

Acceptable maximum waiting time between

primary service demand point i and secondary (and

lower class) service points when customers feel very

satisfied.

The shortest waiting time between service

demand point i and secondary (and lower class)

services point when customers feel very

dissatisfied.

≤

Field processing costs per unit in primary service

point j when customers feel satisfied, including the

cost of cargo handling, sorting and etc.

Demand of service demand point i.

Number of primary service points.

RESEARCH ON LOGISTICS LOCATION OPTIMIZATION MODEL BASED ON TIME DIMENSIONS

657

The ratio of the time and cost, it completes

conversion of time and cost. Its value depends on

specific situation. For example, if the enterprise is

more concerned about customer satisfaction and

weaken the concern of cost,

will be a smaller

value.

()

The satisfaction level of response time

between the secondary (and lower class) service

point i and primary service point j.

The curves of time satisfaction function is of a

variety of situations, many functions can be used to

represent the satisfaction of time (Yun-feng et al,

2006). In this paper, we use linear function of time-

satisfaction, for all

[

]

() 0,1

ft ∈

ij i

tL<

() 1

ft =

; if

ij i

tU>

() 0

; if

[, ]

ij i i

tLU∈

()

iij

−

3.2 Formulation of the Model

In a network G (V, A), V is a vertex set, | V | = n; A

is an edge set

iI∈

J∈

. We define

IV∈

is total

subscript set for the set of service demand points

and

V∈

is total subscript set for the set of primary

service points,

JV∪=

. The model can be

formulated as follows:



() ( )

0jJ

0, 1 j J

iijij ij jiij

iI jJ iI jJ

ij j

ax z h f t Y c c hY

YiI

YX iI

YiI

λλ

∈∈ ∈∈

∈

=−+

=∀∈

−≤ ∀∈∀∈

=∀∈

=∀∈∀∈

≥∈

∑∑ ∑∑

∑

，

(1)

(2)

(3)

(4)

(5)

(6)

(7)

The objective function is to maximize actual

satisfaction of services demand, while ensure the

minimum cost of time. A weight is given

relative to the preference of the logistics

enterprises. Constraints (2) ensure every demand

point is serviced by the only one service point (this

service point can provide the best time satisfaction).

Constraints (3) ensure number of service point

. Constraints (4) limit the satisfaction of

demand points by establishment of service stations

(if service station is not established, the service

satisfaction of it is zero). Constraints (5) and (6) are

the 0-1 Constraint.

Decision variable is seen as follows:

0 not set up a service at point j

1 set up a service at point j

⎧

⎪

∀∈

⎨

⎪

⎩

0 customers at point i don't accept

the service from point j

1 customers at point i accept

the service from point j

iIY

⎧

⎪

∀∈ ∀∈

⎨

⎪

⎩

= ，

3.3 Solving the Model

The specific target of this model is to maximize total

satisfaction of secondary (and lower class) service

points covered by primary service points, while

reducing the cost of it. The relevant algorithm is

proposed to solve the problem. With the introduction

of time satisfaction function, location model will be

more flexible and effective (Gen-gui and Yan-fei,

2008). At the same time, it will increase the

complexity of the algorithm. According to adjusting

classical algorithm of current location model, the

time-based location model can be solved. The

greedy algorithm, Ant colony algorithm, genetic

algorithm, tabu search algorithm, artificial neural

networks method and simulated annealing method

can be adjusted to solve such problems. linear

programming software can also be used for solving

of Small-scale problems, such as lindo and lingo

(Yong, 2008).

4 APPLICATION TO A CASE

STUDY

4.1 The Case

In order to verify the feasibility of modeling, we

apply this model to solve and optimize an actual

location problem. Company A is a large private

express delivery companies. It forces on customer-

oriented strategy, which pays close attention to

customer service and level of customer satisfaction.

A has three primary services points in East China

(respectively in Shanghai, Wuxi, Hangzhou) and

twenty-four secondary service points. Its annual

throughput of 591,000 tons is also the forefront of

all regions. According to the above analysis, there is

an obvious and typical site layout problem in the

region of East China. We number twenty-seven

service points, and the defined number and

Throughputs of twenty-seven service points in East

China are given in Table 1:

ICEIS 2011 - 13th International Conference on Enterprise Information Systems

658

Table 1: The defined number and Throughputs of primary

and secondary service points in East China.

Name of Service point Number

Throughput

s(h

)

kiloton

Shanghai (primary) 1 24

Hangzhou (primary) 2 120

Wuxi (primary) 3 23

Minhang 4 7

Qingpu 5 28

Pudong 6 14

Zhuanqiao 7 8

Huzhou

Wuxing

8 5

Nanhu 9 22

Ningbo

Gaoqiao

10 33

Yuyao

Lanjiang

11 15

Wenzhou

Ouhai

12 44

Suzhou

Wuzhong

13 22

Nantong

Yongxing

14 8

Wuxi

Shuofang

15 13

Jindong 16 23

Yiwu

Heye Tang

17 14

Huangyan 18 11

Keqiao 19 4

Zhuji 20 1

Shaoxing

Donghu

21 25

Xiaoshan 22 64

Xiacheng 23 10

Changzhou

Hengshan Bridge

24 22

Nanjing

Guanghua

25 13

Zhenjiang

Danyang

26 9

Huaian

Wangying

27 11

4.2 Solving of Case

① Numbering

In the given network G (V, A), | V | = n = 27.

Shanghai, Hangzhou, Wuxi are three original

primary service points among them, so their current

handling capacity ranks first in major cities in East

China. After considering the fixed costs of set up a

new primary service point, carrying capacity of

cities and distribution of airports, we assume

Shanghai, Hangzhou and Wuxi are candidate

primary service points.

is set as follows:

: Primary service point in Shanghai;

: Primary service point in Hangzhou;

: Primary service point in Wuxi;

Actually, A Company has realized two location

problems: ① the layout of three primary service

points mentioned above is not suitable; ②the scope

of their distribution is not unreasonable because the

relatively distance between them is short. Therefore,

we reduce number of primary service points. We

assume p = 2.

② Time-satisfaction Function

()

If V is the average speed and

is the distance

between two service points,

. The time can be

figured out by the linear distance between two

service points.

is showed in Table 2:

Table 2: The distance between primary service point i and

secondary service point j.

Distance

Shanghai

Hangzhou

Wuxi

Shanghai

(primary)

— 166.9 120.3

Hangzhou

(primary)

166.9 — 188.7

Wuxi (primary) 120.3 188.7 —

Minhang 15.6 151.1 113.7

Qingpu 34.2 136.4 90.1

Pudong 32.5 171.1 121.8

Zhuanqiao 17.8 149.0 117.0

Huzhou

Wuxing

134.6 78.7 120.2

Nanhu 85.8 81.6 105.9

Ningbo

Gaoqiao

286.6 126.7 312.7

Yuyao

Lanjiang

250.5 93.8 270.6

Wenzhou

Ouhai

444.6 306.7 466.7

RESEARCH ON LOGISTICS LOCATION OPTIMIZATION MODEL BASED ON TIME DIMENSIONS

659

Table 2: The distance between primary service point i an

secondary service point j (cont.).

Distance

Shanghai

Hangzhou

Wuxi

Suzhou

Wuzhong

79.3 144.8 45.7

Nantong

Yongxing

115.8 237.6 127.7

Wuxi

Shuofang

112.1 170.2 13.4

Jindong 298.8 133.5 326.2

Yiwu

Heye Tang

256.3 93.5 261.3

Huangyan 233.4 70.5 248.5

Keqiao 184.6 38.5 211.3

Zhuji 217.4 55.3 241.5

Shaoxing

Donghu

201.2 47.6 225.8

Xiaoshan 165.8 17.5 187.7

Xiacheng 167.4 25.0 183.2

Changzhou

HengshanBridge

142.0 188.2 28.1

Nanjing

Guanghua

271.6 248.4 158.5

Zhenjiang

Danyang

197.7 228.5 82.7

Huaian

Wangying

356.4 423.4 271.6

Data is measured by Google Maps

③ The Cost

The value of cost parameters

and

is given by

the actual data analysis.

=34.3 and

=35.4.

We assume customers can accept service

provided by primary service points and secondary

service points in East China. So the time-satisfaction

is not zero. According to customer-focused strategic

analysis of private express delivery companies, we

give same weight to time and cost.

0.014

4.3 Illustrative Results and Analysis

We solve this model based on the branch and bound

algorithms and lingo software. The lingo result

showed as follows:

①

36.234Max z =

② The site selection resulting of primary service

point is A transit output is

. The final

selection is Hangzhou and Wuxi. Shanghai is

changed into secondary service point. The specific

service scope is showed in Figure 1.

Figure 1: The optimized layout of regional network.

This result shows an optimized layout of

regional networks. It reselects two primary service

points: Hangzhou and Wuxi, and reorganizes the

regional scope. The new program can not only meet

growing business needs, but also improve the

relatively dense layout. It achieves a high level of

customer satisfaction because customers can obtain

service in shorter time. Company A can gain

competitive advantages by improving time-

satisfaction, while cost of services is deceased.

5 CONCLUSIONS

This paper discusses location model of logistics

distribution and service centre based on time

dimensions. The main value added of this study is

the development of the new location model, in

which, both time satisfaction and time cost are taken

into account. We formulated the model as an integer

programming under the goal of maximizing the total

satisfaction and minimizing the total cost. According

to analysing the optimized layout of regional

networks which is solved by this model, we confirm

the model has usage value for the location problem

of logistics facility. Nevertheless, a more research is

needed to develop the model. The following step of

this research could be to replace a part or all of

relevant expressions about transportation cost with

time cost accurately in objective function or

constraints. At the same time, more factors need to

be considered in this model so as to reflect actual

situation.

ICEIS 2011 - 13th International Conference on Enterprise Information Systems

660

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RESEARCH ON LOGISTICS LOCATION OPTIMIZATION MODEL BASED ON TIME DIMENSIONS

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