An Emergency LSCM

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Research paper

An emergency order allocation model based

on multi-provider in two-echelon logisticsservice supply chain

Liu Wei-hua

School of Management, Tianjin University, Tjanjin, China

Xu Xue-cai

Transportation Research Center, University of Nevada, Las Vegas, Nevada, USA, and

Ren Zheng-xu and Peng Yan

School of Management, Tianjin University, Tjanjin, China

AbstractPurpose – On one side, the purpose of this paper is to numerically analyze the emergency order allocation mechanism and help managers tounderstand the relationship between the emergency coefficient, uncertainty and emergency cost in two-echelon logistics service supply chain. On theother side, the purpose of this paper is to help managers understand how to deal with the problem of order allocation in the two-echelon logisticsservice supply chain better in the case of emergency.Design/methodology/approach – The paper presents a multi-objective planning model for emergency order allocation and then uses numericalmethodswithLINGO8.0softwaretoidentifythemodel’sproperties.Theapplicationoftheorderallocationmodelisthenpresentedbymeansofacasestudy.Findings – With the augment of uncertainty, the general cost of logistics service integrator (LSI) is increasing, while the total satisfaction of allfunctional logistics service providers (FLSPs) is decreasing, as well as the capacity reliability; at the same time the emergency cost coefficient is closelycorrelative with the satisfaction and general penalty intensity of FLSPs; finally, the larger the emergency cost coefficient is, the more satisfaction of FLSPs, but the capacity reliability goes up first and down later.Research limitations/implications – Management should note that it is not better when emergency cost coefficient is bigger. The generalsatisfaction degree of FLSP increases with the augment of emergency cost coefficient, but there is an upper limit of the value, i.e. it will not increaseindefinitely with the augment of emergency cost coefficient. This paper also has some limitations. The optional emergency cost coefficient only adopted

a group of data to analyze while the trend of the reliability of logistics capacity needs to be further discussed. In addition, the algorithm of emergencyorder allocation model in the case of multi-objective remains to be solved.Practical implications – Under emergency conditions, LSIs can adopt this kind of model to manage their FLSPs to obtain the higher logisticsperformance. But LSIs should be careful selecting emergency cost coefficient. In accordance with different degrees of emergency logistics demand, LSIscan determine reasonable emergency cost coefficient, but not the bigger, the better, on the premise that LSIs acquire maximum capacity guaranteedegree and overall satisfaction degree of FLSPs. FLSPs can make contract bargaining of reasonable emergency coefficient with LSIs to make both sidesget the best returns and realize the benefit balance.Originality/value – Many studies have emphasized the capacity allocation of manufactures, order allocation of manufacturing supply chain andscheduling model of emergency resources without monographic study of supply chain order allocation of logistics service. Because the satisfactiondegree of FLSPs the cost of integrators needs to be considered in the process of order allocation, and the inventory cost of capacity does not exist, it isdifferent from the issue of capacity allocation planning of manufacture supply chain. Meanwhile, the match of different kinds of logistics servicecapacity must be considered for the reason of the integrated feature of logistics service. Additionally, cost is not the most important decision objectivebecause of the characteristics of demand uncertainty and weak economy. Accordingly, this paper considers these issues.

Keywords Logistics service supply chain (LSSC), Emergency order allocation, Uncertainty, Emergency cost coefficient, Model,

Distribution management, Uncertainty management

Paper type Research paper

The current issue and full text archive of this journal is available at

www.emeraldinsight.com/1359-8546.htm

Supply Chain Management: An International Journal

16/6 (2011) 391–400

q Emerald Group Publishing Limited [ISSN 1359-8546]

[DOI 10.1108/13598541111171101]

The research was supported by the National Science and TechnologyFoundation Planning of China (Project Number 2006BAD30B08). Theauthors appreciate the comments and help from PhD students Ping Yuand Di Zhang from Shanghai Jiaotong University, China. The case studyis supported by the operation manager Shen Yi and marketing manager LiWen-ming from Tianjin Baoyun Logistics Company in China. Thesuggestions of the reviewers are also gratefully acknowledged. This studyis also supported by the National Natural Science Foundation of China(Grant No.70902044).

391



1. Introduction

During the past ten years, all kinds of unexpected incidents

have occurred, such as the wide range of rain and snow

disaster of South China in 2008, Wenchuan earthquake in

China, Indian Ocean tsunami in 2004, various terror attacks,

regional wars, fires, economic crisis, SARS, strikes, etc and all

of these influenced our world more intensely than ten years

ago. Numerous facts have shown that unexpected incidents

not only lead to huge economic losses, but influence people’s

working and daily life, even society and politics stability,

therefore emergency response to the incidents is necessary,

especially in supply chain. During the course of response, the

quality of logistics operation directly determines whether the

impact of unexpected events can be rapidly eliminated or not.

It will be helpful to improve the enterprises and public

departments’ response ability to severe natural disasters and

other unexpected incidents by building up efficient and rapid

responsive logistics system.

The improvement of logistics emergency services relies on

the coordination among the various members of logistics

service supply chain (LSSC). Liu (2007) and Choy et al.

(2007), considered that the main structure of LSCC wasfunctional logistics service included from providers (FLSPs)

to logistics service integrator (LSI) and to manufacturer or

retailer, in which the FLSPs mean traditional third party

logistics firms, such as transportation enterprises, storage

enterprises, etc, and they are classified as the suppliers by LSI

when domestic or international service network is established

because of the singularity, normality and regionality.

Generally speaking, one LSI is associated with many

FLSPs. After the LSI receives the clients’ orders, they will

distribute the orders to FLSPs who would fulfill the logistics

service orders by providing corresponding logistic capability.

The process is called order allocation, and the model

established is order allocation model.

Under emergency condition, how to allocate the orders isthe key to improving logistics operation efficiency when

confronting several logistics service providers. Being different

from single FLSP, the LSI not only needs to consider the

reliability of logistics capacity supply and the reasonable

matching of all kinds’ logistics capacities in the state of

emergency (Lummus et al., 1998), but also takes into account

of the minimum procurement cost and maximum overall

satisfaction degree of LSP. Therefore, the emergency order

allocation of one LSI and various FLSPs is studied in this

paper, and the model established is analyzed.

2. Literature review

The special study of the supply chain order allocation at home

and abroad is still in the early stage while the issue of capacity

allocation closely related to order allocation, was studied in

the early 1990s. So the literature review will be focused on

these two aspects in this paper respectively.

As for supply chain order allocation, Chan et al. (2001)

studied the order release mechanisms in supply chain

management with a simulation approach. A simulation

model of a typical, single channel logistics network was

developed. A new order release approach is proposed which is

found to be superior to those analyzed previously and should

lead to improved supply chain performance. Menon and

Schrage (2002) investigated the customers’ order allocation

within paper making equipment, whose goal was to minimize

the total production cost. The problem can be formulated as

dual-angular integer programming with identical machines

inducing symmetry. Although large-scale mathematical

programming can be decomposed into smaller ones to be

solved, decomposing integer programming problem still

remains unsolved, while the symmetry intensifies the

difficulty. This paper develops an approach to solvedecomposable dual-angular integer programming, which can

be successfully applied to the paper-making industry.

Kawtummachai and Van Hop (2005) considered that there

were less papers focusing on the order allocation problem

after the literature review of supplier selection. Because of this

they studied the structure between one factory and multiple

suppliers. In that paper one method was presented to allocate

the orders and minimize the acceptable procurement costs,

meanwhile to guarantee the necessary order service level.

Moreover the price of order quantity and delivery level was

involved. Chan et al. (2004) proposed a heuristic

methodology for order distribution in a demand driven

collaborative supply chain. The optimization methodology

combines an analytic hierarchy process with genetic

algorithms. Chan and Chan (2006) find an early order

completion contract approach to minimize the impact of

demand uncertainty on supply chains, the Simulation results

indicate that the proposed contract approach is able to

improve the performance measures of the system. Chan et al.

(2006) focuses on optimization of order due date fulfillment

reliability in multi-echelon distribution network problems

with uncertainties present in the production lead time,

transportation lead time, and due date of orders. The

proposed algorithm integrates genetic algorithms with analytic

hierarchy process. A hypothetical three-echelon distribution

network is studied, and the computation results demonstrated

the reliability of the proposed algorithms.

An integrated multi objective decision-making process

between supplier selection and order allocation was studiedby Demirtas and Ustun (2008). In this paper an analytic

network process (ANP) and multi objective mixed integer

linear programming (MOMILP) model was constructed,

which aimed at maximizing the total value of purchasing and

minimizing the budget and deficiency probability. By

adopting ANP method the priority of suppliers was

calculated after comprehensive consideration of the profit,

opportunity, cost and risk, and then the solution of the

MOMILP model was given.

In recent years, Chinese researchers also have focused on

the order allocation. Ji (2005) established a mixed integer

linear programming model of order allocation oriented to

multi-product, multi-order and multi-period. In order to

shorten the solving time and avoid the illegal chromosome

occurrence, a mixed genetic algorithm based on genetic

algorithm with heuristic rules was designed. Aiming at the

dynamic game problem with incomplete information, Zhang

et al. (2006) established a dynamic game model with

incomplete information, and mechanism of reward and

punishment in the process of supplier selection according to

the data provided by the suppliers, such as the quality,

delivery timing, price, etc. By identifying the data the order

distribution of suppliers was discussed and the game model

and mechanism were validated by an example. Focusing on

maximizing the group profits, Xiang (2006) put forward an

order allocation model of single 0-1 programming with

An emergency order allocation model based on multi-provider

Liu Wei-hua, Xu Xue-cai, Ren Zheng-xu and Peng Yan


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optimization theory. In the model, the factors, such as stock

share, capital cost, fixed operation cost, etc, were taken into

account, and the optimal allocation of the market orders, can

be obtained by solving the 0-1 programming model, thus

compiling the production and transportation plans for the

member enterprises.

Since the order allocation process is closely related to the

allocation of capacity, it is necessary to review the relevantresearch. Since the 1990s, the allocation of supply chain

capacities has been concentrated on, whose research mainly

emphasized on the coordination m echanism , the

mathematical programming model and mathematical

algorithm of capacity allocation.

Hung and Wang (1997) proposed a linear programming

model to solve the production plan and resource allocation

problem. Bard et al. (1999) studied the capacity planning

problem of semiconductor manufacturing facilities by the

method of queuing and simulation. Swaminathan (2000)

developed a heuristic method to solve the problem of capacity

planning and equipment procurement, and also proposed

integer programming model of random resource, which

considered demand uncertainty and make-to-order

production environment. Furthermore, Tiwari and Vidyarth

(2000) proposed a genetic algorithm to allocate the orders

and facilities. Wang and Lin (2002) applied genetic algorithm

t o s ol ve c ap ac it y e xp an si on a nd a ll oc at io n f or a

semiconductor testing facility with a constrained budget.

Korpela et al. (2002) proposed that conventional supply chain

capacity allocation only considered cost and profit

optimization, which is obviously not enough under the

competitive business environment nowadays. They thought

supply chain allocation should not only consider customer

demand, but also the strategic importance and risks. Then a

solution framework was proposed by using Analytic Hierarchy

Process (AHP) and Mixed Integer Programming (MIP),

which included five steps: step 1 is the definition of the

problem; step 2 is to analyze the strategy importance of customers; step 3 is to analyze the risks of relationship

between suppliers and customers, step 4 is to analyze the

preference of supply chain structure from customers, and the

last step is the optimization employing the method of MIP.

Among these steps AHP is used to identify the importance

and risks of suppliers, while MIP is for the selection of the

supply chain capacity allocation. Sheu (2006) brought out a

novel dynamic resource allocation model for demand-

responsive city logistics distribution operations. The

proposed methodology is developed based on the following

five developmental procedures, including:

1 classification of demand attributes;

2 customer grouping;

3 customer group ranking;4 container assignment; and

5 vehicle assignment.

The numerical results indicated that the model can be

permitted dynamically to manage both the time-varying

customer order data and logistics resources allocation.

Considering the long-term investment of production

facilities and the speediness of demand variety Wang et al.

(2007) thought it is crucial for the decision of capacity

allocation. Then they solved the problem of resource

allocation of make-to-stock manufactures by means of

Constraint Programming Genetic Algorithm (CPGA).

As for the emergency order allocation, Dai and Da (2000)

presented a mathematic model of multi-resource emergency

problem. By introducing the definition of continuous feasible

scheme, the problem can be solved by using the existing

results of single resource model. Al and Gong (2007) built up

multi-objective supplier selection model on the basis of

delivery timing, quality and cost, but the solution algorithm

was not given. Li and Zhao (2007) constructed an emergencymaterial storage double scale limited location model based on

time-satisfaction. Integrating strategic emergency stock with

real options supply, Liu and Ji (2007) set up a resilient supply

model based on contingency supply. Li e t a l. (2007)

established an evaluation model of emergency logistics

warranty capacity.

To sum up, the researches above mainly emphasized on the

capacity allocation of manufactures, long-term investment of

capacities, order allocation of manufacturing supply chain and

scheduling model of emergency resources without

monographic study of supply chain order allocation of

logistics service. Because the satisfaction degree of FLSPs

the cost of integrators needs to be considered in the process of

order allocation, and the inventory cost of capacity does not

exist, it is different from the issue of capacity allocationplanning of manufacture supply chain. Meanwhile, the match

of different kinds of logistics service capacity must be

considered for the reason of the integrated feature of

logistics service. Additionally, cost is not the most important

decision objective because of the characteristics of demand

uncertainty and weak economy. What is more, when the

emergency order is allocated, the speed of service is very

important. So the emergency order is strongly required to be

completed on schedule. Accordingly, the emergency order

allocation of two-echelon LSSC is mainly studied in this

paper, and then a model is constructed, finally, the effects of

demand uncertainty and emergency cost coefficient on order

allocation are discussed in detail.

3. Emergency Order Allocation Model and itssolution method in two-echelon LSSC

Under emergency situation, assume that emergency logistics

orders are assigned to each FLSP by LSI and various

capacities provided by FLSPs match with each other possibly.

For example, if logistics service provider B offers 200

transport vehicles, he should give the warehouse of 1,000

square meters in accordance with the matching requirement

between transport and storage capacity, but if B cannot

provide such a warehouse, he might only provide the 500

square meters warehouse, or even not, in this way the

transport capacity and storage capability of B constitutes of a

incomplete matching binding relationship.

In the case of emergency logistics demand, two aspects

need to be considered specially: one is to guarantee the

quantity of logistics capacity required by the emergency order,

the other one is that within the limited time, the faster the

service speed, the better. Assume there are M kinds of

logistics service orders, and the total demand of the j th

logistics service is R j . Let the interval u 2ij ; u þij

h idonate the j th

logistics capacity interval provided by the i th FLSP,

andP N

i ¼1 u 2

ij # R j #P N

i ¼1 u þij , furthermore, the capacity of

each logistics service provider is supposed to be independent,

so there is no correlation among them. There exists a time




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393



reliability interval T 2ij ; T þij

h i0 # T 2ij # 1; 0 # T þij # 1

of

accomplishing the logistics capacity within the range of

quantitative interval provided by each FLSP. And also it is

assumed that the larger the logistics capacity by the provider

is, the less the time reliability.

Let xij denote the j th logistics order provided by LSI to the

i th FLSP, and the value of xij may either lie within the range of

u 2ij ; u þij

h ior out of it. Considered the uncertainty of customer

requirements, the demand R j is regarded as a stochastic

variable following the normal distribution N ðm j ;s 2 j Þ, so the

random variable is included in the equation of constraint

condition of planning model – chance constraint, i.e. the

equation Pr obðP N

j ¼1 xij $ R j Þ ¼ a can be expressed as the

chance constraint meeting the customer requirements of the

total capacity of the j th logistics service provided by i FLSP,

while a denotes the satisfied probability. For example, a ¼ 95

percent means the total capacity of the j th (Guan et al., 2005;

Liu and Zhao, 1998) p roviding th e method of

converting uncertainty constraints into certainty ones, the

capacity provided should satisfy the condition of P N i ¼1 xij ¼ m j þ F

21

að Þs j .When the model is applied actually, LSI should not only

take into account of the quantity guarantee of logistics

capacity and time guarantee of logistics service, but also

consider the matching of different logistics capacity, overall

satisfaction of FLSPs and overall cost of LSI, and all the

factors mentioned will be discussed in the followings.

3.1 Reliability of logistics capacity

Reliability of logistics capacity Rij means supply reliability of the

j th logistics capacity provided by the i th FLSP under emergency

condition. The reliability can be measured comprehensively

from twoaspects:one is numericreliability, reflectingthe degree

of meeting thecapacity provided by FLSP, theother one is time

reliability, reflecting the degree of punctuality. The numericreliability r ij of the j th logistics capacity provided by the i th

FLSP can be described as

r ij ¼

u þij

xij ; xij . u þ

ij

1; xij # u þij

8><>: ð1Þ

The time reliability t ij is expressed as

t ij ¼

u þij

xij T 2ij ; xij . u þij

T 2ij þu þ

ij 2xij

u þij 2u 2

ij

ðT þij 2T 2ij Þ; u 2ij # xij # u þ

ij

T

þ

ij ; xij ,

u

2

ij

8>>>>>><>>>>>>:

ð2Þ

Reliability of logistics capacity Rij is total reflection of numeric

reliability and time reliability. According to the preference of r ij

and t ij required by emergency orders, weighted l1 and l2 can be

given, Then the Rij can be

Rij ¼ l1r ij þ l2t ij ð3Þ

3.2 Degree of capacity matching

When emergency logistics order is allocated, LSI need to

disassemble clients’ logistics order, and allocate all kinds of

logistics orders (e.g. transportation service order, storage service

order, processing service order) required by clients among

FLSPs. In this model, when each FLSP conducts the business,

their logistics capacities are required to match with each other.

For example, if FLSP A provides 200 highway transport

vehicles, it should provide 1,000 square meters warehouse

possibly to match its transportation capacity. But if it cannot, it

can accommodate nothing or just 500 square meters warehouse.Degree of capacity matching is introduced to describe

matching situation of different logistics capacities. Let w kl

denote the capacity matching degree between the kth logistics

service capacity (e.g. transport capacity) and the l th logistics

service capacity (e.g. storage capacity). If k ¼ l , then w kl ¼ 1,

w kl ¼ 1=w lk. In incomplete matching relations d ikl denotes the

degree of non-exact matching between the kth logistics service

capacity (e.g. transport capacity) and the l th logistics service

capacity (e.g. storage capacity) provided by i th FLSP. The

equation d ikl ¼ 0 denotes exact match, while the equation

d ikl ¼ 1 denotes they do not match completely.d ikl can be defined as equation (4).

d ikl ¼ 12w kl

xil

xik 2

ð4Þ

Considered xik can be equal to 0, equation (4) can be

converted into the following equation (5).

d ikl ¼12 w kl

xil

xik

2

; xik – 0

1; xik ¼ 0

8<: ð5Þ

3.3 Degree of FLSP’s satisfaction

In the actual process of emergency order allocation, generally

speaking, the larger the emergency order quantity allocated to

FLSP, the more satisfactory of FLSP, because the more the

emergency order to FLSP, the greater the return of FLSP. But

the order allocated cannot be infinite, when the order quantity

is beyond the maximum capacity valueu þij , the satisfaction of

FLSP decreases, because the extra costs should be paid by

FLSP for the extra orders.

Assume d ij is the i th FLSP’s satisfaction degree of the j th

logistics task. The model of satisfaction degree is constructed

as follows:

d ij ¼

u þij

xij ; xij . u þ

ij

d 0ij þxij 2u

2

ij

u þij 2u 2

ij *ð12 d 0ij Þ; u

2

ij # xij # u þij

xij

u 2ij *d 0ij ; 0 # xij , u 2ij

8>>>>><>>>>>:

ð6Þ

where d 0ij denotes the i th FLSP’s initial satisfaction degree of

the j th logistics capacity value, when the value of the j th

logistics service order assigned to FLSP i th by LSI is equal to

u 2ij which is the minimum value of capacity provided.

Since different FLSP’s satisfaction of different logistics

capacity has different preference, it can be divided into two

types, which are single capacity satisfaction degree and

general capacity satisfaction degree. The weight of single

satisfaction degree of capacity is assumed to be 11, the weigh

of general satisfaction degree of capacity is 12, and

11 þ 12 ¼ 1. The values of 11 and 12 can be obtained by

questionnaires filled by FLSP.




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394



1 Single capacity satisfaction degree: it means order

allocation satisfaction degree of a certain capacity. Let

lij denote the j th logistics capacity preference of FLSP i th,

whereP M

j ¼1 lij ¼ 1. So the total satisfaction degree of i

FLSP’s single capacity is 11

P M j ¼1 lij d ij

.

2 General capacity satisfaction degree: it means order

allocation satisfaction degree of multi-capacity for FLSP.For example, in many cases, logistics service provider

would like to provide integrated logistics service, which

means not only the transport capacity and storage

capacity, but also distribution processing capacity will be

provided. Its logistics capacity is integrated, the

coordination and balance of various capacities is

emphasized. In general, the more the average quantity of

various emergency order allocations gotten by providers

is, the better the allocation result of integrated logistics

orders will be, then the higher its satisfaction degree of

general capacity, so the general capacity satisfaction

degree of i th FLSP is 121

M P M j ¼1 d ij

.

3 In this way, the ultimate satisfaction of order allocation of i th FLSP is d i ¼ 11

P M j ¼1 lij d ij

þ 12

1 M

P M j ¼1 d ij

.

3.4 Construction of Emergency Order Allocation Model

Due to the different importance of FLSPs, the distribution

status of FLSPs in the course of emergency orders allocation

is different. Let b i denote the importance of the i th FLSP andP N i ¼1 b i ¼ 1. The j th logistics demand’s unit operating costs

of the i th FLPS is cij , the emergency order allocation of LSI

should meet the following four requirements:

1 maximizing the reliability of logistics capacity;

2 maximizing the degree of FLSP’s satisfaction, which is the

minimum difference between application value and

optimal allocation value of FLSP;

3 minimizing the cost of LSI;

4 maximizing the degree of capacity matching for each

FLSP as much as possible.

In incomplete match relations, the optimal objective function

of this model is

max Z 1 ¼X N

i ¼1

X M

j ¼1

b i Rij ¼X N

i ¼1

X M

j ¼1

b i ðl1r ij þ l2t ij Þ ð7Þ

maxZ2 ¼X N

i ¼1

b i 11ðX M

j ¼1

lij d ij Þ þ 12

1

M

X M

j ¼1

d ij

! !ð8Þ

min Z 3 ¼X N

i ¼1

X M

j ¼1cij xij ð9Þ

minZ4 ¼X N

i ¼1

X M

l ¼1

Xk¼l

k¼1

d ikl ð10Þ

s:t :

P N i ¼1 xij ¼ m j þ F

21 að Þs j

xij $ 0

8<:

0@i ¼ 1; 2; · · ·; N ;

j ¼ 1; 2; · · ·; M Þ

ð11Þ

3.5 Solution of Emergency Order Allocation Model

The model above is a multi-objective planning problem. Due

to conflicting and incommensurability of each objective in

multi-objective decision problem, it is hard to find an

absolutely optimal solution, thus the common method used is

to compromise among objectives in order to get Pareto

optimal solution required by the decision-maker (Liu and

Huang, 2001). At present, there are specific solutions tomulti-objective problems (Xu and Li, 2005; Qian, 1990; Liu

et al., 2003), such as evaluation function method (linear

weighting method, reference to objective method, minimum

maximum basis method), objective programming method,

hierarchical sequence method, interactive programming

method, subordination function method, etc. Different from

the methods mentioned above, because there are four aims in

this model, so we could use the thought of the solution, which

is to transfer the multi-objective problem into single objective

problems. The basic steps are as follows.Step 1: Considered objective functions Z1, Z2 and Z3

without Z4, objective function Z3 is changed into the

following equation by introducing emergency cost coefficient.

Z 3 # ð1 þ d Þ Z *

3 ð12Þ

Where Z *

3 denotes the minimum of Z 3.

The objective of this approach is not minimizing the total

cost, but limiting the cost within a reasonable range. In fact,

because of the week economy of emergency logistics, cost

reduction is not a major objective, so this method is feasible.

Let d , a small positive number, be emergency cost coefficient.

If d ¼ 0.1, it means LSI can support the emergency cost

10 percent higher than minimum cost to speed up emergency

response time, and also it will be helpful for completing

emergency order.

Then the objectives Z1 and Z2 are merged into a new max

type function, which is as follows:

max F ¼ a1 Z 1 þ a2 Z 2 ð13Þ

s:t :

Z 3 # ð1 þ d Þ Z *

3P N i ¼1 xij ¼ m j þ F

21 að Þs j

xij $ 0

8>>>><>>>>:

0BBBB@i ¼ 1; 2; · · ·; N ;

j ¼ 1; 2; · · ·; M Þ

ð14Þ

The optimal F value can be gotten, i.e. F *.Step 2: Since Z4 is close to zero as much as possible, the

positive deviation u þ2 can be added to it, where u þ2 $ 0; As for

the objective function F already solved, negative deviation u 21can also be added, where u 2

1$ 0. Then let P

1; P

2denote its

priority, then the objective function can be changed into:

min P 1u 2

1 þ P 2u þ2 ð15Þ

s:t :

Z 3 þ u 21 # ð1 þ d Þ Z *

3P N i ¼1 xij ¼ m j þ F

21 að Þs j

Z4 2 u þ2 $ 0

xij $ 0

8>>>>>>><>>>>>>>:

0BBBBBBB@

i ¼ 1; 2; · · ·; N ;

j ¼ 1; 2; · · ·; M Þ

ð16Þ




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395



Step 3: Solve the new model gotten from Step 2 by using

multi-objective planning method.

4. The effects of demand uncertainty andemergency cost coefficient on order allocation intwo-echelon LSSC

In view of the model built in this paper, software LINGO 8.0

is used to examplify.

4.1 Assumption of essential data of the model

Under an emergency situation, there arefive FLSPs, namely, B,

C, D,E, F, providing logistics service to a LSI A. The integrator

A distributes transportation orders to the five FLSPs. Assume

the transportation capacity that LSI A requires follows normal

distribution D1,N (200, s 21), where a ¼ 95 percent; storage

capacity required follows normal distribution D2,N (130, 16),

where a ¼ 9 5. LSI dem ands that the proportion of

transportation capacity to storage capacity should meet the

ratio of 20 to 13 as nearly as possible. Correlation parameters of

transportation capacity and storage capacity of B, C, D, E andFare shownin Table I. The weight l1 and l2 of number reliability

and time reliability are equal, and both is 0.5.

4.2 Effects of demand uncertainty on emergency order

allocation

If the mean value of transportation orders is 200, the variance

s 21 are 4, 16, 36, 64 respectively, and the mean value of

storage orders subjects to D2,N (130, 16), the values of

effects of demand uncertainty on emergency orders are shown

in Tables II–III.

Table displays that under emergency circumstances the

demand uncertainty has great impact on total cost of LSI.

The larger the demand uncertainty is, the more the total cost

of LSI is, and the lower the general satisfaction of FLSPs is,and the capacity reliability.

4.3 Effects of emergency cost coefficient d of LSI on the

results of order allocation

The effects of correlation parameters(total cost, reliability of

logistics capacity and overall satisfaction degree) on the order

allocation results based on the analysis above are shown in

Table IV and Figure 1, when the emergency cost coefficient

are 5 percent, 10 percent, 15 percent and 20 percent

respectively.As shown in Table IV, emergency cost of LSI is positively

correlated with its total cost. The larger the emergency cost

coefficient is, the more total cost of LSI is. From Figure 1 it

can be seen that emergency cost coefficient has positive

correlation with the general capacity satisfaction degree of

FLSP. The larger the emergency cost coefficient is, the more

total cost of LSP will be. However, as shown in Table IV, the

reliability of logistics capacity does not increase with the

emergency cost coefficient; it rises first then drops later.

Furthermore, if the range of emergency cost coefficient is

made from 0 to 100%, new results showed in Figure 2 will be

gotten. According to the Figure 2, in the curve of general

reliability of logistics capacity, point A is the highest point andthe corresponding emergency cost coefficient is 5 percent.

Point B is the balance point of general reliability of logistics

capacity, which means the general reliability of logistics

capacity will keep stable with the emergency cost coefficient

increasing, and the emergency cost coefficient of point B is 85

percent. In the curve of general capacity satisfaction degree,

with the increasing of the emergency cost coefficient, the

general capacity satisfaction degree tends to go up, but the

amplitude will become slower. From the point view of

management results of Figure 2 show that it is not better

when emergency cost coefficient is bigger. The general

satisfaction degree of FLSP is increasing with the augment of

emergency cost coefficient, but there is an upper limit of the

value, i.e. it will not increase indefinitely with the augment of emergency cost coefficient.

Table I Correlation parameters of logistics capacity of FLSP B, C, D, E, F

FLSP c i 1 u 2i 1 ;u

1

i 1

Â ÃT 2

i 1; T 1

i 1

Â Ãc i 2 u 2

i 2 ;u 1

i 2

Â ÃT 2

i 2 ; T 1i 2

Â Ãl i 1 l i 2 1 1 1 2 b i k i d

0i 1 d

0i 2

B 10 [50, 70] [0.1,0.9] 15 [20, 40] [0.2, 0.9] 0.4 0.6 0.4 0.6 0.22 0.55 0.2 0.3

C 8 [25, 40] [0.3,0.9] 13 [20, 35] [0.3, 1] 0.35 0.65 0.5 0.5 0.13 0.3 0.35 0.35

D 9 [35, 90] [0.2,0.7] 16 [25, 40] [0.5, 0.8] 0.5 0.5 0.3 0.7 0.3 0.6 0.15 0.3

E 12 [40, 60] [0.4,1] 20 [25, 50] [0.4, 0.7] 0.6 0.4 0.6 0.4 0.15 0.4 0.3 0.2

F 11 [30, 80] [0.4,0.8] 18 [10, 40] [0.2, 0.9] 0.45 0.55 0.65 0.35 0.2 0.5 0.25 0.3

Table II Effects of uncertainty demand on emergency order allocation (1)

Distribution value of

transportation Distribution value of storage Total satisfaction degree Reliability of logistics capacity

FLSP s 2154 s 21516 s 21536 s 21564 s 2154 s 21516 s 21536 s 21564 s 2154 s 21516 s 21536 s 21564 s 2154 s 21516 s 21536 s 21564

B 28.55 50.01 43.01 12.12 20 29.96 24.57 21.63 0.195 0.397 0.298 0.135 0.95 0.862 0.91 0.95

C 26.77 28.87 36.6 40.00 48.01 29.27 32.35 34.94 0.555 0.617 0.866 0.469 0.695 0.828 0.715 0.312

D 76.17 84.23 80.41 87.23 28.57 44.58 46.17 40.00 0.393 0.904 0.859 0.161 0.765 0.649 0.646 0.875

E 6.016 13.47 19.84 0 0 0.0 0.00 0 0.021 0.046 0.068 0.042 0.925 0.925 0.925 0.925

F 65.77 30.00 30.00 73.80 40.00 32.76 33.49 40 0.890 0.530 0.538 0.828 0.91 0.933 0.933 0.899




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4.4 Model results discussion

Based on the model results, we can draw the following

conclusions:. It shows a positive correlation between cost coefficient and

FLSP’s overall satisfaction; the large the cost coefficient is,

the more the FLSP’s overall satisfaction is. But cost

coefficient and reliability of logistics capacity are not

entirely positively correlated, but first positivelycorrelated, then negatively correlated.

. For LSI, in the actual distribution of emergency logistics

orders, increasing the emergency cost coefficient will

reduce their own profits, but can improve FLSP’s

satisfaction, enable the emergency logistics mission to be

completed better. So on the premise of obtaining

maximum reliability of logistics capacity and FLSP’s

satisfaction, LSI must develop an appropriate emergency

cost coefficient in accordance with the emergency logistics

demands, rather than pursuit the maximum emergency

cost coefficient. To win the game about emergency orders

allocation with FLSP, LSI can set in advance the different

arrange of emergency cost coefficient according to the

different emergency logistics demands. Once there were

Table III Effects of uncertainty demand on emergency order allocation(2)

s 21 Total cost

Overall satisfaction

degree

Reliability of logistics

capacity

4 4082.232 0.5442759 0.849421

16 4113.816 0.4519563 0.837756

36 4145.4 0.4141338 0.83255464 4172.487 0.3112 0.8307

Table IV Effects of emergency cost coefficient of LSI on the results of order allocation

Total cost

General capacity

satisfaction degree

General reliability of

logistics capacity

5 3599.589 0.0528 0.8264

10 3770.998 0.2110 0.8487

15 3942.407 0.47372 0.8635

20 4113.816 0.55196 0.8378

Figure 1 Schematic diagram of overall satisfaction degree reliability of logistics capacity and emergency cost coefficient (a)

Figure 2 Schematic drawing of overall satisfaction degree reliability of logistics capacity and emergency cost coefficient (b)




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emergency logistics demands, they can make a decision

easily.. For FLSP, increasing the emergency cost coefficient may

increase their profits. They can negotiate the appropriate

emergency cost coefficient with LSI so that both sides get

the best returns. For instance, before the emergency

logistics demands occurring, both sides make an

agreement to take the price increasing ratio intoconsideration under different situations. When it

happened, they can easily choose the price increasing

ratio.

5 Model extensions: emergency order allocationproblem related to a multi-echelon LSSC

The two-echelon logistics service supply chain is the typical

structure of LSSC, whose order allocation model can be

extended to multi-echelon LSSC. Taking a three-echelon

LSSC as an example, as shown in Figure 3, the FLSP of LSI

A is LSI B,while the FLSP of LSI B is FLSP C. As for the

two-echelon LSSC comprised of A and B, the order allocation

model of this study can be applied, likewise, the two-echelon

LSSC comprised of B and C can be done.Under the condition of emergency order allocation of

multi-echelon LSSC, LSI A needs to take into account of the

operation quality and performance of FLSP. Because the

logistics service is intangible and the quality cannot be easily

measured, LSI A can take two measures to guarantee the

service performance. On one hand, A should sign detailed

order service standard contract with provider B, if B can not

complete the logistics service due to various reasons

(including the operation mistakes of FLSP C), B will be

published by LSI correspondingly. On the other hand, A can

ask B to provide the relevant information of FLSP C, once

F LSP C ma ke s m is ta ke s o r c an n ot c omp le te t he

requirements within the standards, A can communicate and

coordinate with B by the relevant information of FLSPC. These two steps can completely make sure that A can

realize emergency logistics service performance requested by

clients.

6. Application of Emergency Order AllocationModel: an empirical example from Tianjin BaoyunLogistics Company in China

The emergency order allocation model proposed in this paper

has been put into practice. Tianjin Baoyun Logistics

Company in China is one of the successful examples, whose

operational experience is worth learning by many logistics

service integrators.

Tianjin Baoyun Logistics Co. Ltd is a professional third

party logistics provider and also is an outstanding logistics

integrator. In 2005, 2006 and 2007, the company was reputed

as the Top 100 logistics enterprises in China and Top Five

logistics enterprises in Tianjin city. Currently, the company

has set up 28 divisions and built good collaboration relations

with 32 large warehousing companies, 20 transportation

companies and 15 professional logistics company. By

integrating these functional logistics service providers,

Baoyun has successfully established widespread business

relations with more than 20 multi-national enterprises, such

as P&G, Siemens, Delphi etc and provided personalized

service according to clients’ requirements.

According to emergency logistics demand, Baoyun

Logistics Company has much practical experience of dealingwith emergency order allocation, which is worth learning.

With many years’ operation experience, Baoyun Logistics

Company divided demand of emergency logistics into three

degrees, important emergency event (degree A), big

emergency event (degree B) and general emergency event

(degree C). The emergency cost coefficient increases with the

emergency degree rising, but it’s not infinite and confined to

some extent. Under the condition of general emergency

events (degree C), emergency cost coefficient of the company

is no more than 20 percent. In degree B, emergency cost

coefficient is no more than 50 percent and in degree A, the

emergency cost coefficient is no more than 80 percent.

Before the emergency logistics demand occurs, Baoyun

Logistics Company set up a dedicated file for every FLSPwhen they signed cooperation agreements with these FLSP.

These files not only record the type and quantity of service

capacities, but also the time range of service operation and the

service speed. Based on the files, Baoyun Logistics

Company’s Operations Management Department judge and

classify the service operation capacity of each FLSP, normally

as three types: Highly Flexible Service, General Flexible

Service and Poor Flexible Service. The classification results

are key references to allocate emergency logistics demands.

In order to improve the capacity reliability of FLSP under

the emergency condition, Baoyun Logistics Company

considers the price increasing ratio in the contract with

FLSP, and the range of the price increasing is confined within

certain limits. For example, when general emergency events

(degree C) happen, the price of transportation outsourced to

FLSPs will increase by 10 per cent to 20 percent. If some

emergency events are beyond the scope of the contract,

Baoyun Logistics Company will coordinate with FLSP to

reach an agreement of the specific price ratio, and the

contracts with FLSP must be approved by general manager.

After the emergency logistics demand occurs, Baoyun

Logistics Company firstly determines the timing requirements

of clients to emergency logistics demands, then classifies

emergency logistics demands based on timing requirements.

Baoyun Logistics Company notifies each FLSP the timing

requirements, and with the detailed files of FLSP, it chooses

the FLSP who has rapid service speed and highly flexible

service as the alternative supplier to join the emergency

logistics orders allocation. Secondly, Baoyun LogisticsCompany needs to estimate the demand degree based on

the classification from clients, determines the emergency cost

coefficient, which can be afforded by the company, and then

consults with each FLSP. As a logistics service integrator,

Baoyun Logistics Company has many FLSPs. Once a client

requires emergency logistics, specific persons from market

department of Baoyun Logistics company will take charge of

emergency order allocation; consider comprehensively various

factors, such as service speed, capacity reliability, capacity

matching, satisfaction, etc for FLSP, then sign the contract

with allocation result and service implementation standard,

Figure 3 Typical structure of three-echelon LSSC




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and finally transfer it to the operation management

department for uniform monitoring.

As to emergency order allocation of multi-echelon LSSC

network, Baoyun Logistics Company has its own operation

procedure. For example, Delphi Company, one of the clients,

had one emergency logistics demand in June 2007. Baoyun

Logistics Company outsourced the emergency logistics order

to Qidong Logistics Company, Xingsheng LogisticsCompany, Feilong Freight Logistics Company and Wanfang

Logistics Company. Among them, the transport volume to the

Qidong logistics company was the largest, and 100 5T-trucks

were required, which surpassed its available maximum

transport capacity of 80. But at the same time because

Qidong Logistics Company is also a small-scale LSI, the

company provided another 20 5T-trucks from its FLSPs to

satisfy the demand of Baoyun Company. In order to

guarantee that the FLSP can finish the tasks in accordance

with the standards, Baoyun Company and Qidong Company

signed the detailed logistics service standards, meaning that if

the FLSPs of Qidong logistics company cannot reach the

service standards, Qidong Company would be punished

accordingly. Baoyun Company did not participate in the

coordination of Qidong Company and its FLSPs.

The successful practice of Baoyun Logistics Company

dealing with emergency order allocation verifies the

effectiveness of the model results in this paper. For

example, when deals with emergency logistics orders,

Baoyun Logistics Company considers service speed firstly.

With files recorded, it can choose high service speed FLSP as

the alternative supplier to join the emergency logistics orders

allocation. Then in the actual allocation of orders, Baoyun

Logistics Company also gives full consideration to: the

FLSP’s ability to provide the right quantity of logistics service

in the right time; the degree of overall satisfaction of FLSP;

the total cost of SI. These factors are also considered in the

model built in my paper. So the model is in line with the

actual operation of enterprises, and it is scientific andreasonable.

In addition, the operation experiences of Baoyun Logistics

Company proof the validity of the model results. For instance,

under the condition of three different emergency demands,

the emergency cost coefficient of Baoyun Company varies

correspondingly, i.e. the conclusion of this study is

reasonable, the bigger the emergency cost coefficient, the

results are not better. Before the emergency logistics demand

happens, Baoyun Company takes the price increasing ratio

into consideration under different situations in the contract

signed with FLSP, which indicates that, it would be helpful

for the overall satisfaction of providers to appoint the

emergency cost coefficient with the clients in advance in

order to realize superior reliability of logistics capacity.

7. Conclusions and future work

The issue of emergency order allocation, under emergency

circumstance, when LSI facing various FLSP is investigated

in this paper. The model of emergency order allocation based

on multi logistics capacity is presented, which considers the

maximization of reliability of logistics capacity, the

minimization of the cost of LSI, the maximization of

general satisfaction degree of FLSP and the match of each

capacity. The solution is given in the model and the effects of

demand uncertainty and emergency cost coefficient on order

allocation in two-echelon LSSC are analyzed by using

practical example. The results show that with the augment

of uncertainty, the total cost of LSI is increasing, while the

general satisfaction of all FLSPs is decreasing, which is the

same as the reliability of logistics capacity of all FLSPs.

Meanwhile, the emergency coefficient is closely correlated to

the general satisfaction degree. The greater of emergency cost

coefficient, the more satisfaction of FLSPs, but the reliabilityof logistics capacity does not have the same trend; it rises first

then drops later.

The model of emergency order allocation in this paper has

some limitations. For example, the paper mainly considers the

emergency order allocation model of single-cycle; the future

study can be extended to multi-cycle situation to investigate

the emergency order allocation tactics. The optional

emergency cost coefficient only adopted a group of data to

analyze while the trend of the reliability of logistics capacity

needs to be further discussed. In addition, the algorithm of

emergency order allocation model in the case of multi-

objective remains to be solved.

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Corresponding author

Liu Wei-hua can be contacted at: [email protected]




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