Proceedings of World Business Research Conference
11 - 13 June 2015, Hotel Novotel Xin Qiao, Beijing, China, ISBN: 978-1-922069-78-8
Allocating Credit Borrowing Quantities through Analytical
Hierarchy Process and Linear Optimization
Feng Jiao1, Jingxin Dong2 and Christian Hicks3
Companies apply commercial credits from a multiple source, which involves
traditional lenders as banks and traders, and a new emerging lender known as
third party logistics (3PL) companies. In addition, credit selection is affected by
both qualitative and quantitative concerns, which is treated as a multiple criteria
problem. This problem forces companies to evaluate their concerns’ importance
before selecting lenders. Therefore, two questions are raised: What is priority
ranking of borrowers’ basic concerns in borrowing credits? How much should
be allocated to borrow from these three credits with considering the high
importance concerns? In this article, an integrated method of using analytic
hierarchy process (AHP) and linear programming (LP) is presented. The
method aims to measure the importance of borrowers’ concerns, and issue one
LP model for placing optimal borrowing quantities with constraints of important
criteria. This method can be applied to different borrowers to allocate their
borrowing arrangement with specific distinct considering criteria.
Field of Research: Logistics Finance
1. Introduction
Companies are more or less budget constrained. Therefore, commercial credit is important
and necessary for their survival. Banks as a traditional lender, absorb savings from public
and lend part of capital to enterprises (Rosenberg, 1993). Bank offers different categories of
credits to companies in financial market (Cook, 1999). However, rigorous application criteria,
uncertainty of approval time, and high failure rate lead many companies to abandon their
borrowing applications with fear of rejection (Eurosystem, 2014). Trade credit contributes
another reliable approach for credit borrowers. It takes a main role for offering short-term
credit in commercial credit market (Wilner, 2000). As a credit maintained by trust between
lenders and borrowers, it has a more flexible payback period and a negotiable interest rate
comparing with bank credit (Wilson and Summers, 2002).
However, bank and trade credit have been pointed out the weakness in monitoring the
transactions of products. This situation can be relieved by a service called Integrated
Logistics Financial Service (ILFS). ILFS works through a third party logistics (3PL) company
allies with traditional financial institutions to provide credits and monitor borrowers’ business
(Xiangfeng Chen and Cai, 2011). Although some literatures imported a new credit which is
called 3PL credit (Xiangfeng Chen and Wang, 2012), they only contributed a debate for
explaining 3PL credits’ profit making to borrowers. While borrowers’ concerns in selecting
3PL credit have been ignored. As the description of Christina E. Bannier et al. (2012), credit
selection is a process influenced by both tangible and intangible factors. Furthermore,
1
Feng Jiao, Newcastle University Business School, Newcastle University, Newcastle upon Tyne, UK, NE1 4SE.
Email: f.jiao@newcastle.ac.uk
2
Dr Jingxin Dong, Newcastle University Business School, Newcastle University, Newcastle upon Tyne, UK,
NE1 4SE. Email: jingxin.dong@newcastle.ac.uk
3
Prof. Christian Hicks, Newcastle University Business School, Newcastle University, Newcastle upon Tyne, UK,
NE1 4SE. Email: chris.hicks@ncl.ac.uk
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Proceedings of World Business Research Conference
11 - 13 June 2015, Hotel Novotel Xin Qiao, Beijing, China, ISBN: 978-1-922069-78-8
companies in reality consider credit selection as a multiple sourcing choice instead of a
single selection, in order to avoid the risk of rejection (Alec R. Levenson and Willard, 2000).
The current literatures are seldom in studying various borrowers’ concerns together.
Moreover, single credit source is against the reality, which borrowers are likely to apply
credits from different credits. Therefore, a deep analysis is needed to answer two raised
questions: what is priority ranking of borrowers’ basic concerns in borrowing credits? How
much should be allocated to borrow from these three credits with considering the high
importance concerns?
The reminder of this study is structured as the follows: Chapter 2 reviews the current
literatures about credit borrowers’ concerns. Chapter 3 introduces the methodological design
of using AHP and LP. Chapter 4 discusses the contribution of AHP, and offers a numerical
example to explain that how the LP model optimizes borrowing quantities. Chapter 5
conducts contributions of this study.
2. Literature Review
Seldom literatures focus on studying enterprises’ consideration in their credit selection.
Therefore it needs to address what components exactly involved in influencing credit
selection. Due to the deficiency of one literature describes these factors; it is necessary to
summarize these concerns through reviewing different literatures. The borrowers’ concerns
are conducted as the follows.
Interest Rate: Interest is treated as the main cost in credit borrowing. High interest rate is
hardly accepted by enterprises, and they are always ready to transfer their choice to a
cheaper one (Rajeev Dehejiaa et al., 2012, Ching-Chung Lin et al., 2015). The constantly
seeking for lower interest rates for lenders actually aims to help themselves to reduce cost
(Abhijit V. Banerjee and Duflo, 2014).
Administration Fees: Matteo P. Arena and Dewally (2012) stated the administration fees
spent in managing loan could not be ignored. Borrowers will invest in labours and facilities to
manage their loan carefully, in order to avoid causing fault expenditure (Tennent, 2012).
Transaction Cost: Borrowers sometimes need to take the transaction costs, especially in
international trade (Cristina Martínez-Sola et al., 2012). It is generally caused by fluctuant
exchange rates (Ġlhan Eroğlu and Eroğlu, 2012). The borrower will take the extra cost in
changing the domestic currency to a foreign currency if the exchange rate increases.
Openness: Openness mainly refers to the trust of borrowers to accept the request from
lenders in the business history investigation. Nishant Dass and Massa (2011) evaluated
borrowers’ accepance level of information openness in bank credit, which more open level
means they could easier to achieve bank credit (Novita Ikasari et al., 2012).
Organizational Structure: Chen Lin et al. (2011) showed that the openness of one
enterprise is decided by its organizational structure. Fan et al. (2013) proved that
organizations’ pyramidal structure causes low demoracy in debating the necessary of
seeking for external financial help.
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Proceedings of World Business Research Conference
11 - 13 June 2015, Hotel Novotel Xin Qiao, Beijing, China, ISBN: 978-1-922069-78-8
Human Capital: Jens M. Unger et al. (2011) found human capital influences the success of
knowledge and skills- related tasks. In the process of credit selection and decision making, a
knowledgeable decision maker who has capability in searching for a low interest rate credit,
and better managing it by his/her professional skills (J.Huston, 2012).
Business Duration: Longer business duration could better prove that one organization has
a well performance in market, and also it is worthy to be invested (Paul Robsona et al., 2013).
Borrowers prefer to enhance their competiveness and credibility by presenting their business
durations (Karolin Kirschenmann and Norden, 2012), which would benefit their success in
applying loans, and accessing competitive interest rates (Sofia A. Johan and Wu, 2014).
Distance: Matteo P. Arena and Dewally (2012) described that communication is a bridge
links the both sides for exchanging their consideration and aims. Far distance is believed as
a barrier for communication. Robert DeYoung et al. (2008) claimed far distance easily delays
in-person assessment and approval, as well as increase costs in financial institutes and
enterprises.
Debt-credit Relationship: Borrowers’ good history of debt-credit relationship is a guarantee
of their application approval (Mingfeng Lin et al., 2013). One hand, long debt-credit
relationship raises lenders’ trust for believing in borrowers’ willingness to take repayment
obligation (Vuyisani Moss et al., 2013). On the other hand, the relationship lending formed by
long debt-credit relationship benefits a shortcut for borrowers accessing loans and also with a
negotiable interest rate (Giannetti, 2012).
Approval Time: Alec R. Levenson and Willard (2000) found small firms are difficult to wait
unpredictable approval time. The borrowers’ worry is the delay of their credit access which
caused by long approval time. They will compare and identify one most effective approval
from their selection(Srisai Chilukuri and Rao, 2014).
Repayment Period: A well setting repayment period could minimize borrowers’ risk of late
repayment which might causes extra interest payment (Trumbull, 2012). Flexibility payment
periods reduce borrowers’ financial stresses, and a well-designed repayment time offers
borrowers to raise more profit (Marc Cowling and Siepel, 2013).
Lending Volume: Bo Becker and Ivashina (2014) mentioned that borrowers concern on how
much credit they could access from lenders. The lending volume of financial institutions is the
metric to be considered and measured by borrowers. In addition, complex procedure and
unpredictable assessing period increase lenders’ uncertainty in issuing credit volumes.
Credit Issued Time: Borrowers are passive for waiting their credit issued. Therefore, credit
issued time significantly influences borrowers’ willingness for applying loans, and borrowers’
satisfaction is proportional to their waiting period (Doh-Shin Jeon and Lovo, 2013). On-time
issued credit may help enterprises survive in budget constrained(Santiago Carbó-Valverde et
al., 2012).
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Proceedings of World Business Research Conference
11 - 13 June 2015, Hotel Novotel Xin Qiao, Beijing, China, ISBN: 978-1-922069-78-8
3. Methodology
Utilizing Analytic Hierarchy Process (AHP) is a possible way to arrange tangible and
intangible factors together into a hierarchy structure. According to principle of setting criteria
and sub criteria in AHP hierarchy structure (Saaty, 1990), all factors should link with the goal
and aim to find the solution directly. Therefore, through reviewing current literature in
previous chapter, all mentioned borrowers’ concerns could explain the relationship between
borrowers’ credit selection and alternative credits. Table 1 summarizes the following metrics
as the criteria in AHP.
Internal Part
1. Interest Rate
2. Administration Fees
3. Transaction Cost
4. Openness
5. Organizational Structure
6. Human Capital
7. Business Duration
External Part
8. Distance
9. Approval Time
10. Repayment Period
11. Lending Volume
12. Credit Issued Time
13. Debt-credit Relationship
Table 1, the summary of criteria in AHP hierarchy structure
Based on above listed criteria, for the criteria in internal part, it could summarize 1 to 3 as the
criteria of Costs, and 4-7 as criteria of Organization’s Conditions. For the metric in external
part, 1 and 6 could be categorized as the criteria of Borrowing Constraints, 2 to 5 are treated
as the main criteria of Credit Requirements. These systematic criteria will be set as main
criteria, and all these 13 criteria will be treated as sub-criteria. Therefore, it could set the AHP
Hierarchy structure as the following Figure 1.
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Proceedings of World Business Research Conference
11 - 13 June 2015, Hotel Novotel Xin Qiao, Beijing, China, ISBN: 978-1-922069-78-8
Figure 1, the AHP Hierarchy Structure
As the description by Ordoobadi (2013) about benefits of AHP, utilizing AHP can determine a
ranking of importance for the selected factors. Bases on above structure, the next step is
calculating the weights of criteria and final ratings of alternative credits.
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Proceedings of World Business Research Conference
11 - 13 June 2015, Hotel Novotel Xin Qiao, Beijing, China, ISBN: 978-1-922069-78-8
3.1
Weights of the Criteria and Alternative Credits
According to the AHP theory (Saaty, 1990), the calculation of each weight should follow the
sequence from top to bottom by using pairwise comparison, and their weight will be marked
by a scale from 1 to 9 which are referring that importance is from lowest to highest.
The principle of AHP pairwise comparison is referring that for the two options i and j, how
many times i is referred to j. Therefore, it could assume that the values of i and j are wi and
w
wj respectively. Therefore, for the preference of option i to j is wi (Saaty, 1990). For the subj
criteria, it also follows the above matrix to calculate the weights. Finally, for the weights of
w
each criterion, it is equal to: Weight of ith ∑n i wi, (n≤4). All weights should be measured by
i 1
the consistency ratio (CR) in order to check their validity (S. H. Ghodsypour and O'Brien,
1998).
A two-stage questionnaire is sent for collecting data. The data in first stage is used for
measuring weights of the criteria, and the data in second stage is for evaluating ratings of
alternative credits. The weights of the criteria and alternative credits are the main contribution
of AHP in this study.
3.2
Set the Objective Function for Linear Programming
Setting objective function is aim to link the contribution of AHP with LP. The aim of utilizing
LP model is allocating optimal borrowing quantities for a credit borrower. Maximizing loans
borrowing value (LBV) is objective in LP model. LBV is referring that the borrower could
optimize credits borrowing volumes with lowest costs. Therefore, the objective function and
constraints in the linear model are designed as follows:
wi : Ratings of ith credit
xi : Borrowing quantity for
credit
As above introduction, the objective function aims to calculate the maximum LBV, and wi
denotes to the ratings of alternative credits, and xi denotes to the borrowing quantity from the
th
i credit. Therefore the objective function is created as:
( BV)
n
i 1
wi xi .
For the constraints of this objective function, they should follow the result from AHP analysis,
which the weight of each criterion is referring the importance of borrower’s concerns. The top
importance concerns will be selected as the constraints of this function.
4. Discussion
The questionnaire collected 15 companies about their marks for rating criteria. According to
the data in first stage, the respondents offered their marks in evaluating the concerns. These
marks are calculated through the pairwise comparison, which shows the result as following
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Proceedings of World Business Research Conference
11 - 13 June 2015, Hotel Novotel Xin Qiao, Beijing, China, ISBN: 978-1-922069-78-8
Table 2.
D1
A2
D4
D3
D2
A1
B1
B3
C2
A3
B4
C1
B2
Approval Time
Administration Fees
Credit Issued Time
Lending Volume
Repayment Period
Interest Rate
Openness
Human Capital
Debt-credit Relationship
Transaction Cost
Business Duration
Distance
Organizational Structure
Table 2, the ratings of criteria
0.28466
0.19720
0.15817
0.13346
0.12885
0.09143
0.04933
0.04866
0.04180
0.04076
0.03691
0.03206
0.01243
Table 2 lists the importance of each concern in influencing borrowers’ credit selection. Based
on these criteria’s importance ratings, the second stage data collection selects top 6
important criteria (D1 to A1) to rate bank credit, trade credit and 3PL credit. Therefore, with
considering the criteria from D1 to A1 in Table 2, the final ratings of these three credits are
listed as the following Table 3.
Bank Credit
Trade Credit
3PL Credit
Approval Time *
0.09632
0.27958
0.62410
Administration Fees *
0.10689
0.26581
0.62731
Credit Issued Time
0.14452
0.25063
0.60485
Lending Volume
0.12203
0.22679
0.65117
Repayment Period
0.12135
0.27084
0.60781
Interest Rate *
0.08564
0.29661
0.61776
Final Rating
0.11279
0.26504
0.62217
Table 3, the final ratings of bank credit, trade credit and 3PL credit
4.1
Modelling the Borrowing Allocation by Linear Programming
Table 3 offers the final ratings of alternative credits. The LP model assumes that one budget
constrained company requires specific amount of capital. There are three kinds of credits
which involve bank credit, trade credit and 3PL credit can be accessed. The borrower
considers and compares these credits by measuring their approval time, administration fees,
accurate of credit, lending volume, repayment periods and interest rate, in order to allocate
the borrowing quantities from these three credits. Therefore, in this model, it could set these
six concerns as the constraints of the objective function. They are formulated as follows:
vi : Maximum lending volume of ith credit
ti : Approval waiting period of each borrowing quantity from ith credit
fi : Percent of administration cost in each borrowing quantity from ith credit
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Proceedings of World Business Research Conference
11 - 13 June 2015, Hotel Novotel Xin Qiao, Beijing, China, ISBN: 978-1-922069-78-8
ri : Interest rate of ith credit
pi : Repayment period of each borrowing quantity for ith credit (Monthly)
oi : Occurrence rate of
credit issued credit inaccurately in one credit period
tn : Extra waiting period when lenders issued credit inaccurately
C1 : Maximum acceptable rate of overall waiting cost in each borrowing
C2 : Maximum acceptable rate of administration cost in each borrowing
C3 : Maximum acceptable rate of interest payment in each borrowing
C: Daily waiting cost of the borrower
B: The overall volume of credit which the borrower needs to borrow
T: Borrowing Period
Bases on the above notations, the constraints are created as follows:
Approval Time & Accurate of Credit: The borrower applies credit from three lenders with
different waiting periods ti . ti denotes to approval waiting time of ith credit. The borrower has a
daily cost for approval waiting period, which is set as C.
The borrower should consider the lender’s occasional delay in issuing credits. The
occurrence rate of delay is . It will increase the waiting time , and the extra waiting time is
set as tn . The cost caused by overall waiting time should be less than the value of maximum
acceptable overall waiting cost. It is presents as the maximum acceptable rate of overall
th
waiting cost times the borrowing quantities from i credit. Therefore, the constraint of
approval time and accurate of credit is shown as the follows.
C ti (1 oi ) oi (ti tn )C≤C1 B
Administration Fees: Administration fees are spent by borrower in managing their credit. fi
denotes to percent of administration cost in each borrowing quantity from
credit, which is
referring that the borrower should pay fi xi administration fees if it achieve xi quantity of credit
from ith credit. The overall administration fees have been set as C2 . Therefore, this constraint
is:
n
fx≤
i 1 i i
C2 B
Lending Volume: xi denotes to the borrowing volume of the borrower borrows from ith credit.
As the assumption which maximum lending volumes of each credit is vi , this constraint is:
xi ≤vi , i 1, 2, n
And ni 1 xi B
Repayment Period: pi is referring the repayment period of each borrowing quantity for ith
credit. Repayment period is essential factor which can decide borrower’s interest payment.
Therefore, this criterion should be combined with interest rate to be set as a constraint.
Interest Rate: Interest rate decides the borrower’s interest payment. It normally calculated
by principal repayment method, which can minimize the borrower overall interest payment
(Broverman, 2010). In this method, the amount of interest for the borrower paying to the
lender is presented as:
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Proceedings of World Business Research Conference
11 - 13 June 2015, Hotel Novotel Xin Qiao, Beijing, China, ISBN: 978-1-922069-78-8
PV(1 r)n r
C
(1 r)n 1
PV: the credit volume which the borrower got from the lender
C: Overall interest payment to the lender
n: number of repayment
r: Interest rate
If ri denotes to the interest rate which needs to pay for the ith credit, the repayment period is
pi borrowing period T, and the maximum acceptable rate of paying interest has been set
as C3 . This constraint is:
T
n
i 1
xi (1 ri )pi ri
(1 ri
4.2
T
)pi
≤ C3 B
1
Numerical Example of Linear Programming Model
In the modelling numerical example, assuming a budget constrained manufacturer aims to
maximize its LBV. It supposes that the manufacturer needs to borrow £2 million for 6 months
from bank, trade and 3PL credit. The maximum acceptable administration cost takes 18% of
borrowing credits, and the maximum acceptable interest payment takes 20% of borrowing
credits. Specifically, the approval waiting time would cost the manufacturer £1,000/day, and
the maximum acceptable rate of overall waiting cost takes 3% of borrowing credits. The
details about interest rates, repayment periods and maximum lending volumes of these three
credits are introduced as the following Table 4.
Bank Credit
Trade Credit
3PL Credit
Interes
t Rate
(Year)
Repaymen
t Period
(Days)
6.15%
6.00%
5.80%
90
60
30
Maximum
Lending
Volume
(Million)
Occurrence Rate of
Inaccurate Credit
(per Period)
& Extra Waiting
Time
2.5
0.010% (3)
2.1
0.015% (4)
1.9
0.013% (4)
Table 4, Credits’ Information
Percent
of
Administr
ation
Fees
Approval
Length
(Days)
0.20%
0.17%
0.15%
25
20
15
Bases on the above credits’ information, and combines with the design of objective functions
and constraints, it could establish an optimal allocation model through using LP technique.
The model can be written as:
. BV 0.11279x1 0.26504x2 0.62217x3
Overall Waiting Costs: 1,000 25 (1-0.01 )
0.01
3 1,000≤3 x1
→ x1 833,260
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Proceedings of World Business Research Conference
11 - 13 June 2015, Hotel Novotel Xin Qiao, Beijing, China, ISBN: 978-1-922069-78-8
x2 666,586.6667
x3 499,952.3333
Administration Fees: 0.20x1 0.17x2 0.15x3 ≤360,000
Maximum Lending Volume:
x1 ≤2,500,000,
x2 ≤2,100,000,
x3 ≤1,900,000
Interest Payment: 0.01028x1 0.01508x2 0.02935x3 ≤400,000
Through the optimization function in Excel, it could achieve the result and sensitivity check as
the following Table 5 and 6.
Result
The Borrower
Constraints
Administration
Fees
Interest
Payment
Overall
Borrowing
Minimum
Borrowing
Volume
Maximum
Lending
Volume
Optimal Borrowing Schedule
Bank
Trade
3PL Credit
Credit
Credit
833,260
666,586.67 500,153.33
Sum
Maximum
166,652
113,319.73
75,023
354,994.73
360,000
8,565.91
10,052.13
14,679.5
33,297.54
400,000
833,260
666,586.67
500,153.33
2,000,000
2,000,000
833,260
666,586.67
499,952.33
2,500,000
2,100,000
2,000,000
581,835.92
49
Table 5, The optimal borrowing quantities from bank, trade and 3PL credits
Max LBV
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Proceedings of World Business Research Conference
11 - 13 June 2015, Hotel Novotel Xin Qiao, Beijing, China, ISBN: 978-1-922069-78-8
Sensitivity check
Constraints
Name
Administration Fees
Sum
Interest Payment
Sum
Overall Borrowing
Sum
Final
Value
Shadow
Price
Constraint
R.H. Side
Allowable
Increase
Allowable
Decrease
354994.7333 0
360000
1E+30
5005.266666
33297.54007 0
400000
1E+30
366702.4599
2000000
2000000
33368.44444 201
0.62217
Table 6, Sensitivity check for optimal allocation
5. Conclusion
Through the integration of AHP and LP, this article helps a budget constrained company to
rate the priority of concerns in selecting credits, and also offer a solution for optimizing its
borrowing quantities bases on its highly important concerns. The integration of AHP and LP
can be applied into different scenarios. A new scenario can be created if LP model considers
different concerns for optimizing borrowing quantities. Overall, the findings of this article have
been obtained as the follows:
1. Both qualitative and quantitative concerns are measured.
2. Real data achieved through the questionnaire could reflect borrowers’ concerns in
selecting credit.
3. Borrowers’ concerns are identified and rated according to their importance. The weights of
concerns and final ratings of credits are calculated by pairwise comparison, which avoids
the error caused by human judgement.
4. Integration of AHP and LP offers a strategy for optimizing borrowing quantities. AHP sets
constraints and coefficients for LP, and LP optimizes borrowing quantities. Changing AHP
criteria would transform constraints in LP model, and create another scenario.
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