International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 7, July 2015
ISSN 2319 - 4847
Supplier selection in supply chain disruption
with credit concept and Exponential demand
function
Dhirendra Singh Parihar1, Manmohan Rahul2
1
Ansal University, Gurgaon-122003(India)
2
Ansal University, Gurgaon-122003(India)
ABSTRACT
In this study a supply chain model is developed to select the suppliers in a disruption state. Two critical probabilities of
disruption are derived and various options of supplier’s selection are determined with the help of these critical probabilities.
One buyer and two suppliers are considered in this study. One of the suppliers is located outside of the buyer’s geographical
scope and offers competitive price. This supplier is prone to breakdowns. Another supplier is a local supplier more reliable but
expensive. The credit concept is also included in the model. The application of the model is explained with the help of a
numerical example. Sensitivity experiments are carried out to examine the effect of the variation of model parameters on
buyer’s profit.
Keywords: Supply Chain Management, Demand Function, Sensitivity Analysis. Modeling
1. INTRODUCTION
When Supply chain risk management emerged as an important research area due to two reasons: i) the series of crises
and catastrophes have attracted public attention. Natural disasters like hurricane Katrina devastating the Gulf coast of
United States, terrorist acts as such the attacks on September 11, 2001, and epidemics like SARS in South –East Asia
in 2003 are violent reminders that we live in an unpredictable and increasingly unstable world.
The modern supply chain seems to be more vulnerable than ever. Almost all industries have seen increased competitive
pressure in the business environment and the globalization of markets. These changes have compelled firms to make
their intra-firm business processes and inter-firm supply chain either more efficient or more responsive, for instance, by
outsourcing many manufacturing and R&D activities, reducing inventories, collaborating more intensively with other
supply chain actors (Fisher, 1997: Hult et al, 2004:Lee2004; Wiser, Joel, D. 2003). In summary, we find a relatively
unstable world on the one hand, and increasingly sensitive supply chains on the other. The supply chain perspective is
predicated due to the fact, that the competition is shifting from firm verses firm to supply chain verses supply chain. A
number of papers focus closely on supply chain disruptions and discuss the measures that companies should use to
design better supply chains, or study different ways that could help buying firms to mitigate the consequences of a
supply disruption (Horowittz, 1986, GerchakParlar, 1990; Burke et al, 2007).
Supplier selection is one of the most critical activities of purchasing management in supply chain. The supply chain
management as strategic sourcing has been one of the faster growing area of management. The cost of purchasing raw
materials and components parts from external suppliers are very important. The decisions of purchasing activities are
very important. They determine the most important part of the final cost of the product. Among the decision related to
this activity, the supplier selection is most capital decision. This selection is the one of decisions which determines the
long term viability of the company (Thompson, 1990). The ability to identify which supplier has greater potential of a
disruption is a critical step in managing the frequency and impact of these disruptions that often significantly impact on
the supply chain.
The concept of credit period is considered as a strategy in SCM. In today’s business transactions, frequently allow
credit for fix time periods to encourage buyers to increase the size of their orders (Huang, 2010).
Allowing credit for a specific time period is advantageous for the buyer. First, under a credit contract, the buyer does
not have to pay the supplier immediately and therefore it is possible to pay the supplier from future earnings. Therefore
low capital buyers can enter the business. Secondly as the major portion of the inventory holding cost is associated with
investment depreciation, using credit therefore reduces the cost. Third, the unpaid balance can be invested during the
credit period to create additional income. Various researchers have developed SCM models including credit concept.
The problem of supplier selection becomes more complex if we also take into consideration the discounts which
suppliers give on the total order value within a specific period. Hauang Yong-FU et al.(2007) investigated the case
where the retailer’s unit selling price and the purchasing price are not necessarily equal within the EPQ frame work
under the cash discount and permissible delay in payments. Liang-Yuh et al investigated an optimal strategy for an
Volume 4, Issue 7, July 2015
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 7, July 2015
ISSN 2319 - 4847
integrated system with variable production rate, when the freight rate and trade credit are both linked to the order
quantity. Ibrahim Abdul and Atsuo Murata (2011) discussed the discounted cash flow approach to obtain the optimal
results.
In order to capture market share and increase sales, in highly competitive free markets of liberalized economic firms
have to compete not only with their prices, but also with rebates, product quality, advertising and other promotional
expenditures. The degree of effectiveness of these competitive factors in increasing sales depends on how much of these
factors influence the consumer’s purchasing decisions. A considerable number of researchers in economics and
different functional area of business have studied the impact of various operational and marketing activities on the
consumer’s demand. These researchers have developed variety of mathematical functions to characterize the demand.
The linear and exponential demand functions are two popular deterministic demand functions. Y-W Zhou and D Zhou
(2013) considered a two echelon supply chain where one supplier sells through a retailer a product with a stable market
demand. They find that the unconditional trade credit scenario is always beneficial to the retailer but harmful to
supplier in most situations while the conditional trade conditions scenario is always beneficial to both parties. Chen L
H and KANG F S (2010) proposed a mathematical model for a supply chain under the effect of unexpected disruptions
in transport. The supplier offers the buyer a trade credit period and the buyer in turn offers a permissible delay period.
Narain Singh et al studied order size dependent trade credit in a three echelon supply chain model. Mei-Chuan et al
(2012) considered different financial environments when the supplier provides a permissible delay in payments and
developed a mathematical model to find the optimal order quantity and pay off time for maximizing the buyer’s total
profit for each financial environment.
In this study we have followed the Yu et.al. (2009) and Ali Arkan (2011) methodology to study the selection between
single and dual sourcing using exponential demand function. The effect of price sensitivity on single (main supplier)
and local supplier is illustrated with the help of a numerical example. The effect of variation of demand portion
allocated to local supplier, in buyer’s profit is also illustrated. In the analysis the credit given to buyer by local supplier
is included in the analysis while selecting appropriate
2. MODEL
It is assumed that the supply chain deals with a single product. The supplier selection criterion is developed in the case
of supply chain disruption risk. One buyer and two suppliers are considered. One supplier is located outside of the
buyer’s geographical scope, and offers competitive price, but this supplier is prone to breakdowns. Another supplier is
local supplier that is more reliable but more expensive. The local supplier allows credit for a fixed period to encourage
buyer to increase the size of his order. The buyer has following three alternatives for outsourcing the material.
i) Single sourcing (outside supplier as main supplier).
ii) Single sourcing (local supplier as main supplier).
iii) Dual sourcing with local supplier as secondary supplier.
In Dual sourcing case the local supplier allow the credit period. The following analysis provided a criterion how to
choose the sourcing out of above three alternatives to optimize the buyer’s profit.
The price demand function is deterministic. The market demand Q is decreasing function of retail price p and is given
by the following exponential function.
Q=D e-k p
(1)
Where
D is the market scale and
P denotes the product price.
k price sensitivity.
Expected profit functions in the normal state.
i) Single sourcing (outside supplier as main supplier).
Q= D e(-kCms)
(2)
Where Cms is the outside supplier’s unit price in single sourcing.
The profit function is given as
фnso =(S-Cms ) D e-kCms
Where
фnso denotes the profit function and
S is the buyer’s unit sale price of the product.
ii) Single sourcing (local supplier as main supplier).
The demand function is given as
Q= De-kCbn
Where
Volume 4, Issue 7, July 2015
(3)
(4)
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 7, July 2015
ISSN 2319 - 4847
Cbn is the local supplier’s unit sales price.
In this case the local supplier offers a credit period T.
The buyer’s total interest saved during the credit period is given as
Interest= Cbn De-kCbn T i
Where T and i are the length of the credit period and the buyer’s cost of capital respectively.
The profit, Ψnsl, in this case is given by following equation.
Ψnsl = (S-Cbn )De-kCbn +Cbn D e-kCbn Ti
(5)
iii) Dual sourcing.
The profit function when the buyer selects two suppliers is given below.
фnd = (1-x)(S-Cmd ) D e-0.5k(Cmd+Cbn) +x(S-Cbn )D e- .5k(Cmd+Cbn) +
Cbn x D e- .5k (Cmd+Cbn) Ti
(6)
Where Cmd and x are outside supplier’s unit sale price in dual sourcing and the portion of the demand allocated to the
secondary y supplier respectively.
Expected profit functions in the disruption state.
i) Single sourcing (outside supplier as main supplier).
In this case the outside supplier faces breakdown, the supply disruption occurs, therefore, the profit function is
calculated as follows.
фdso = -De-kCms Cu
(7)
Where
фdso is the profit function and
Cu is the buyer’s unit loss of unsatisfied demand.
The breakdown occurs for the outside supplier hence the breakdown does not affects the local profit function.
ii) Dual sourcing.
In this alternative the local supplier allotted a portion of demand, x, of the average demand each cycle. In this case, the
unit price of the product of the local supplier is different to normal state. The unit prices are Cbn for x portion of the
demand and Cbd for (1-x) portion of demand respectively. The buyer’s profit may be expressed as
фdd = (1-x) (S-Cbd) D e- . 5k(Cmd+Cbn) +x(S-Cbn )D e-.5k(Cmd+Cbn)
+ Cbn x D e- . 5k (Cmd+Cbn ) Ti
(8)
It may be noted that in this case the credit period is considered just for a portion x, of the average demand hence the
buyer’s total interest saved is given by
Interest saved = Cbn x D e- . 5k (Cmd+Cbn) Ti
(9)
The expected profit functions of buyer in the event of disruption are given below.
i) Ψmso = (1-p)фns0 +pфdso
(10)
Where Ψmso denotes the expected profit function of buyer.
ii) Ψd = (1-p) фnd +p фdd
(11)
Where Ψd is the profit function in dual case.
iii) Ψmsl =(S-Cbn ) D e –kCbn + Cbn D e-kCbn Ti
(12)
Where Ψmsl is the profit function in the case where local supplier is selected as single source.
Sourcing methods
When the probability of disruption P satisfies the relationship Lp < P<Up then the buyer should prefer dual sourcing
where Lp and Up are given by the following equations.
Lp = [1+ (фdd - фdso )/( фnso -фnd )] -1
(13)
Up = [(фnd -Ψdso)/ (фnd - фdd )]-1
(14)
Where Lp is the first critical probability that’s breaks even the profit with the outside supplier as the single supplier and
the profit with dual sourcing and Up the second critical probability that breaks even the profit with the local supplier as
the single source and the profit with dual sources. The proof is given by Ali Arkan et al (2011) and is given in
appendix.
There are following three options which give optimal buyer’s profit.
i) If p<= Lp, chose the outside supplier as the single source.
ii) If Lp < p < Up chose the dual sourcing.
iii) If p >= Up chose the local supplier as the single source.
For any given p there is a lower boundary of T (Tmin ) given as
Tmin = [ (1-p) фnd +p фdd - (S-Cbn ) D e- kCbn ] / Cbn D e-kCbn (15)
(See appendix)
The local supplier as the only supplier out performs both the suppliers when
T=Tmin
The range of T > Tmin is very important for local supplier, because he can adjust the length of credit period and earn
the whole buyer’s purchased quantity. Thus the credit period has a critical role in supply chain.
Numerical example
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 7, July 2015
ISSN 2319 - 4847
In order to illustrate the application of the model ,let us consider the same hypothetical values of the model parameters
as in (Ali Arkan et. al.): x=.3, Cms =330, Cmd =340,Cbn =360,Cbd =400, Cu =200,S=420, k=.087,D=6* 106
i=0.15,T=0.15
These values of parameters are base value for further sensitivity study.
Applying model to these hypothetical parameters, the lower critical probability (LP) of disruption and the upper critical
probability of disruption (Up) are calculated and found to be 0.21 and 0.47 respectively.
Fig. 1 The rxpected profits under various sourcing alternatives.
60000
Buyer's Profit
50000
40000
Dual sourcing
30000
Single sourcing(main supplier)
Only local supplier(reference line)
20000
10000
0
0
0.2
0.4
0.6
0.8
1
1.2
Probability
Figure 1 The expected profits under various sourcing alternatives
Fig.1. illustrate the buyer’s profit for various options. Three options which provide the optimal profit are listed below.
i) If p<= 0.21, chose the outside supplier.
ii) If 0.21< p < 0.47, chose the dual sourcing.
iii) If p>= 0.47, chose the local supplier as a single source.
Fig.2 The effect of price sensitivity on single
sourcing(main supplier)
80000
Buyer's profit(Rs.)
70000
60000
50000
k=0.027
40000
k=0.08
30000
k=0.09
20000
10000
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
probability
Figure 2 The effect of price sensitivity on single sourcing (main supplier)
Fig.2. shows the effect of variation of the portion of demand allocated to local supplier on dual sourcing. It is found that
at lower probability of disruption the small values of the portion of demand allocated to local supplier is beneficial to
buyer. At the higher values of probabilities of disruption the large values of the portion of demand allocated to local
supplier provides the higher profit.
Fig. 3 Effect of price sensitivity on dual sourcing.
40000
Buyer's profit(Rs.)
35000
30000
25000
k=0.07
k=0.08
k=0.09
20000
15000
10000
5000
0
0
0.2
0.4
0.6
0.8
1
1.2
Probability
Figure 3 The effect of price sensitivity on dual sourcing
The expected effect on buyer’s profit with the variation in product cost of local supplier in disruption state are
illustrated in Fig.3. The buyer’s profit decreases with an increase in price sensitivity parameter (k). The decrease in the
buyer’s profit as k varies from 0.07 to 0.09 is shown in Fig. 3.
Volume 4, Issue 7, July 2015
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Fig-2 Effect of the variation of the portion of the demand
allocated to local supplier on dual sourcing option
280000
B u ye r's p ro fit x 1 0 (R s.)
260000
240000
220000
x=0.1
x=0.3
200000
180000
x=0.5
160000
140000
120000
100000
80000
60000
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
Probability
Figure 4 Effect of the variation of the portion of the demand allocated to local supplier on dual sourcing option
The effect of price sensitivity parameter k on the buyer’s profit in the case when single sourcing (outside supplier) is
shown in Fig.4. In this case as sensitivity parameter k increases the decrease in buyer’s profit is more rapid as
compared to dual source case. The profit tends to zero at higher values of disruption probabilities in this case.
Fig. 5. The effect of increase in the unit price of the local supplier on
the buyer's profit in dual sourcing in disruption state.
30000
Buber's profit
25000
20000
Incerment in price(2%)
15000
Base price
10000
Increment in price(5%)
5000
0
0
0.2
0.4
0.6
0.8
1
1.2
Probability
Figure 5The effect of increase in the probe of the local supplier on the buyer’s profit in dual sourcing in disruption
state
In disruption state the local supplier is more expensive. The local supplier increases the price of product. The effect of
increase in product price by local supplier on buyer’s profit is shown in Fig.5. In the Figure the base price corresponds
to a unit price equal to Rs.400. The decrease in buyer’s profit with an increase of 2% and 5% in product price is shown
in Fig.5.
3. CONCLUSIONS
Equalize the in this study, a decision making model with the consideration of buyer’s optimal profiting disruption risk
is considered. Two critical probabilities of disruption are formulated and various options of supplier selection are
determined with the help of these critical probabilities. Two suppliers, one outside of the buyer’s geographical scope
and another local are considered. Outside supplier is prone to disruption and with competitive product price and local
more expensive. The credit concept is also included in the model. A numerical example illustrates the application of the
model. The sensitivity experiments conducted to show the effect of the variation of the portion of the demand allocated
to local supplier, the effect of variation in price sensitivity parameter and the effect of variation in the price of the
product of local supplier, on buyer’s profit.
REFERENCES
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[2] Hult, G. Tomas, M., David, J., Ketchen, Jr., Stanley, F.Stater, 2004. Information processing, knowledge
development and strategic supply chain performance. Academy of Management Journal, 47, 2,241-253.
[3] Lee, Haul, L., 2004. Aligning supply chain strategies with product uncertainties. California Management Review,
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[4] Wisner, Joel, D. 2003. A structural equation model of supply chain management strategies and firm performance
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[5] Thompson, 1990. Vender profile analysis. Journal of Purchasing and Material Management, 11-18.
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Production Economics, 115, 1,151-162.
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Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 7, July 2015
ISSN 2319 - 4847
[7] Ibrahim Abdul and Atsuo Murata, 2011. Optimal production strategy for deteorating items with varying demand
pattern under inflammation. International Journal Engineering Computations, 2,449-466.
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[9] Horwitz, I., 1986.On two source factor purchasing. Decision Science, 17,274-279.
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[12] Yu, H., Zeng, A.H. Zhao, L. Single or Dual sourcing decision making in the presence of supply chain disruption
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5. APPENDIX
The following constraint must be satisfied to choose the dual sourcing as optimal alternative.
Ψmso < Ψd
(1)
Ψmsl <Ψd
(2)
From eq. (1) we obtain
(1-P) фnso +P фdso < (1-P) фnd +P фdd
(3)
Eq. (3) may be arranged as
P > [1+ (фdd -фdso)/ (фnd -фnso )]-1
(4)
Hence first critical probability Lp is given a
Lp = [1 + (фdd - фdso)/ (фnd -фnso )]-1
From eq. (2) we obtain
(1-P) фnd +P фdd >Ψmsl
(5)
eq.(5) may be rearranged as
P < (фnd - Ψmsl)/ (фnd -фdd)
(6)
The second critical probability is given as
Up = (фnd -Ψmsl)/ (фnd - фdd )
The expression for Tmin can be derived as follows
eq. (2) may be written as
(1-P) фnd + Pфdd > (S-cbn ) D e-kcbn +cbn D e-kcbn T i
(7)
eq.(7) implies
(1-P) фnd + P фdd > cbn D e-kcbn T
(8)
Tmin = [(1-P) фnd +Pфdd ]/ cbn D e-kcbn
AUTHORS
Dhirendra Singh Parihar received the degree of B.Sc. (Hons.) Physics and M.Sc. Physics with
specialization in Materials during the year 1993 and 1995 respectively from a highly reputed central
university of India. During 1996-1998, he received the degree of PGDBM with specialization in
\marketing Management. After serving in some of the world’s best known MNC’s for a dacade, since last
eight years he is a full time Faculty and active researcher in the areas of Inventory and Supply
ChainManagement.while working at Ansal University,Gurgaon.India.
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