M01249
Two-stage newsboy problem for healthcare products and medical
devices with channel integration
Hui-Ming Wee
a
Department of Industrial & Systems Engineering, Chung Yuan
Christian University, Chungli 32023, Taiwan, ROC.
Joshua Chin Yee-Whah
School of Social Sciences, Universiti Sains Malaysia
11800 Penang, Malaysia
Tsai-Chi Kuo
a
Department of Industrial & Systems Engineering, Chung Yuan
Christian University, Chungli 32023, Taiwan, ROC.
Yugowati Praharsi
Department of Information Technology,
Satya Wacana Christian University, Salatiga 50711, Indonesia
Abstract
In this study, we consider a two-stage newsboy problem for healthcare products and
medical devices with channel integration. The risk of demand uncertainty is reduced
when both parties consider revenue sharing and return policies. This paper considers
channel integration strategy by manufacture and retailer with joint decision. This will
reduce bullwhip effect and demand uncertainty. The objective is to maximize the profit
of the manufacturer and retailer. A numerical example and sensitivity analysis are
provided to illustrate the theory.
Keywords：Inventory; Revenue sharing; Return policy; Channel integration
1
1. Introduction
In recent years, healthcare products and medical devices supply chain are facing
increasing challenges due to demand uncertainty and business competitions. These
conditions may result in overstocking or shortage for the supply chain players; and it
will affect the profit of the whole supply chain. In the long run, the manufacturer and
the retailer supply/demand chains will lose their competitiveness.
In viewed of this,
strategic cooperation by equitable sharing contract can be achieved through a win-win
integration strategy for the manufacturer and the retailer. It can reduce bullwhip effect
and lead to an increase in the overall supply chain profit. In this study, an optimal
decision using the integrated strategy reveals the differences between a centralized and a
decentralized decision making. Two contract strategies such as revenue sharing and
return policy are considered. Revenue sharing strategy means the supplier motivates the
retailer to increase his order quantity with preferential price; the retailer in turns will
share a certain percentage of the profit to the supplier. Because of uncertain demand,
shortage/overstocking may incur when the demand is greater/less than the order quantity.
In the supply chain partnership, the manufacturer and the retailer share both their
shortage cost as well as their revenues. A return policy is contracted to reduce the cost
of overstocking. In this research, we develop an integrated strategy for stochastic
demand environments.
In section two, we show the motivation and literature review. Section three presents a
basic model of a single manufacturer and a single retailer newsboy problem under
integrated decision environments. Sensitivity analysis and comparisons of results are
shown in Section four, and concluding remarks are given in Section five. The analysis in
this study provides enterprises managerial insights in making strategic decision to
2
achieve a win-win strategy.
2. Literature review
Return policy or buy back contract is widely used for short life cycle products.
When the product demand declines, the manufacturer would provide the retailer a return
mechanism for unsold goods. This is especially necessary for healthcare products such
as drugs which have expired dates. The policy reduces the retailers' cost of overstocking
and the risk of under-stocking, thus achieve risk pooling. Yao et al. [1] used Stackelberg
game to establish return policy model under uncertain demand and price dependency.
Qin and Yang [2] discussed an optimal decision making model of profit maximization
from different viewpoints. They proposed a part of manufacturing cost paid by the
retailer at discount price. He et al. [3] discussed the relationship between demand and
sale price in revenue sharing, return policy and supplier-retailer partnership strategy.
The other strategy to optimize supply chain profit is revenue sharing contract.
There are many intensive researches to analyze the benefit of revenue sharing contract
in the supply chain. Wang et al. [4] analyzed the performance of the supplier and the
retailer under consignment contract with revenue sharing. Giannoccaro and
Pontrandolfo [5] developed a supply chain contract model based on revenue sharing
mechanism in a three-stage supply chain. Chauhan and Proth [6] proposed an approach
to maximize provider and retailer profits by using revenue sharing mechanism. Hou et
al. [7] developed a coordination model between one supplier and one retailer under
revenue sharing and bargaining. However, this cooperation is difficult to realize since
each player wants to optimize his own profit. A win-win strategy is therefore necessary.
Supply chain management for healthcare and medical devices is important as they
significantly influence medical industries. However, its significant is not well explored.
3
Our study investigates its significant and ways to improve the existing system. The
operations management theory and methodologies together with information technology
can provide flexible and robust mechanism that could drives the industry to function
more orderly. Kuo and Shen [8] made a review on the development of lean healthcare,
and King et al. [9] discussed the application of lean thinking to health care in emergency
department. Acharyulu and Shekhar [10] did an empirical study in India on the role of
value chain strategy in healthcare supply chain management. Callender and Grasman,
[11] studied the barriers and best practices for material management in the healthcare
sector. Mustaffa and Potter [12] developed a case study on the healthcare supply chain
management in Malaysia.
Price is the most significant factor in purchasing behavior from the downstream to
the upstream of a supply chain. Researches on stochastic demand have been conducted
extensively. Emmons and Gilbert [13] discussed the optimal ordering, pricing and return
policy with uncertain demand. Petruzzi and Dada [14] explored the newsboy problems
and developed a two-level newsboy inventory and pricing model. Lau and Lau [15]
discussed how to reduced uncertainty and resolved the newsboy problem with uncertain
demand. Taylor [16] suggested that the manufacturers should compare different data of
demands to coordinate the supply chain. Granot and Yin [17] suggested the
manufacturer can focus on the wholesale price and the retailer can focus on pricing and
ordering method in newsboy model with uncertain demands.
From our literature research, there was no research that analyzes the integrated
strategy for healthcare products and medical devices supply chain using newsboy
problem. This research tries to fill the gap in this area.
3. Basic model for a single manufacturer and a single retailer
4
Due to the bullwhip effect in a supply chain, uncoordinated chains usually lead to a
higher risk of overstocking or shortages. This study considers profit sharing, shortage
cost sharing, and return policy to develop an integrated strategy model. The assumptions
and parameters are as follows:
(1) All stockouts entails shortage cost.
(2) A single manufacturer and a single retailer are considered.
(3) Delivery is instantaneous.
(4) Demand is uncertain.
(5) The manufacturer production capacity is unlimited
All the parameters used in this study are summarized in Table 1.
-----------------------Table 1
-----------------------The classical newsboy model is extended for a single-retailer and a
single-manufacturer with one-time ordering. When a transaction occurs, the
manufacturer incurs a manufacturing cost c with a product wholesale price w. The
retailer offers a retail price p to its customers. At the end of the selling season, if the
demand is greater than the production quantity, a shortage cost, s, is incurred. On the
other hand, excessive products resulting in inventory cost of r per unit. The basic
assumption is expressed as p w c r , and s p c . The process flow for the model
is depicted in the Figure 1 below:
-----------------------Figure 1
-----------------------The function between the retailer's order quantity and the demand are as follows:
5
px wQ r (Q x)
f (Q, x)
pQ wQ s ( x Q )
,xQ
,xQ
(1)
The retailer’s total expected profit consists of product sales revenue, wholesale cost,
shortage cost, and surplus value of products. This can be expressed as:
R px wQ r (Q x) f ( x)dx pQ wQ s ( x Q ) f ( x)dx
Q
0
Q
( pQ s sQ wQ ) Q ( p s r ) f ( x)dx ( p s r ) xf ( x)dx
Q
Q
0
0
Q ( p s w) s ( p s r ) F ( x)dx
Q
(2)
0
The manufacturer’s total expected profit consists of the retailer’s wholesale revenue and
the manufacturing cost. It can be modeled as:
M (w c)Q
(3)
The total expected profit for the supply chain can be calculated by summing (2) and (3).
One has:
T px wQ r (Q x) f ( x)dx pQ wQ s ( x Q ) f ( x)dx ( w c )Q
Q
0
Q
Q ( p s c) s ( p s r ) F ( x)dx
Q
(4)
0
The aim is to maximize the overall expected profit of the supply chain and determine
the retailer’s optimal order quantity. Taking the first derivative of R and T with
respect to Q, the maximum expected profit is derived as follows:
6
R (Q)
wf ( x) dx ( p s w) f ( x)dx p s w ( p s r ) F (Q) 0
Q
Q
0
Q
F (QR* )
psw
psr
p s w
QR* F 1
p
s
r
(5)
T (Q )
wf ( x) dx ( p s w) f ( x)dx w c p s c ( p s r ) F (Q ) 0
Q
Q
0
Q
F (QT* )
psc
psr
p s c
, obtained QT* F 1
psr
(6)
Solving the second derivative of (2) and (4) with respect to Q, one has:
2 R (Q )
( p s r ) f (Q ) 0
Q 2
2 T (Q )
( p s r ) f (Q ) 0
Q 2
(7)
(8)
It can be observed in (7) and (8) that since p, s, r, f(Q) > 0 and p s > r , the models are
concave. Thus, the retailer can maximize its individual profits under the optimal order
quantities QR* and QT* .
The difference between the retailer’s order quantity in the channel integration and
his independent order quantity is shown by the following equation:
F (QT* ) F (QR* )
p s c p s w
0
psr psr
(9)
The result in (9) indicates that:
1. The retailer’s order quantity under coordination would be greater than his order
under the non-coordination model; and
2. The retailer’s order quantity for the coordination model leads to higher
manufacturer’s profit than the non-coordination model as shown by the equation
below:
M (QT* ) M (QR* ) (w c)(QT* QR* ) 0
(10)
7
Hence, the manufacturer can encourage the retailer to increase his order quantity
considering profit sharing. An integration policy is presented and discussed in the
subsequent sections.
4. Strategic contract model
This study extends the revenue sharing model by Qin and Yang (2008) and considers
the shortage cost sharing and return policy by Leng and Parlar (2010). The channel
integration is applied to examine results under different business environments. In the
revenue and shortage cost sharing contract, high sharing rate α of the manufacturer leads
to a preferred wholesale price for the retailer as a feedback mechanism. In the return
policy contract, manufacturers will buy back the entire surplus product with price b. To
avoid double profit, the price b follows the condition: b w c r .
We define the following conditions: (0,1] and s(1 ) where p and s
denotes respectively the sharing rate and shortage cost shared by both players in the
contract. The flow of the contract is shown in Figure 2.
-----------------------Figure 2
-----------------------The manufacturer adopts shortage cost sharing and buy-back mechanism to
encourage the retailer to co-operate in the revenue sharing contract. Under the cost
sharing contract, the unit shortage cost is the unit product retail price minus the
manufacturing cost plus reputation/goodwill loss (g). The unit shortage cost can be
expressed as s p c g , where g 0 . Under the revenue sharing contract, when the
manufacturer proposes a high sharing rate , he would offer a lower wholesale price
8
w' to the retailer as a feedback mechanism. The relationship can be expressed as:
w' (1 2 )w
(11)
Similar feedback mechanism has been used by Qin and Yang (2008).
According to the basic assumptions, the manufacturer’s wholesale price is greater than
his manufacturing cost. Thus w' c and 0
w c
.
w
Channel integration model
The supply chain's total expected profit is the sum of R and M . It can be
expressed as:
T (Q ) Q p c s s ( p s r ) F ( x)dx
Q
(19)
0
Taking the first and second derivative of (19) with respect to Q, and derive QT* , one
has:
F (QT* )
pcs
pcs
, therefore QT* F 1
psr
p
s
r
2 T (Q )
( p s r ) f (Q ) 0
Q 2
(20)
(21)
where p, s, r, f (Q ) > 0, and p s > r .
5. Numerical examples and sensitivity analysis
In this section, we use the following data: c= $20/unit; w= $40/unit; p= $70/unit;
r= $5/unit; s= $52/unit; b= $25/unit and demand x is uniformly distributed U(50, 250).
9
5.1 Numerical examples
Table 2 shows the calculation results. It shows that the retailer’s ordering quantity in
the integrated model is 17.98% higher than the independent model. The total expected
supply chain profit for the integrated model is also 5.84% higher than the independent
model. Substituting the optimal ordering quantity of the integrated model into the
equation (2) and (3), we can derive the retailer and the manufacturer’s expected profit
respectively. The profits for the manufacturer and the retailer deviate from the
independent policy by nearly 18% and -16.7% respectively. In the integrated model, the
difference between the manufacturer and the retailer’s expected profit is 14.91% more
than the independent model. However, the retailer‘s profit is reduced by 16.70%; it is
therefore not in the interest of the retailer to integrate. There is a need to provide some
incentives for the retailer
-----------------------Table 2
-----------------------Since α is a known parameter, substituting it into (19) and (20), one has the optimal
order quantity QT* 224.3589 and the expected profit for the integrated channel T
= $ 6,192.3076.
The comparison of the model is summarized in Table 3. The expected retailer’s
profit and the optimal order quantity in the channel coordination are less than without
coordination.
The expected manufacturer’s profit in the channel distribution is higher
than coordination. The result supports a common insight that coordination with known
information in a business environment is better than unknown information.
------------------------
10
Table 3
-----------------------The summary with/without the contract strategy is shown in Table 5. It shows that
the contract strategy results in a higher profit in all business environments than the
non-contracted strategy. It can be observed that channel integration model can improve
the total expected supply chain profit. If a contract strategy is used for the integrated
channel, with a value of =0.11412, the manufacturer's expected profit and the
retailer's expected profit can effectively be increased by 5.84%. Table 4 shows the
differences between with integration and without integration. The manufacturer
receives more profit in the integration strategy at the expense of the retailer.
-----------------------Table 4
-----------------------5.2. Sensitivity analysis
The parameters (Ф) are set to be fixed at values Ф = {c=20, w=40, p=70, r=5, s=52,
b=25}. The sensitivity is performed by increasing and decreasing the values of Ф by
-30%, -20%, -10%, 0%, 10%, 20%, and 30%. The correlation and sensitivity analysis of
the parameters are shown in Table 5.
-----------------------Table 5
-----------------------For the channel integration, p and c are the most sensitivity parameters to
T (QT* , * ) . When p and c are increased or decreased by 30%, the expected total profit
symmetrically increases or decreases by 50% and 22.24% respectively. Parameters w, r ,
11
s, and b are moderately sensitivities to the expected total profit.
From the sensitivity analysis, we find p and c are the most sensitive parameters to
T (QR* , * ) in the scenario. It shows that the total profit increase dramatically for
decreasing the unit manufacturing cost of the manufacturers c and increasing the unit selling
price of the retailers p. It helps the supply chain members pay more attention to the key
parameters to dramatically increase their profits.
6. Conclusions and Future Research
This study discusses a contract strategy under channel integration using a newsboy
model. To depict real life business scenarios, the contract strategy adopts the
revenue/cost sharing, and return policy for collaborative decision-making strategy in a
supply chain. It is found that the total supply chain profit can be increased by the
contract strategy using revenue/cost sharing and return policies. The manufacturer and
retailer’s profit can effectively increase when the supply chain achieves channel
coordination with the contract strategy.
Several possible extensions of this study can be conducted for possible research
endeavors. Multi-products can be explored in future research instead of single product.
Multiple-manufacturer or retailers and three-level supply chain model can also be
considered to reflect the global supply chain environment. The buy-back price and
return percentage for the return policy can also be considered as the manufacturer’s
decision variable.
References:
[1] Yao, Z., S.C.H. Leung, and K.K. Lai, “Analysis of the impact of price-sensitivity
12
factors on the returns policy in coordination supply chain”, European Journal of
Operational Research, 187, 275-282, (2008).
[2] Qin, Z., and J. Yang, “Analysis of a revenue-sharing contracts in supply chain
management”, International Journal of Logistics：Research and Applications, 11(1),
17-29, (2008).
[3] He, Y., X. Zhao, L. Zhao, and J. He, “Coordinating a supply chain with effort and
price dependent stochastic demand”, Applied Mathematical Modeling , 33,
2777-2790, (2009).
[4] Wang Y., L. Jiang, and Z.J. Shen, “Channel performance under consignment contract
with revenue sharing”, Management Science, 50(1), 34 – 47, (2004).
[5] Giannoccaro I., and P. Pontrandolfo, “Supply chain coordination by revenue sharing
contracts”, International Journal of Production Economics, 89(2), 131–139, (2004).
[6] Chauhan S.S., and J.M. Proth, “Analysis of a supply chain partnership with revenue
sharing”, International Journal of Production Economics, 97(1), 44 – 51, (2005).
[7] Hou J., A.Z., Zeng, and L. Zhao, “Achieving better coordination through revenue
sharing and bargaining in a two-stage supply chain”, Computers & Industrial
Engineering, 57(1), 383 – 394, (2009).
[8] Kuo, T. and Shen, J.P., The Review and Development of Lean Healthcare, Service
Science and Management 服务科学和管理, 2013, 2, 27-31
doi:10.12677/ssem.2013.21005 Published Online February 2013
(http://www.hanspub.org/journal/ssem.html)
[9] King, D. L., D. Iben-Tovim and J. Bassham. Redesigning emergency department
patient flows: Application of lean thinking to health care. Emergency Medicine
Australasia , 2006, 18(4): 391-397.
[10] Acharyulu, G.V.R.K. and Shekhar, B. R., Role of Value Chain Strategy in
Healthcare Supply Chain Management: An Empirical Study in India, International
Journal of Management, Vol. 29 No. 1 Part 1 Mar 2012, 91-97
[11] Callender, C and Grasman, S. E., Barriers and Best Practices for Material
Management in the Healthcare Sector, Engineering Management Journal Vol. 22 No.
4, December 2010, 11-19.
[12] Mustaffa, N. H. and Potter, A., Healthcare supply chain management in Malaysia: a
case study", Supply Chain Management- an international journal, 14, (2009)
[13] Emmons, H. and S.M. Gilbert, “Note. The role of returns policies in pricing and
inventory decisions for catalogue goods”, Management Science, 44(2), 276-283,
(1998).
[14] Petruzzi, N.C., and M. Dada, “Pricing and the newsvendor problem：A review with
extensions”, Operation Research, 47(2), 183-194, (1999).
[15] Lau, A.H.L., and H.S. Lau, “The effects of reducing demand uncertainty in a
manufacturer-retailer channel for single-period products”, Computers & Operations
Research, 29, 1583-1602, (2002).
[16] Taylor, T.A., “Supply chain coordination under channel rebates with sales effort
effects”, Management Science, 48(8), 992-1007, (2002).
[17] Granot, D., and S. Yin, “Price and order postponement in a decentralized
13
newsvendor model with multiplicative and price-dependent demand”, Operations
Research, 56(1), 121-139, (2008).
Table 1. The notations of parameters
Parameters
Description
c
The unit manufacturing cost of the manufacturers
w
The unit wholesale prices that wholesales buy from the manufacturers
The unit selling price of the retailers with supplier chain contract model
The surplus value of unit product.
The shortage cost of unit product
The unit price the manufacturers buy back the surplus product from the retailers.
The contract of revenue and cost-sharing rate
The parameter of market demand change due to price fluctuation
The slope of demand change due to price fluctuation.
The retailer’s order quantity
p
r
s
b
a
l
QR
QT
x
f ( x)
f ( x, p )
F ( x)
The retailer’s order quantity in channel integration
The market’s random demand during sale season
The probability density function of demand x under the supply chain contract
model
The probability density function of demand x under the price dependent
contract strategy
The cumulative probability density function of demand x
R
M
T
The retailer’s expected profit model
The manufacturer’s expected profit model
Assumptions
The total supply chain’s expected profit model in channel integration
p w c r
s p c
b w c r
Table 2. The numerical example results
M R
Q
R
M
T
Independent
190.1709
2047.0085
3803.1488
5850.4273
30.01%
Integrated
224.3598
1705.1282
4487.1794
6192.3076
44.92%
rate of increase/
17.98%
-16.70%
17.99%
5.84%
14.91%
supply chain
type
／ T
14
decrease
Table 3. Comparison for under the different business decision-making models
Strategy
Modes
Channel
integration
Increase rate (%)
Channel
integration
Increase rate (%)
M
Q
R
M R
T
T
0.5401
224.36
5921.04
280.27
6192.31
91.09%
0
-1.85%
0.27%
-0.50%
0.08%
0.21%
0.5591
224.36
5920.26
272.05
6192.31
91.21%
0
-3.57%
0.43%
-1.8%
0.33%
0.19%
Table 4. Differences between with contract and without contract
Strategy
Models
No-contract
Individual
Channel
Contract
integration
Increase rate (%)
Q
M
R
T
0
190.17 3803.15 2047.09 5850.43
0.114
224.36 4025.63 2166.68 6192.30
1
—
0
5.84
5.84
5.84
M R
T
30.47%
30.02%
-0.45
Table 5. The correlation and sensitivity analysis
Correlative
analysis
Sensitivity
analysis
Positive correlation
Channel
integration
p、r
Negative correlation
Non-Correlation
c、s
w、b
High sensitivity
p、c
Medium sensitivity
Low sensitivity
w、r 、s、b
-
15
Figure 1
$w
$c
$p
Manufacturer
Retailer
Customer
f ( x)
Q
$r
$s
Figure 1. Model construction
Figure 2
$ p
$c
Manufacturer
$r
$(1 2 )w
$p
Retailer
$b
Customer
f ( x)
Q
$ s
$s(1 )
Figure 2. The contract flow
16
devices with channel integration
Hui-Ming Wee
a
Department of Industrial & Systems Engineering, Chung Yuan
Christian University, Chungli 32023, Taiwan, ROC.
Joshua Chin Yee-Whah
School of Social Sciences, Universiti Sains Malaysia
11800 Penang, Malaysia
Tsai-Chi Kuo
a
Department of Industrial & Systems Engineering, Chung Yuan
Christian University, Chungli 32023, Taiwan, ROC.
Yugowati Praharsi
Department of Information Technology,
Satya Wacana Christian University, Salatiga 50711, Indonesia
Abstract
In this study, we consider a two-stage newsboy problem for healthcare products and
medical devices with channel integration. The risk of demand uncertainty is reduced
when both parties consider revenue sharing and return policies. This paper considers
channel integration strategy by manufacture and retailer with joint decision. This will
reduce bullwhip effect and demand uncertainty. The objective is to maximize the profit
of the manufacturer and retailer. A numerical example and sensitivity analysis are
provided to illustrate the theory.
Keywords：Inventory; Revenue sharing; Return policy; Channel integration
1
1. Introduction
In recent years, healthcare products and medical devices supply chain are facing
increasing challenges due to demand uncertainty and business competitions. These
conditions may result in overstocking or shortage for the supply chain players; and it
will affect the profit of the whole supply chain. In the long run, the manufacturer and
the retailer supply/demand chains will lose their competitiveness.
In viewed of this,
strategic cooperation by equitable sharing contract can be achieved through a win-win
integration strategy for the manufacturer and the retailer. It can reduce bullwhip effect
and lead to an increase in the overall supply chain profit. In this study, an optimal
decision using the integrated strategy reveals the differences between a centralized and a
decentralized decision making. Two contract strategies such as revenue sharing and
return policy are considered. Revenue sharing strategy means the supplier motivates the
retailer to increase his order quantity with preferential price; the retailer in turns will
share a certain percentage of the profit to the supplier. Because of uncertain demand,
shortage/overstocking may incur when the demand is greater/less than the order quantity.
In the supply chain partnership, the manufacturer and the retailer share both their
shortage cost as well as their revenues. A return policy is contracted to reduce the cost
of overstocking. In this research, we develop an integrated strategy for stochastic
demand environments.
In section two, we show the motivation and literature review. Section three presents a
basic model of a single manufacturer and a single retailer newsboy problem under
integrated decision environments. Sensitivity analysis and comparisons of results are
shown in Section four, and concluding remarks are given in Section five. The analysis in
this study provides enterprises managerial insights in making strategic decision to
2
achieve a win-win strategy.
2. Literature review
Return policy or buy back contract is widely used for short life cycle products.
When the product demand declines, the manufacturer would provide the retailer a return
mechanism for unsold goods. This is especially necessary for healthcare products such
as drugs which have expired dates. The policy reduces the retailers' cost of overstocking
and the risk of under-stocking, thus achieve risk pooling. Yao et al. [1] used Stackelberg
game to establish return policy model under uncertain demand and price dependency.
Qin and Yang [2] discussed an optimal decision making model of profit maximization
from different viewpoints. They proposed a part of manufacturing cost paid by the
retailer at discount price. He et al. [3] discussed the relationship between demand and
sale price in revenue sharing, return policy and supplier-retailer partnership strategy.
The other strategy to optimize supply chain profit is revenue sharing contract.
There are many intensive researches to analyze the benefit of revenue sharing contract
in the supply chain. Wang et al. [4] analyzed the performance of the supplier and the
retailer under consignment contract with revenue sharing. Giannoccaro and
Pontrandolfo [5] developed a supply chain contract model based on revenue sharing
mechanism in a three-stage supply chain. Chauhan and Proth [6] proposed an approach
to maximize provider and retailer profits by using revenue sharing mechanism. Hou et
al. [7] developed a coordination model between one supplier and one retailer under
revenue sharing and bargaining. However, this cooperation is difficult to realize since
each player wants to optimize his own profit. A win-win strategy is therefore necessary.
Supply chain management for healthcare and medical devices is important as they
significantly influence medical industries. However, its significant is not well explored.
3
Our study investigates its significant and ways to improve the existing system. The
operations management theory and methodologies together with information technology
can provide flexible and robust mechanism that could drives the industry to function
more orderly. Kuo and Shen [8] made a review on the development of lean healthcare,
and King et al. [9] discussed the application of lean thinking to health care in emergency
department. Acharyulu and Shekhar [10] did an empirical study in India on the role of
value chain strategy in healthcare supply chain management. Callender and Grasman,
[11] studied the barriers and best practices for material management in the healthcare
sector. Mustaffa and Potter [12] developed a case study on the healthcare supply chain
management in Malaysia.
Price is the most significant factor in purchasing behavior from the downstream to
the upstream of a supply chain. Researches on stochastic demand have been conducted
extensively. Emmons and Gilbert [13] discussed the optimal ordering, pricing and return
policy with uncertain demand. Petruzzi and Dada [14] explored the newsboy problems
and developed a two-level newsboy inventory and pricing model. Lau and Lau [15]
discussed how to reduced uncertainty and resolved the newsboy problem with uncertain
demand. Taylor [16] suggested that the manufacturers should compare different data of
demands to coordinate the supply chain. Granot and Yin [17] suggested the
manufacturer can focus on the wholesale price and the retailer can focus on pricing and
ordering method in newsboy model with uncertain demands.
From our literature research, there was no research that analyzes the integrated
strategy for healthcare products and medical devices supply chain using newsboy
problem. This research tries to fill the gap in this area.
3. Basic model for a single manufacturer and a single retailer
4
Due to the bullwhip effect in a supply chain, uncoordinated chains usually lead to a
higher risk of overstocking or shortages. This study considers profit sharing, shortage
cost sharing, and return policy to develop an integrated strategy model. The assumptions
and parameters are as follows:
(1) All stockouts entails shortage cost.
(2) A single manufacturer and a single retailer are considered.
(3) Delivery is instantaneous.
(4) Demand is uncertain.
(5) The manufacturer production capacity is unlimited
All the parameters used in this study are summarized in Table 1.
-----------------------Table 1
-----------------------The classical newsboy model is extended for a single-retailer and a
single-manufacturer with one-time ordering. When a transaction occurs, the
manufacturer incurs a manufacturing cost c with a product wholesale price w. The
retailer offers a retail price p to its customers. At the end of the selling season, if the
demand is greater than the production quantity, a shortage cost, s, is incurred. On the
other hand, excessive products resulting in inventory cost of r per unit. The basic
assumption is expressed as p w c r , and s p c . The process flow for the model
is depicted in the Figure 1 below:
-----------------------Figure 1
-----------------------The function between the retailer's order quantity and the demand are as follows:
5
px wQ r (Q x)
f (Q, x)
pQ wQ s ( x Q )
,xQ
,xQ
(1)
The retailer’s total expected profit consists of product sales revenue, wholesale cost,
shortage cost, and surplus value of products. This can be expressed as:
R px wQ r (Q x) f ( x)dx pQ wQ s ( x Q ) f ( x)dx
Q
0
Q
( pQ s sQ wQ ) Q ( p s r ) f ( x)dx ( p s r ) xf ( x)dx
Q
Q
0
0
Q ( p s w) s ( p s r ) F ( x)dx
Q
(2)
0
The manufacturer’s total expected profit consists of the retailer’s wholesale revenue and
the manufacturing cost. It can be modeled as:
M (w c)Q
(3)
The total expected profit for the supply chain can be calculated by summing (2) and (3).
One has:
T px wQ r (Q x) f ( x)dx pQ wQ s ( x Q ) f ( x)dx ( w c )Q
Q
0
Q
Q ( p s c) s ( p s r ) F ( x)dx
Q
(4)
0
The aim is to maximize the overall expected profit of the supply chain and determine
the retailer’s optimal order quantity. Taking the first derivative of R and T with
respect to Q, the maximum expected profit is derived as follows:
6
R (Q)
wf ( x) dx ( p s w) f ( x)dx p s w ( p s r ) F (Q) 0
Q
Q
0
Q
F (QR* )
psw
psr
p s w
QR* F 1
p
s
r
(5)
T (Q )
wf ( x) dx ( p s w) f ( x)dx w c p s c ( p s r ) F (Q ) 0
Q
Q
0
Q
F (QT* )
psc
psr
p s c
, obtained QT* F 1
psr
(6)
Solving the second derivative of (2) and (4) with respect to Q, one has:
2 R (Q )
( p s r ) f (Q ) 0
Q 2
2 T (Q )
( p s r ) f (Q ) 0
Q 2
(7)
(8)
It can be observed in (7) and (8) that since p, s, r, f(Q) > 0 and p s > r , the models are
concave. Thus, the retailer can maximize its individual profits under the optimal order
quantities QR* and QT* .
The difference between the retailer’s order quantity in the channel integration and
his independent order quantity is shown by the following equation:
F (QT* ) F (QR* )
p s c p s w
0
psr psr
(9)
The result in (9) indicates that:
1. The retailer’s order quantity under coordination would be greater than his order
under the non-coordination model; and
2. The retailer’s order quantity for the coordination model leads to higher
manufacturer’s profit than the non-coordination model as shown by the equation
below:
M (QT* ) M (QR* ) (w c)(QT* QR* ) 0
(10)
7
Hence, the manufacturer can encourage the retailer to increase his order quantity
considering profit sharing. An integration policy is presented and discussed in the
subsequent sections.
4. Strategic contract model
This study extends the revenue sharing model by Qin and Yang (2008) and considers
the shortage cost sharing and return policy by Leng and Parlar (2010). The channel
integration is applied to examine results under different business environments. In the
revenue and shortage cost sharing contract, high sharing rate α of the manufacturer leads
to a preferred wholesale price for the retailer as a feedback mechanism. In the return
policy contract, manufacturers will buy back the entire surplus product with price b. To
avoid double profit, the price b follows the condition: b w c r .
We define the following conditions: (0,1] and s(1 ) where p and s
denotes respectively the sharing rate and shortage cost shared by both players in the
contract. The flow of the contract is shown in Figure 2.
-----------------------Figure 2
-----------------------The manufacturer adopts shortage cost sharing and buy-back mechanism to
encourage the retailer to co-operate in the revenue sharing contract. Under the cost
sharing contract, the unit shortage cost is the unit product retail price minus the
manufacturing cost plus reputation/goodwill loss (g). The unit shortage cost can be
expressed as s p c g , where g 0 . Under the revenue sharing contract, when the
manufacturer proposes a high sharing rate , he would offer a lower wholesale price
8
w' to the retailer as a feedback mechanism. The relationship can be expressed as:
w' (1 2 )w
(11)
Similar feedback mechanism has been used by Qin and Yang (2008).
According to the basic assumptions, the manufacturer’s wholesale price is greater than
his manufacturing cost. Thus w' c and 0
w c
.
w
Channel integration model
The supply chain's total expected profit is the sum of R and M . It can be
expressed as:
T (Q ) Q p c s s ( p s r ) F ( x)dx
Q
(19)
0
Taking the first and second derivative of (19) with respect to Q, and derive QT* , one
has:
F (QT* )
pcs
pcs
, therefore QT* F 1
psr
p
s
r
2 T (Q )
( p s r ) f (Q ) 0
Q 2
(20)
(21)
where p, s, r, f (Q ) > 0, and p s > r .
5. Numerical examples and sensitivity analysis
In this section, we use the following data: c= $20/unit; w= $40/unit; p= $70/unit;
r= $5/unit; s= $52/unit; b= $25/unit and demand x is uniformly distributed U(50, 250).
9
5.1 Numerical examples
Table 2 shows the calculation results. It shows that the retailer’s ordering quantity in
the integrated model is 17.98% higher than the independent model. The total expected
supply chain profit for the integrated model is also 5.84% higher than the independent
model. Substituting the optimal ordering quantity of the integrated model into the
equation (2) and (3), we can derive the retailer and the manufacturer’s expected profit
respectively. The profits for the manufacturer and the retailer deviate from the
independent policy by nearly 18% and -16.7% respectively. In the integrated model, the
difference between the manufacturer and the retailer’s expected profit is 14.91% more
than the independent model. However, the retailer‘s profit is reduced by 16.70%; it is
therefore not in the interest of the retailer to integrate. There is a need to provide some
incentives for the retailer
-----------------------Table 2
-----------------------Since α is a known parameter, substituting it into (19) and (20), one has the optimal
order quantity QT* 224.3589 and the expected profit for the integrated channel T
= $ 6,192.3076.
The comparison of the model is summarized in Table 3. The expected retailer’s
profit and the optimal order quantity in the channel coordination are less than without
coordination.
The expected manufacturer’s profit in the channel distribution is higher
than coordination. The result supports a common insight that coordination with known
information in a business environment is better than unknown information.
------------------------
10
Table 3
-----------------------The summary with/without the contract strategy is shown in Table 5. It shows that
the contract strategy results in a higher profit in all business environments than the
non-contracted strategy. It can be observed that channel integration model can improve
the total expected supply chain profit. If a contract strategy is used for the integrated
channel, with a value of =0.11412, the manufacturer's expected profit and the
retailer's expected profit can effectively be increased by 5.84%. Table 4 shows the
differences between with integration and without integration. The manufacturer
receives more profit in the integration strategy at the expense of the retailer.
-----------------------Table 4
-----------------------5.2. Sensitivity analysis
The parameters (Ф) are set to be fixed at values Ф = {c=20, w=40, p=70, r=5, s=52,
b=25}. The sensitivity is performed by increasing and decreasing the values of Ф by
-30%, -20%, -10%, 0%, 10%, 20%, and 30%. The correlation and sensitivity analysis of
the parameters are shown in Table 5.
-----------------------Table 5
-----------------------For the channel integration, p and c are the most sensitivity parameters to
T (QT* , * ) . When p and c are increased or decreased by 30%, the expected total profit
symmetrically increases or decreases by 50% and 22.24% respectively. Parameters w, r ,
11
s, and b are moderately sensitivities to the expected total profit.
From the sensitivity analysis, we find p and c are the most sensitive parameters to
T (QR* , * ) in the scenario. It shows that the total profit increase dramatically for
decreasing the unit manufacturing cost of the manufacturers c and increasing the unit selling
price of the retailers p. It helps the supply chain members pay more attention to the key
parameters to dramatically increase their profits.
6. Conclusions and Future Research
This study discusses a contract strategy under channel integration using a newsboy
model. To depict real life business scenarios, the contract strategy adopts the
revenue/cost sharing, and return policy for collaborative decision-making strategy in a
supply chain. It is found that the total supply chain profit can be increased by the
contract strategy using revenue/cost sharing and return policies. The manufacturer and
retailer’s profit can effectively increase when the supply chain achieves channel
coordination with the contract strategy.
Several possible extensions of this study can be conducted for possible research
endeavors. Multi-products can be explored in future research instead of single product.
Multiple-manufacturer or retailers and three-level supply chain model can also be
considered to reflect the global supply chain environment. The buy-back price and
return percentage for the return policy can also be considered as the manufacturer’s
decision variable.
References:
[1] Yao, Z., S.C.H. Leung, and K.K. Lai, “Analysis of the impact of price-sensitivity
12
factors on the returns policy in coordination supply chain”, European Journal of
Operational Research, 187, 275-282, (2008).
[2] Qin, Z., and J. Yang, “Analysis of a revenue-sharing contracts in supply chain
management”, International Journal of Logistics：Research and Applications, 11(1),
17-29, (2008).
[3] He, Y., X. Zhao, L. Zhao, and J. He, “Coordinating a supply chain with effort and
price dependent stochastic demand”, Applied Mathematical Modeling , 33,
2777-2790, (2009).
[4] Wang Y., L. Jiang, and Z.J. Shen, “Channel performance under consignment contract
with revenue sharing”, Management Science, 50(1), 34 – 47, (2004).
[5] Giannoccaro I., and P. Pontrandolfo, “Supply chain coordination by revenue sharing
contracts”, International Journal of Production Economics, 89(2), 131–139, (2004).
[6] Chauhan S.S., and J.M. Proth, “Analysis of a supply chain partnership with revenue
sharing”, International Journal of Production Economics, 97(1), 44 – 51, (2005).
[7] Hou J., A.Z., Zeng, and L. Zhao, “Achieving better coordination through revenue
sharing and bargaining in a two-stage supply chain”, Computers & Industrial
Engineering, 57(1), 383 – 394, (2009).
[8] Kuo, T. and Shen, J.P., The Review and Development of Lean Healthcare, Service
Science and Management 服务科学和管理, 2013, 2, 27-31
doi:10.12677/ssem.2013.21005 Published Online February 2013
(http://www.hanspub.org/journal/ssem.html)
[9] King, D. L., D. Iben-Tovim and J. Bassham. Redesigning emergency department
patient flows: Application of lean thinking to health care. Emergency Medicine
Australasia , 2006, 18(4): 391-397.
[10] Acharyulu, G.V.R.K. and Shekhar, B. R., Role of Value Chain Strategy in
Healthcare Supply Chain Management: An Empirical Study in India, International
Journal of Management, Vol. 29 No. 1 Part 1 Mar 2012, 91-97
[11] Callender, C and Grasman, S. E., Barriers and Best Practices for Material
Management in the Healthcare Sector, Engineering Management Journal Vol. 22 No.
4, December 2010, 11-19.
[12] Mustaffa, N. H. and Potter, A., Healthcare supply chain management in Malaysia: a
case study", Supply Chain Management- an international journal, 14, (2009)
[13] Emmons, H. and S.M. Gilbert, “Note. The role of returns policies in pricing and
inventory decisions for catalogue goods”, Management Science, 44(2), 276-283,
(1998).
[14] Petruzzi, N.C., and M. Dada, “Pricing and the newsvendor problem：A review with
extensions”, Operation Research, 47(2), 183-194, (1999).
[15] Lau, A.H.L., and H.S. Lau, “The effects of reducing demand uncertainty in a
manufacturer-retailer channel for single-period products”, Computers & Operations
Research, 29, 1583-1602, (2002).
[16] Taylor, T.A., “Supply chain coordination under channel rebates with sales effort
effects”, Management Science, 48(8), 992-1007, (2002).
[17] Granot, D., and S. Yin, “Price and order postponement in a decentralized
13
newsvendor model with multiplicative and price-dependent demand”, Operations
Research, 56(1), 121-139, (2008).
Table 1. The notations of parameters
Parameters
Description
c
The unit manufacturing cost of the manufacturers
w
The unit wholesale prices that wholesales buy from the manufacturers
The unit selling price of the retailers with supplier chain contract model
The surplus value of unit product.
The shortage cost of unit product
The unit price the manufacturers buy back the surplus product from the retailers.
The contract of revenue and cost-sharing rate
The parameter of market demand change due to price fluctuation
The slope of demand change due to price fluctuation.
The retailer’s order quantity
p
r
s
b
a
l
QR
QT
x
f ( x)
f ( x, p )
F ( x)
The retailer’s order quantity in channel integration
The market’s random demand during sale season
The probability density function of demand x under the supply chain contract
model
The probability density function of demand x under the price dependent
contract strategy
The cumulative probability density function of demand x
R
M
T
The retailer’s expected profit model
The manufacturer’s expected profit model
Assumptions
The total supply chain’s expected profit model in channel integration
p w c r
s p c
b w c r
Table 2. The numerical example results
M R
Q
R
M
T
Independent
190.1709
2047.0085
3803.1488
5850.4273
30.01%
Integrated
224.3598
1705.1282
4487.1794
6192.3076
44.92%
rate of increase/
17.98%
-16.70%
17.99%
5.84%
14.91%
supply chain
type
／ T
14
decrease
Table 3. Comparison for under the different business decision-making models
Strategy
Modes
Channel
integration
Increase rate (%)
Channel
integration
Increase rate (%)
M
Q
R
M R
T
T
0.5401
224.36
5921.04
280.27
6192.31
91.09%
0
-1.85%
0.27%
-0.50%
0.08%
0.21%
0.5591
224.36
5920.26
272.05
6192.31
91.21%
0
-3.57%
0.43%
-1.8%
0.33%
0.19%
Table 4. Differences between with contract and without contract
Strategy
Models
No-contract
Individual
Channel
Contract
integration
Increase rate (%)
Q
M
R
T
0
190.17 3803.15 2047.09 5850.43
0.114
224.36 4025.63 2166.68 6192.30
1
—
0
5.84
5.84
5.84
M R
T
30.47%
30.02%
-0.45
Table 5. The correlation and sensitivity analysis
Correlative
analysis
Sensitivity
analysis
Positive correlation
Channel
integration
p、r
Negative correlation
Non-Correlation
c、s
w、b
High sensitivity
p、c
Medium sensitivity
Low sensitivity
w、r 、s、b
-
15
Figure 1
$w
$c
$p
Manufacturer
Retailer
Customer
f ( x)
Q
$r
$s
Figure 1. Model construction
Figure 2
$ p
$c
Manufacturer
$r
$(1 2 )w
$p
Retailer
$b
Customer
f ( x)
Q
$ s
$s(1 )
Figure 2. The contract flow
16