2016 現代經營管理研討會
網路行銷商品之定價策略
許炳輝
德霖技術學院 企業管理系 教授
摘要
網路行銷是一種利用網路提供折扣銷售價格的行銷策略。因為客戶的需求取決於銷售的
價格，如何確定折扣定價是零售商重要的議題。本研究利用報童利潤模型，推導出該模
型的最優解。
關鍵字：網路行銷、定價、報童問題
Pricing Strategies for Product with Internet Marketing
Ping-Hui Hsu
Department of Business Administration, De Lin Institute of Technology, Professor
Abstract
Internet marketing is a form of marketing strategy which utilizes the internet always to
promote business by providing discounted selling price. Since the customers’ demand
depends on the selling price, how to determine the pricing strategy is important to the retailer.
In this study, a newsboy profit model is developed and the optimal solution of the model is
derived.
Keywords: Internet marketing, Pricing, Newsboy problem
1. Introduction
Internet marketing is a form of marketing strategy which utilizes the internet to promote
business. However, face to the consumers concerns of information security, discounted sale
price is more important to marketing. Some researchers such as Sari et al. (2012), Tamjidzad
and Mirmohammadi (2014) considered discount issue.
The classic single-period inventory problem with random demand always referred to the
newsboy problem model such as ordering and selling out newspaper, milk, flight ticket. The
model proposed by Silver and Peterson in 1979.
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2016 現代經營管理研討會
In this study, the newsboy problem model is used. The retailor orders the products and then
sells to the customers. The retailor has to consider the uncertainty in customers’ need.
Ordering an optimal quantity for selling the products on internet with optimal discount is vital
to the retailor. An algorithm is presented to derive an optimal ordering quantity and unit
selling price such that the expected profit is maximized.
2. Notations
The following notations are used in our analysis:
the expected profit for the retailor
EB
Q
the ordering quantity for the retailor; decision variable
*
Q
the optimal ordering quantity for the retailor
cp
p1
k
b
p(k)
s
r
x
the wholesale price per unit ; constant
the lower bound of selling price per unit; constant
the % increased price; 0  k ; decision variable
the upper bound of selling quantity
the selling price per unit
the salvage value per unit s < c p
the shortage cost per unit; represents costs of lost goodwill
the random demand with the PDF (Probability Density Function), f(x), and CDF
(Cumulative Distribution Function), F(x)
3. Modeling and Assumptions
In this section, a model is formulated to obtain the expected profit. Throughout this study,
single product is assumed. The retailor orders a batch of the products, Q, and sells to
customers. The unit wholesale price of the product is c p . The unit selling price is a function of
increased price, P( k ). When the sale quantity is less than the batch Q, the leftover is sold with
the unit salvage value s. When the demand is more than the batch, Q, the shortage occurs. In
here, shortage backordered is not allowed and the shortage unit cost is r. If the customers’
demand is x, the retailor will order an optimal batch of the products according to its optimal
expected profit.
If the retailor manages the unit selling price of the products for marketing and business
purposes, then the consumers’ perceived value and purchase decisions are usually influenced
by the low price and convenience. However, the customer demand will decrease due to the
higher selling price simultaneously. Thus, in this study the random demand depends on the
unit selling price, p(k). That means the PDF, f(x,k), of the random demand x depends on k. The
retailor’ expected profit function EB is given as follows:
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2016 現代經營管理研討會
Q
EB(Q, k )   {[ P(k )  c p )]x  (c p  s)(Q  x)} f ( x, k )dx
0
+
B(k )
Q
{[ P(k )  c p )]Q  ( x  Q)r} f ( x, k )dx , 0  k .
(1)
Our problem can be formulated as:
Max: EB(Q, k )
(2)
4. An illustrative case study
In this section, the practical selling price and probability distribution are used to explain
the results of the previous section. The selling price per unit P (k ) is assumed as
P(k )  p1 (1  k %), 0  k .
(3)
The random demand is uniformly distributed over the range 0 and B (k ) ), where
B(k )  b(1  ak %).
(4)
is a function of k with positive constant a, b (b is the upper bound of the selling quantity). This
means that a higher selling price would decrease the demand. Thus, the PDF of the supplier’s
demand is
f ( x, k ) 
1
.
B(k )
(5)
The numerical examples are provided to illustrate the model.
Example 1. Given p1=30, b=5000, s=5, and r=2, a=10 and c p =20 then
(Calculated by mathematical software Maple 13)
Fig. 1. Shape of EB(Q, k ) on [800,8000]  [1,60]
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2016 現代經營管理研討會
Fig. 2. Shape of Hessian matrix of EB(Q, k ) on [800,8000]  [1,60]
The concavity of EB(Q, k ) is illustrated in Figures 1, and 2. Figure 1 presents the shape of EB(Q, k ) on
[800,8000]  [1,600]. Figure 2 presents the shape of Hessian matrix function of EB(Q, k ) on
[800,8000]  [1,600]. Set both


EB(Q, k ) equal to zero, using Software
EB(Q, k ) and
k
Q
*
*
Maple 13, Q*=5561 and k =11 are derived, the selling price per unit is p( k )=$26.7, and the optimal
*
*
expected profit for the supplier is EB(Q , k ) =$25234.
5. Conclusion
This study derives a newsboy problem model with discount selling price. Analyzing the
system provides managerial insights on how to develop strategies for making the greatest
profit. An illustrative case study and numerical examples are presented to demonstrate our
argument.
Reference
Fournier, S., & Yao, J. L. (1997). Reviving brand loyalty: A reconceptualization within the
framework of consumer-brand relationships. International Journal of Research in
Marketing, 14(5), 451-472.
Sari, D. P., & Rusdiansyah, A., & Huang, L. (2012), Models of Joint Economic Lot-sizing
Problem with Time-based Temporary Price Discounts. International Journal of
Production Economics, 139, (1), 145-154.
Tamjidzad, S., & Mirmohammadi, H. (2014). An optimal (r, Q) policy in a stochastic
inventory system with all-units quantity discount and limited sharable resource.
European Journal of Operational Research, 247(1), 93-100.
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