INFORMATION FORECAST IN A SUPPLY CHAIN WITH
ELECTRONIC MARKET
Pingping Hu, Wei Xing
School of Management, Qufu Normal University, Qufu, China
Ling Jiao
Department of Elementary Education of Computer Science, Ocean University of China, Qingdao, P.R.China
Keywords: Supply chain management, Electronic market, Asymmetric information, Forecasting.
Abstract: This paper considers a supply chain consists with a risk-neutral supplier and a risk-averse manufacturer in
the presence of electronic market. We study how superior demand-forecast information for the manufacturer
affects the supplier’s profit and strategy. Our study shows that if the profit margin is large for the
manufacturer, the supplier will set a higher the wholesale price to a better-forecast manufacturer. We also
find that if the correlation coefficient is zero, the forecast accuracy does not affect the supplier’s profit. At
last, we numerically study how the forecast accuracy affects the supplier’s profit.
1 INTRODUCTION
Information technology has stimulated many
business model innovations. Among them, the B2B
electronic market is shown to be particularly
powerful and enduring (Grey 2003). Thousands of
B2B online exchanges have been opened on the
Internet since the end of last century (e.g. e-
Steel.com, ChemConnect; Turban et al. 2002). The
kind of electronic market is widely used in the
transactions of a variety of standardized
commodities, such as commodity metal, chemical
products, semiconductors, plastics, electrical power
(Wu et al. 2002), and serves as a spot market
providing the supply chain members new avenue to
readjust their inventories.
Forecast accuracies on future demand and price
obviously and directly influence the firms’ planning
processes and the supply chains decision making.
Accurate forecasting can contribute to better
inventory management and better price structuring.
With the popularity of electronic markets, the
manufacturer no only has to pay attention to the end
customer demand uncertainty, but also has to
concern the price volatility of the intermediate good.
Many papers study the direct effect of supply
chain information sharing. This line of research
includes Bourland et al. (1996), Chen (1998),
Gavirneni et al. (1999), Lee et al. (2000) and Cachon
and Fisher (2000). However, these studies on supply
chain information forecast have mainly considered
the forecast on the demand uncertainty, and thus
they do not analyze the effect of the spot price
volatility.
In this paper, we will construct a supply chain in
which one supplier contracts an intermediate good to
one manufacturer, who uses the good to produce a
product selling in the customer market. The supplier
and the manufacturer negotiate a supply contract
which specifies a transfer payment between them
before the spot trading. After a period, the supplier
and the manufacturer can trade the intermediate
good in the electronic market. To deal with market
uncertainties (including demand uncertainty and spot
price volatility), the manufacturer (and the supplier)
may invest in relevant software to create more
accurate forecasts. This paper applies game theory to
investigate the pricing strategies in the presence of
electronic market. We investigate how the
manufacturer’s forecast accuracies on the demand
affect the supplier’s strategies and performance.
The rest of this paper is organized as follows. In
section 2, we develop a mathematical model. In
section 3, we analyze the effect of the
manufacturer’s forecast accuracy on the demand
uncertainty, and provide some numerical examples
507
Hu P., Xing W. and Jiao L..
INFORMATION FORECAST IN A SUPPLY CHAIN WITH ELECTRONIC MARKET.
DOI: 10.5220/0003580805070510
In Proceedings of the 13th International Conference on Enterprise Information Systems (DMLSC-2011), pages 507-510
ISBN: 978-989-8425-55-3
Copyright
c
2011 SCITEPRESS (Science and Technology Publications, Lda.)
in section 4. Finally we offer some concluding
remarks.
2 THE MODEL
Consider a decentralized supply chain consists of a
risk-neutral supplier and a risk-averse manufacturer
with a fully-liquid electronic market. The supplier
sells an intermediate good via forward contract to
the manufacturer, who use the good as one to one
input to a product selling in the customer market
with revenue
p . The customer market faces a
stochastic demand
d . The supplier decides her
wholesale price w to the manufacturer for the
targeted period. In response to the offer, the
manufacturer must decide the contracted quantity
q .
The contracted quantity is shipped to the
manufacturer at the beginning of the period, and the
supplier will sell her remaining production quantity
(not ordered by the manufacturer) in the spot market
with a stochastic spot price
s
. Besides contract
procurement, the manufacturer can also purchase
from the spot market during the targeted period. At
the same time, he can sell his excessive inventory in
the spot market. We assume that once the targeted
period starts, the manufacturer cannot reorder from
the supplier for this period. The interactions between
the supplier and manufacturer form a Stackelberg
game, in which the supplier is the leader and the
manufacturer is the follower.
The customer demand
d and the spot price
s
are typically positively correlated (Litzenberger and
Rabinowitz. 1995, Seifert et al. 2004). That means
that if the customer demand is high, the spot price
usually goes up, and vice versa. For model
tractability, we assume that
d and
s
follow a
bivariate normal distribution with a correlation
coefficient
0
, i.e.
22
,,,,,.
dsd s
ds BN
Normal distribution assumption is commonly used
in the literature, e.g., Seifert et al. (2004) and Van
Mieghem (2007). To deal with a possible negative
value, we further assume that the standard deviations
of the normal random variables are relatively small
compared to their means. In reality, the spot price
and demand fluctuations in one period usually do
not exceed a certain level.
Let
s
and
m
be the supplier’s and the
manufacturer’s profits, respectively. Following to
Seifert et al. (2004)’s model, the manufacturer’s
profit function is
m
pd wq s d q s q d
The supplier’s profit includes the profits from the
forward contract and the online spot market. We
have
,
s
wq s Q q
where
Q
represents the supplier’s capacity. More
general model should include the production cost,
which will not influence our analysis.
While seeking profit maximization, the
manufacturer also needs to limit their risk exposures.
In this paper, we explicitly incorporate the player's
risk tolerances in the decision model. Let
k
measures his risk attitudes, and assume
0k
. Let
mm m
UE kVar
be the manufacturer's utility.
This mean-variance utility function has been widely
used to characterize decision makers' risk-averse
behaviors since the seminal work of Markowitz
(1959), and has been widely adopted in recent
operations management studies, e.g., Van Mieghem
(2007).
Lemma 1 (Seifert et al. 2004).
If
22
(,) , , , ,
dsds
ds BN
, then
*
2
2
sd
ds
ss
w
qp
k
Before the targeted period, the manufacturer
observes a customer demand forecast Fd
,
where
1
0,N
. We assume that the forecast
errors
is independent of
d
and s . Since this
paper mainly analyze the effect of forecast accuracy,
we assume that the distributions of underlying
customer demand
d and the spot price
s
are fixed
and only the level of noise in the manufacturer’s
forecast varies.
We denote
222
11d
a
as the demand
forecast accuracy of the manufacturer. The larger the
value of a , the less accurate the manufacturer’s
forecast. In the limiting case where
1a , the
forecast contains no valuable information about
demand and the posterior distribution is identical to
the prior. In the opposite limiting case where
0a
,
the forecast perfectly reveals the exact demand. For
simplicity, we only focus our discussion to
0,1a .
To simply the following analysis, we denote
1aa
, and define the demand conversion factor
and price conversion factor
as
/
s
d
and /
ds
, respectively. Then,
ICEIS 2011 - 13th International Conference on Enterprise Information Systems
508
we have the following lemma.
Lemma 2. The posterior demand and spot price
distributions under the forecast
F
still follow
bivariate normal distributed, i.e.,
222
1
,
[, ,,1 ,].
ds dd s
dF sF
BN a aF a F a a
where
2
1
=1aa
. (3)
Notice that the manufacturer’s information
acquisition upon the demand will also be used to
update his conditional belief about the spot price.
The posterior expectation on the spot price is linear
function of the conditional variable
F . The more
accurate forecast on the demand uncertainty (smaller
a
), the larger the weight of
d
F
in determining
the posterior expectation of the spot price. And this
effect is achieved through the conversion factor
.
The posterior deviation of the spot price will become
less if the manufacturer improves his forecast
accuracy. We also find that
1
and increases in
a .
3 MODEL ANALYSIS
In this section, we first present the manufacturer’s
best response to the supplier’s decision. We then
investigate the supplier’s decision to derive the
Stackelberg equilibrium. At last, we present some
properties to describe the supplier’s strategy and
profit.
We denote
s
p
as the expected profit
margin for the manufacturer, and assume
0
since
the price of the customer production should be more
than the expected spot price of the intermediate good.
Then, we obtain the manufacturer’s best response
function as follow.
Proposition 1. If the manufacturer only forecasts the
demand, the optimal contract quantity for the
manufacturer is
*
22
2
2 1
.
1
sd
d
s
d
aF w
qa aF
ka
aaF
a
Anticipating the manufacturer’s responses, the
supplier chooses the wholesale price strategically to
optimize her profit.
Proposition 2. If the manufacturer only forecasts on
the demand, the equilibrium wholesale price are
given by
*22
1
ss d
wk a a
Proposition 3. If the manufacturer only makes
forecast on the demand and
d
, the wholesale
price
*
w always decreases in forecast accuracy a .
Otherwise,
*
w
increases in a .
As the manufacturer’s forecast accuracy improves
(
a
decreases), it is optimal for the supplier to charge
a higher wholesale price. This result is intuitive
because when the manufacturer is very confident
about his forecast, he will order a quantity that is
close to his forecast regardless of the wholesale
price.
The expected profit of the supplier is
2
22
2
2
22
1
2 1
1 .
12 1
sd
ss
ds
ka a
EQ
a
a
a
aka
Proposition 4.
If 0
, the manufacturer’s forecast
accuracy does not affect the supplier’s profit.
4 NUMERICAL ILLUSTRATION
We use the following data: 10, 100, 2,
sd s
20, 0.2, 0.01, 150
d
kQ
As the increase of a , the expected profit of the
supplier will decrease for all value of
d
as shown
in Figure1. We also find that the larger value
d
,
the expected profit decreases more sharply.
1520
1540
1560
1580
1600
1620
1640
1660
1680
1700
0 0.2 0.4 0.6 0.8
1
E[
π
s
]
a
σ
d
=10
σ
d
=20
σ
d
=30
Figure 1: Effect on the Forecast Accuracy.
INFORMATION FORECAST IN A SUPPLY CHAIN WITH ELECTRONIC MARKET
509
5 CONCLUSIONS
This paper investigates how superior demand-
forecast information for the manufacturer affects the
supplier’s profit and strategy in the presence of
electronic market. Our study reveals some important
managerial insights. First of all, our study shows that
if the profit margin is large for the manufacturer, the
supplier will set a higher the wholesale price to a
better-forecast manufacturer. We also find that if the
correlation coefficient is zero, the forecast accuracy
does not affect the supplier’s profit. At last, we
numerically study how the forecast accuracy affects
the supplier’s profit.
ACKNOWLEDGEMENTS
The research is supported by National Natural
Science Foundation of China (No. 70971076).
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