Product Pricing in Supply Chains
ZÜMBÜL BULUT
Department of Industrial Engineering, Bilkent University, Ankara
Term Paper
Production Planning Systems Design, IE 572
Abstract. Each organization involved in production of some king of goods tries to
do its best in terms of some performance criteria. Firms may have different
objectives as to increase the profit, increase the market share, increase the service
level, reduce the operating costs etc. In order to achieve these goals companies
follows different ways. They may try to introduce more efficient transportation,
marketing, advertisement strategies or they may be involved in more profitable
manufacturing means.
One of easier but riskier way to achieve the intended objectives is a proper
adjustment of the product prices. The one that set the prices can be any company
in the supply chain. The level that will be discussed in this statement will be a
retailer company. However, all results apply to other levels in the supply chain as
well.
The main objective of this paper is to summarize the analysis about the pricing
strategies of perishable products. The main factors affecting the prices are
analyzed and the trade-offs faced by the retailer when setting its price either low or
high are discussed. This study will form a base for the future studies, which are
intended to be about pricing strategies of competitive and substitutable products.
Key Words: Perishable Products, Pricing Strategies.
do not have the option of resupplying
inventories.
Retailers and service providers have
the opportunity to enhance their revenues
through the optimal pricing of their
perishable products that must be sold within
a fixed period of time. Of course, dynamic
adjustment of the prices depending on the
remaining time for completion of the
planning horizon, inventory on hand, actions
of competitors etc. can work well. However,
it is practically impossible for retailers of
perishable products to change the list price
every hour because of the coordination and
management cost. Therefore, more stable
pricing strategies are required.
Chun (2001) states that the optimal
pricing problem for a perishable asset is
similar in many respects to the house selling
problem and newsboy problem. In house
selling problem, an asset is for sale for a
limited period of time. Differences between
the house selling problem and optimal
pricing problem are discussed in this paper
as follows: In the house selling problem, it is
the seller who decides whether or not to
1. Introduction
Retailer managers always face with
rapid changes in fashion and customer
preferences. The “perishability” of the
products leads to short selling periods,
during which inventory management and
pricing strategies are central to success
(Bitran, Caldentey and Mondschein, 1998).
The problem of deteriorating inventory has
received considerable attention in recent
years. This is a realistic trend since most
products such as medicine, dairy products
and chemicals start to deteriorate once they
are produced. Not only manufacturing goods
but also services may deteriorate, for
example, flight seats, hotel rooms, theatre
seats.
Many industries face the problem of
selling a fixed stock of items over a finite
horizon. In most of these industries, capacity
decisions are fixed for the sales horizon and
cannot be changed in the short run. For
example, hotel, resorts and airlines have a
fixed number of rooms or seats to offer.
Once, the sales season starts, these industries
1
accept a buyer’s offer. In the optimal pricing
problem, on the other hand, it is the buyer
who decides whether or not to buy the
product at the list price. The similarity
between the newsboy problem and the
optimal pricing problem is that several units
of product are being sold for some fixed
time after which they must be discarded. In
the newsboy problem, however, the seller is
to determine the optimal supply level under
the assumptions of the stochastic demand
and the fixed product price. On the other
hand, the major decision variable in the
pricing problem is the list price, along with
the order quantity.
There are plenty of researches about
the optimal pricing strategies, which appear
in publications related to many different
areas as economy, marketing science,
operations research etc. In Section 2, I
review the literature describing research into
perishable product pricing and related
problems. In Section 3, the most important
factors that affect the pricing decisions are
discuses. I study the question of how retailer
should dynamically adjust the price of a
perishable product as the time at which the
product will perish approaches and the
inventory of the product diminishes. What
are the main factors that affect the pricing
decision of the retailer? is the question to be
elaborated. The trade-offs faced by the
retailer when he sets the prices high or low
are tried to be determined. In Section 4, the
most common logic behind the formulation
of the pricing problems and the solution
procedures are described. Section 5 will
reveal the plans for the further studies on the
pricing of complementary and substitutable
products. This statement will be concluded
in Section 6 by a brief discussion.
Situation, Product Line Pricing Situation and
Cost-Based Pricing Situation.
In this study, the conditions that
determine when a given strategy should be
used are referred as determinants. Examples
of
determinants
are
the
product
differentiation, economies of scale, capacity
utilization, demand elasticity, product age
etc.
The first situation, which is new
product, is appropriate in the early life of the
product. This category has been divided into
three strategies;
1. Price Skimming: In this strategy
the initial price is set high and then it is
reduced over time gradually. The aim behind
the initial high price is to discriminate
between the customers who are insensitive
to the initial high price. As this segment is
saturated, the price is lowered to increase the
appeal of the product.
2. Penetration Pricing: In this
strategy initially the price of the product is
set low. The aim is to make customers
accustomed to the product.
3. Experience Curve Pricing: In this
strategy again the initial price is set low.
However, the aim is to adopt the producer to
this new product by building cumulative
volume quickly and driving the unit cost
down.
The second situation, which is
called competitive pricing, is appropriate
when the price of the product is determined
relative to the price of one or more
competitors’ prices. This situation is
categorized into three pricing strategies as;
1. Leader Pricing: The price leaders
initiate price changes and they expect that
others in the industry will follow their way
in price adjustments. Generally, the price of
an identical product is higher if it is sold by
the leader company.
2. Parity Pricing: Firms that follow
this strategy either tries to maintain a
constant relative price between competitors
or it imitates prevailing prices in the market.
3. Low Price Supplier: In this
strategy, the firm sets the price lower than its
competitors and it aims to have higher
demand than the others.
Other situation is the product line
pricing situation, where the price of the main
product is affected by the other related
products or services from the same
2. Literature Review:
Before providing a literature review
about the pricing strategies for perishable
products, I would like to mention about the
classification provided by Noble and Gruca
(1999) about the pricing strategies of any
kind of products. Actually in most of the
economics books the pricing strategies are
categorized as in this paper. They divide the
pricing strategies encountered in the industry
into 4 broad categories: New Product
Pricing Situation, Competitive Pricing
2
company. There are three pricing strategies
that are mentioned under this heading;
1. Complementary Product Pricing:
The price of the main product is set low then
the other complementary products. This
strategy is well illustrated by Gillette’s
strategy of selling razors cheaply and blades
dearly.
2. Price Bundling: The product is
offered as a component of a bundle of
products. The total price of the bundle is set
lower than the total price of the products
bundled.
3. Customer Value Pricing: In this
strategy one version of the product is offered
at a very competitive price level, however
the product involves fewer features than the
other versions.
The fourth situation is the costbased pricing situation. The firm decides on
how much to charge based on the cost
incurred in obtaining the product under
consideration. The price is set higher that its
cost.
In most of the classical inventory
models, it is assumed that the items do not
deteriorate no matter how long they stay on
the shelf. Although this assumption is valid
for most of the durable goods, it may not be
realistic for many other products as
discussed before.
It has been stated in the literature
that, many industries face various types of
perishing structures. Perishing can be in the
form of a continuous deterioration where the
decay occurs with a rate depending on the
amount and age of the items. Radioactive
materials, some food types, volatile
chemical substances, etc. are typical
examples for continuously deteriorating
inventory. On the other hand, blood
products, fresh food, drugs and electronic
components are some examples that display
negligible or no loss in quality and value
during a fixed lifetime, but after which these
items become useless and/ or obsolete. In
this case, lifetime of the items is said to be
constant. In some other cases, the lifetime
may be fixed but random. The fixed-life
perishability problem is criticized because
the lifetime of an item may depend on
external factors such as heat, temperature
etc. leading to random shelflives.
Perishable inventory theory received
great interest in the recent years. This is
particularly because most inventory types
perish or become obsolete after a finite
amount of time.
In the following paragraphs the
literature (in chronological order) about the
pricing strategies, mostly about the
perishable items will be explained;
Rajan, Rakesh and Steinberg (1992)
considered the relationship between pricing
and ordering decisions for a monopolist
retailer facing a known demand function
where, over the inventory cycle, the product
may exhibit physical decay or decrease in
market value. They investigated linear and
nonlinear demand cases and exhibited
propositions on the optimal price changes
and optimal cycle length. In their
comparison between the dynamic pricing
with fixed price it was shown that the
difference between profits depends on the
extend the optimal dynamic prices varies
over the cycle.
Gallego and Ryzin (1994) studied
the problem of dynamic pricing of
inventories for a given stock of items that
must be sold by a deadline. Demand is price
sensitive and stochastic and objective is
revenue maximization. In this study authors
derived an optimal pricing policy in closed
form when demand functions are
exponential. For the general demand
functions, they analyzed a deterministic
version of the problem and obtained an
upper bound on the revenue. By using this
upper bound, they were able to develop a
single price policy that is asymptotically
optimal when either remaining shelf life or
inventory volume is large.
In 1994, again Gallego and Ryzin
(1994), studied a multiproduct dynamic
pricing problem and its applications to
network yield management. It was assumed
that a firm had inventories of a set of
components that are used to produce a set of
products and over a finite horizon the firm
need to sell its products. The problem was to
price the finished products so as to
maximize total expected revenue. An upper
bound on the optimal expected revenue was
established by analyzing a deterministic
version of the problem. By using this
solution, authors suggested two heuristic for
the stochastic problem and these were
shown to be asymptotically optimal as the
expected sales volume tends to infinity.
3
Feng and Gallego (1995) addressed
the problem of deciding the optimal timing
of a single price change from a given initial
price to either a given lower or higher
second price. In was shown that it is optimal
to decrease (resp., to increase) the initial
price as soon as the time-to-go falls below
(resp., above) a time threshold that depends
on the number of yet unsold items.
Subrahmanyan and Shoemaker
(1996) developed a model for use by
retailers that incorporates learning or
updating of demand by observing the system
through previous periods and creating
posterior demand distribution via Bayes
Rule. Their model can be used to determine
the optimal pricing as well as the optimal
stocking policy. The model is a dynamic
programming model for a given period
review inventory system with uncertain
demand and it was solved numerically using
backward recursion.
Bitran and Mondschein (1997)
addressed the problem of determination of
optimal pricing strategy for perishable
products in retailer stores, which must sell
the products in a fixed period of time. The
price is allowed to change at discrete
intervals of time but it is never allowed to
rise. Although, the authors presented
empirical analysis for their study, no
theoretical results are provided.
Later Bitran, Caldentey and
Mondschein (1998) studied coordination of
clearance markdown sales of seasonal
products in retailer chains. They proposed a
methodology to set prices of perishable
items in the context of a retailer chain with
coordinated prices among its stores and
compared its performance with actual
practice in a real case study. In this paper, a
stochastic dynamic programming problem is
formulated and heuristic solutions that
approximate optimal solutions satisfactorily
are developed.
Federgruen and Heching
(1999)
address
the
simultaneous
determination of pricing and inventory
replenishment strategies in the face of
demand uncertainty. This paper is the one
that reveals the fact that the pricing
decisions must be done in coordination with
other managerial decisions. The overall
objective of the firm can only be achieved
by considering all the important decisions at
once. The authors showed that base stock
list price is optimal for the finite horizon
with bi-directional price changes. If the
inventory level is below base stock level, it
is raised to base stock level and the list price
is charged. If inventory level is above the
base stock level, then nothing is ordered and
price discount is offered.
Feng and Gallego (2000) addressed
the problem of deciding the optimal timing
of price changes within a given menu of
allowable price paths each of which is
associated with a general Poisson process
with Markovian, time dependent, predictable
intensities. Authors showed that a set of
variational inequalities characterizes the
value functions and the optimal time
changes. They developed an algorithm to
compute the optimal value functions and the
optimal pricing policy.
Zhao and Zheng (2000) considered a
dynamic pricing model for selling a given
stock of a perishable product over a finite
time horizon. They identified a sufficient
condition under which the optimal price
decreases over time for a given inventory
level. Also they illustrated that the optimal
price decreases with inventory. By a
numerical study, authors calculated that their
policy
achieves
2.4-7.3%
revenue
improvement over the optimal single price
policy.
Chatwin (2000) analyzed the pricing
of perishable products where the set of
available prices is finite. He indicated that
for this problem as well as the problem in
which the price is selected from an interval,
the maximum expected revenue function is
nondecreasing and concave in the remaining
inventory and in the time-to-go and the
optimal price is nondecreasing in the
remaining inventory and nondecreasing in
the time-to-go. He also showed that these
results hold when prices and corresponding
demand rates are functions of time-to-go but
not when the demand rates are functions of
inventory level.
Wee and Law (2001) developed a
replenishment and pricing policy by taking
into account the time value of money. The
inventory system under consideration is
deterministic and demand is price-depended.
They presented a heuristic approach to
derive the near optimal replenishment and
4
pricing policy that tries to maximize the total
net present-value profit.
Chun (2001) considered a problem
in which the seller must determine the price
for several units of a perishable or seasonal
product to be sold for a limited period of
time. He assumed that the customer’s
demand can be represented as a negative
binomial distribution and determined the
optimal product price based on the demand
rate, buyers’ preferences and the length of
the sales period. Since the seller’s average
Issues Covered
Perishing Structure
Decay
Random (Expo./Gen.)
Fixed
Replenishment Policy
Ordering Decision
Initial Stocking level
Demand Process
Poisson
General
Deterministic
Implicit
Price Dep.demand rate.
Additive
Exponential
Predetermined
Pricing Policy
Fixed
Dynamic
Single Price Change
Mult. Price Change
Discounting
References
Cohen Lazear
1977
1986
x
revenue decreases as the number of items for
sale increases, Chun also considered the
optimal-order-quantity that maximizes the
seller’s expected profit. He also developed a
multi-period pricing model, for the cases
where the seller can divide the sales period
into several short periods.
The following table is taken from
Prof. Dr. Ulku Gurler’s notes. It provides a
summary of some pricing studies on
perishable products.
Rajan
1992
Gall.Ry FengGal
1994
1995
x
x
x
Abad
1996
Feder. Feng.Xi Chatwin
1999
2000
2000
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Table 2.1. Summary of Some Pricing Studies on Perishable Inventory
5
x
3. Factors
Decision:
Affecting
the
and the prices of complementary and
substitutable products. Of course the list
cannot be limited only with those factors.
There may be others that are less often
mentioned in the literature.
Pricing
A retailer aiming to maximize its
profit may choose different ways to
achieve this objective. He may try to
reduce its transportation costs, inventory
holding costs, maintenance costs etc. or he
may prefer to purchase the products from
the manufacturer who charges the least
cost. Also, changing the price of the
product is a way to increase the profit.
However, the price of the product cannot
be increased or decreased arbitrarily.
There should be some price adjustment
strategy. Which strategy to use is a very
complicated and difficult decision. The
decision mechanism that is most often
used by the agent that changes the price is
provided in the next page. This draw is
taken form Timony M. Devinney’s book
called “Issues in Pricing”. The same
author provides a categorization of the
pricing models, which is also provided in
Appendix A.
In this section I would examine a
very common problem in the pricing
literature. Suppose that we have a finiteplanning horizon that can be divided into
periods. We have a fixed amount of
inventory on-hand at the beginning of the
horizon. There is no opportunity for
replenishments during the planning
horizon (reorders are not allowed). The
retailer store must sell the products within
a preestablished time frame using price
adjustments to influence the demand.
Therefore, the objective is to determine
the pricing policy over a planning horizon
that maximizes the total expected profit.
Suppose that the retailer has decided to
change the product’s price only at the
beginning of each period. Actually, he
decides whether to change the current
price or not. If he decides to change it, in
which direction this change should occur?
Here, I would like to explain the main
factors that are taken into consideration
while deciding on the price changes.
These factors are the distribution of the
reservation prices, the initial inventory
level, the distribution of the arrival
process, the length of the planning
horizon, the behaviour of the competitors
3.1. Reservation Prices:
Reservation price is defined as the
maximum amount the customer is willing
to pay for the product. If the product’s
price is higher than the reservation price of
the customer, the customer buys the
product, otherwise he/she does not.
In marketing literature “value
analysis” is used to explain how customers
decide whether to buy the product or not
by considering “the perceived relative
economic value” of the product.
Accordingly, the maximum price that can
be set is that at which customer disregards
the difference between the product and the
next best economic alternative. The
difference between the maximum amount
customers are willing to pay for the
product and the amount they actually pay
is called customers’ surplus (perceived
acquisition value). That is this difference
represents the customers’ gain from
making the purchase (customers’ net gain
from trade). In most of the papers it is
assumed that customers are fully informed
about the product and about its
competitive alternatives. However, buyers
are seldom fully informed about the
products or prices; hence, perceived value
is the sum of acquisition value plus the
transaction value.
When we are dealing with pricing
from the customers’ perspective, the
concepts like “reference product”, “lifecycle costs” and “the improvement value”
of the product relative to the reference
product should be mentioned.
The reference product is the
customers’ next best alternative for
meeting the same need as the current or
proposed new product. This reference
product may be the existing model about
to be replaced or it may be the competing
product being used by the customers.
Another important term is the lifecycle costs which represents all costs that
a customer will incur over the product’s
6
DEMAND FACTORS
(Buyer’s value perceptions, price sensitivity;
existence of distinct market structures and
segments; demand interdependencies with other
products in the line)
POSITIONING ISSUES
Selection of Target Market
Determination of Product
Positioning
Composition of a Consistent
Marketing Mix
Development of a Pricing Strategy
Cost Factors
(Current and future
costs; cost
interdependencies;
financial objectives)
Legal & Public
SELECTION OF A SET
OF FEASIBLE PRICES
Competitive Factors
(Nature and Intensity
of Competition;
Barriers to Entry)
Policy Issues
(Unfair price
competition; price
discrimination)
Trade Practices
(Channel power
structures; discount
structure; inventory
and promotional
arrangements)
TEST AND REVISE
PRICE DECISION
Figure 3.1. Determination of the Price Strategy
7
useful life. These costs include the actual
purchase cost, start-up costs, and
postpurchase costs. Postpurchase costs
include all costs incurred by the customer
once the product has been installed and is
in use. Start-up costs include installation,
training, and related costs that will be
incurred before the product is fully
operational. These costs show that the
purchase cost of the product is not the only
cost that customers should consider when
they make purchasing decisions.
The improvement value of the
product
represents
the
potential
incremental satisfaction or profits the
customer can expect from this product
over those of the reference product. This
enhancement of customers’ satisfaction or
profit potential may occur because of
attributes of the new product that improve
productivity (reduce cost or increase
output per unit of time), increase the value
of customers’ output and, potentially, the
output’s price, or simply provide more
pleasure (Montgomery, 1988).
Therefore, instead of only the
reservation prices, reference product, lifecycle costs and the improvement value
should also be taken into consideration
when the price of the product is
determined. However, in the literature
only the first one is considered. It assumed
that the reservation prices have a
continuous distribution over a population
of customers and this distribution may
change as time passes. The reasons for the
variance in the reservation price
distribution can be stated as the
heterogeneity of the market segment
(difference in income, age etc.) and a lack
of information about the customer’s tastes
and needs. When making pricing decisions
the seller only knows the distribution of
the reservation prices. The seller faces
with the following trade-off; losing the
sales due to high prices vs. loosing the
customer surplus due to low prices (Bitran
and Mondschein, 1997). Therefore, the
goal of the seller should be to adjust the
prices such that the total expected profit is
maximized over the planning horizon,
while taking into consideration the
heterogeneity of the population of
customers in their willingness to pay for
the product.
3.2. The Initial Inventory Level:
Almost all of the studies I have
encountered in the literature conclude that
the profit increases with increasing level
of initial inventory. It is a logical result
because when the retailer has more goods
to sell, he should expected to obtain more
profit. Suppose that a retailer sells its
products for 5$ and the total cost
(purchase cost, transportation cost,
maintenance cost etc.) he pays per product
is 3.5$. Then if he has initially 10,000
units his profit would be 1.5*10,000$,
whereas if he has 100,000 units his profit
would be much higher as 1.5*100,000$.
In some cases, the initial inventory
is taken to be fixed due to some kind of
commitments between the supplier and the
retailer. However, in most of the cases the
retailer decides how much to order from
the supplier. If he orders more than the
demand, he would carry inventory, which
would lead to increased inventory holding
costs. On the other hand, if he orders less
than the demand, he would lose the sales,
customer goodwill and he may experience
decrease in the market share since the
customers may switch to competitive
retailer stores. Therefore, the retailer
should have an accurate forecasting
strategy to determine the amount to order
at the beginning of the planning horizon.
Suppose that the seller has ordered
a lot and he realizes that the demand will
not be as high as inventory on hand. What
should be the price to trigger the demand
up? Of course, he should set the prices
low. Even in the case when the demand is
not know in advance (and cannot be
forecasted accurately) and the initial
inventory is high, the prices should be set
low to increase the probability that all of
the goods on hand will be sold.
On the other hand, if the initial
inventory is low and demand is know to be
higher than the on hand inventory, the
prices should be set high. In that case, the
products will be sold to those customers
with high reservation prices. However, if
the prices are set low when the initial
inventory level is low then the all of the
products will be sold instantaneously and
the retailer will lose the customer surplus.
He then may experience lost sales, lose of
8
goodwill and decrease in market share
since the inventory will be depleted before
the horizon ends. Therefore, the
relationship between the initial inventory
level and the optimal initial price can be
shown as in the following graph (This
graph may have different shape for
different demand distributions.)
3.3. Probability Distribution of the
Arrival Process:
Initial price
Initial inventory level
Figure 3.2. Relationship btw. the initial
inventory level and optimal price
As a result, for small initial
inventories, the initial prices are high with
respect to a fixed median. In this case, the
probability of selling the product is higher
when the variance of the reservation price
distribution is larger. However, for large
initial inventories, the initial prices are low
compared with the fixed median, and
therefore, the probability of selling a unit
is larger when the variance of reservation
prices distribution is smaller. The number
of unsold units becomes larger when the
initial inventory and variance increase.
Therefore, it is expected that, on average,
the number of unsold units is larger for
new products or when the store faces a
heterogeneous market segment.
Average unsold units
s.d.=a
s.d.=b < a
Inventory
Figure 3.3. Unsold goods vs. inventory
9
The arrival rate of potential
customers to the store is often a response
to their regular purchasing patterns during
the selling season rather than a function of
individual prices (Bitran and Mondschein,
1997). The arrival pattern of the customers
the retailer store can be affected by an
advertisement campaign. At that point I
need to point out that an arrival does not
mean a demand. A customer may arrive to
the customer but he/she may leave without
purchasing anything (although the product
he/she is looking for is available in the
store and his/her reservation price is
higher than the product’s price) then this
customer cannot be considered as a
demand.
By looking at the intensity of the
arrival process the retailer may adjust its
prices. If the arrival intensity is dense,
then the prices are set high than the
median value. Since we have high
intensity, the probability of arrival of the
customers with high reservation prices
increases and high-price products are sold.
However, for the low arrival
intensity, customers do not arrive to the
retailer store as often as in the previous
case. Therefore, it is more convenient to
set the prices low in order to sell the
products to those customers arrived to the
store. However, if the price is set high then
the arriving small number of customers
will not purchase the product. This will
result in increased holding cost, excess
inventory on-hand (It is not desirable since
the products will perish after a while.),
loss of the customer to the competitors etc.
Demand occurs when the arriving
customer buys the product. Demand is
price sensitive and density of its
distribution is a decreasing function of the
price. As price increase, the number of
customers willing to buy the product
decreases. On the other hand, if the price
of the product decreases, the number of
customers with reservation prices higher
than the price of the product increases, and
therefore, demand increases.
3.4. The Length of
Horizon:
seller has fewer possibilities of selling the
products.
the Planning
Suppose that we have a fixed
inventory on hand. If the length of the
planning horizon is too short, we have a
little time to sell this inventory. Since the
products deteriorate or get out of fashion
we need (and aim) to sell all the products.
What should be the price in this case? The
initial price should be set low with respect
to the median price. Low prices will
trigger the demand up and the possibility
of selling all the units in this short period
will increase.
On the other hand, if we have a
long planning horizon, we can set the
initial price high. By setting the initial
price high, we can get the customer
surplus since some customers will buy the
product. After observing the demand
process, the retailer may decrease the price
as time does on in order to prevent the risk
of residual inventory. The following graph
reveals the relationship between the length
of the planing horizon and initial price.
3.5. The Behaviour of the Competitors:
Pricing a product in competition is
more difficult than pricing one isolated by
its uniqueness. In the absence of direct
competition, one can estimate how a price
change will affect sales simply by
analyzing buyers’ price sensitivity. When,
however, a product is just one among
many, competitors can make useless such
sales estimates by changing their own
prices. In doing so, competitors change
buyers’ alternatives to purchasing one’s
product and thus manipulate what they are
willing to pay for it. For example, a
company might reasonably estimate that it
could double sales by pricing 20 percent
below the competitors. But a 20 percent
price cut would not necessarily generate
such a result. Competitors may not allow a
20 percent price cut to become a 20
percent price differential. They may
respond with price cuts of their own to
eliminate, narrow or even reverse the gain
that the company hoped to achieve. In
doing so, they could significantly reduce
the effectiveness of the price cut as a tactic
for increasing sales.
The greater the potential for price
competition, the more important it is for
management to evaluate how competitors
are likely to use price in their marketing
decisions. Pricing strategist should ask
themselves two important questions:
1. What price changes is each of
my competitors likely to make?
2. How will each competitor
respond to my own price changes?
The first in predicting a
competitor’s pricing behaviour is to define
the product market. A firm’s relative size
in a market significantly affects its ability
and incentives to pursue alternative
pricing strategies. Having identified a
competitor’s position in a market, one can
analyze its specific circumstances to
predict its probable pricing behaviour. In
the literature the competitive behaviour is
categorized within one of the following
categories:
Initial price
The length of the planning horizon
Figure 3.4. The relationship between the
initial price and the length of the planning
horizon
As a result, for a given period of
time, the optimal price is a nondecreasing
function of the inventory. Thus, the larger
the inventory, the smaller the optimal
price. And, for a given inventory, the
optimal price is a nonincreasing function
of time. Hence, as long as the inventory
remains constant, the optimal price is
decreasing in time; as time goes by the
10
1. Cooperative Pricing,
2. Adaptive Pricing,
Cooperative
Pricing
Common identifying characteristics
Typical behaviour
Changes prices in
parallel with other
firms to maintain
traditional
differences.
Adjusts output as
necessary
to
maintain traditional
market
share,
reducing
output
when
price
increases, reduce
industry sales and
increasing output
when
price
decreases stimulate
industry sales
3. Opportunistic Pricing,
4. Predatory Pricing.
Adaptive
Pricing
Opportunistic
Pricing
Takes price changes Initiates price cuts.
as given and adjusts Delays or foregoes
prices accordingly.
meeting
price
increase.
Always
Attempts to increase meets price decreases
sales when prices without delay.
increase
and
to
reduce sales when Attempts to use nay
prices
decline, change in pricing to
assuming that it maintain or increase
cannot influence the its
sales
at
pricing structure by competitor’s
its actions.
expense.
Significant share in Market share too
market where a few small to influence
firms dominate.
industry pricing, but
nevertheless viable.
Lack of substantial
excess capacity.
Predatory
Pricing
Initiates large price
cuts
(or
other
actions) to inflict
harm
on
a
financially weaker
competitor,
even
though
those
actions are in the
short
run
not
financially
justifiable.
Attempts
to
increase its sales as
much as possible at
the expense of the
targeted
competitor.
Lower unit costs than Financially stronger
competitors.
than prey due to
lower costs, more
Significant
excess diversification, or a
capacity.
larger war chest.
New to the market Harmed by prey’s
with low share.
opportunistic
pricing
or
Able to negotiate potentially
price cuts without benefited by prey’s
immediate detection. demise.
Unit costs similar
to competitors.
Large portion of
sales concentrated in
few buyers.
Table 3.1. Types of competitive pricing behaviour. (Taken from Nagel (1987)).
in Section 5. Besides, this analysis will be
extended in the future studies since this is
my intended master thesis topic.
Most firms sell multiple products.
For example, supermarkets sell products
as diverse as meats, packaged goods,
furniture, toys and clothing. If one
product’s sales do not affect the sales of
the firm’s other products, then it can be
3.6. The prices of the complementary
products
and
the
substitutable
products:
The last topic to be discussed as a
factor that affects the pricing decision of
the retailer is the prices of complementary
and substitutable products. Actually, this
is the topic that will be analyzed in detail
11
priced in isolation. Most often, however,
the sales of the different products in the
firm are interdependent. To maximize the
profit, prices must reflect that interaction.
The effect of one product’s sales
on another’s can be either adverse or
favorable. If adverse, then the products are
“substitutes”. Most substitutes are
different brands in the same product class.
For example, generic and branded paper
towels are substitutes because increased
sales of one reduce sales of the other.
Sometimes, however, substitutes appear in
completely different product classes. For
example, the sales of macaroni products
may rise whenever price increases reduce
the sales of beef.
If one product’s sales favorably
affect sales of another, then the products
are “complements”. Complementarity can
arise for either of two reasons: (1) the
products are consumed together in
producing satisfaction. For example,
tickets to a movie and popcorn are
complements because, for many people,
each enhances the pleasure they get from
the other. (2) The products are most
efficiently purchased together. Buyers
often seek to conserve time and money by
purchasing a set of products from a single
seller. For example, consumers may get
accustomed to a particular supermarket
and buy all of their needs from there. They
may buy beef but then also buy its canned
goods simply because they are going there
anyway.
Substitutes and complements call
for adjustments in pricing when the
products are sold by the same company as
a part of a product line. To correctly
evaluate the effect of a price change,
management must examine the changes in
revenues and costs not only for the
product being produced, but also for the
other products affected by the price
change.
The topic of pricing substitutes
and complements will be elaborated in
Section 5. What is intended to be done in
the future studies about pricing policies of
these types of products will explained
briefly.
4. The Main Logic behind
Formulation of Pricing Problems:
the
Before explaining the common
idea for formulating the pricing problems,
let me remind the problem under
consideration: A retailer has a fixed
amount of inventory to sell during a finite
planning horizon. This horizon is divided
into periods (of equal or unequal length).
At the beginning of each period the
retailer decides whether to change the
price or not. If he decided to change the
price, he should also decide the amount
and direction of change. As it is studied in
the previous section there are lots of
factors that affect the price of the product.
There are many others that are not
mentioned as the purchasing cost of the
product, maintenance requirements of the
product etc. Therefore, all of these factors
must be combined somehow to determine
the optimal pricing policy. However, I
haven’t encountered any study that does
so.
The articles, I have read consider
only few of the factors and assume that
others have no significant effect. Actually,
most of the papers take into account only
one factor. This situation is reasonable
since it is very difficult to incorporate
more than one factor at a time. As the
number of factors considered increases the
complexity of the formulation increases as
well. Solving complex programs become
tedious and finding heuristics become
impossible.
The factors that are most often
taken into consideration are the initial
inventory level and the length of the
planning horizon. For each period we can
talk about the remaining inventory and
time till the end of the horizon instead of
initial values.
In order to give an example about
formulation of a pricing problem, which
incorporates both the length of the
planning horizon and the initial inventory
level, I will briefly explain the formulation
of Gallego and van Ryzin (1994). The
following is their problem and their
formulation:
At time zero, the firm has a stock
n of items and a finite time t>0 to sell
12
them. The firm controls the intensity of the
Poisson demand s=(ps) at time s using a
non-anticipating pricing policy ps. Let Ns
denote the number of items sold up to time
t. A demand is realized at time s if dNs=1,
in which case the firm sells one item and
receives revenue of ps.
There is a set of allowable prices
+
P=R  {p}. Also there is a set of
allowable demand rates ={(p):pP}.
The authors denoted by U the class of all
non-anticipating pricing policies, which
satisfy:
J * n, t   sup J u (n, t ).
uU
In order to derive the optimality
conditions, the authors derive the
Hemilton-Jacobi sufficient conditions for
J* by considering what happens over a
small interval of time t. By selecting the
intensity , one product is sold over the
next t with probability approximately t
and
no
items
with
probability
approximately 1-t. By the Principle of
Optimality:
t
 dN
s
 n, (a.s.)


J * (n, t )  sup  [t p   J * n  1, t  t 
0
and
ps  P  s  
 1  t J * n, t  t   ot ]
The first inequality is used to turn off the
demand process when the firm runs out of
items to sell. The existence of null price p
in the set P guarantees that it can always
be satisfied.
It is assumed that the salvage
value of any unsold items at time t is zero,
since for any positive salvage value q, a
new regular demand function (p) (pq) and new price pp-q can be defined. It
is assumed that all costs relayed to the
purchase and production of the product are
sunk.
For the pricing policy uU, an
initial stock n>0, and a sales horizon t>0,
the expected revenue is defined by
Using r() = p(), rearranging and taking
the limit as t , one can obtain
J * n, t 
 sup  r     J * n, t   J * (n  1, t )
t


n  1, t  0.
with boundary conditions J*(n,0)=0, n
and J*(0,t)=0, t.
The solution to the last equation is
the optimal revenue J*(n,t) and the
intensities *(n,t) that achieve the
supremum from an optimal intensity
control.
The majority of the formulations
in the literature follow the same logic as
the formulation above. They try to relate
one period’s revenue with the remaining
revenue values, that is a dynamic program
is obtained.
Almost all of the authors state the
optimality conditions and the number of
possible solutions before describing the
solution procedures. The problems are
very difficult to solve optimally, actually
the closed form solutions to the last
equation above is almost impossible to
find. Therefore some bounds and heuristic
t
J u (n, t )  Eu [  p s dN s ],
0
where,
J u (n,0)  0, n
and,
J u (0, t )  0, t.
The firm need to find the pricing policy u*
(if one exists) that maximizes the total
expected revenue generated over [0,t],
denoted by J*(n,t). That is,
13

solutions are developed. In order to obtain
an upper bound for the maximum revenue
the deterministic version of the problem
can be solved. Then, by developing
different heuristics one may obtain a
solution to the problem and determine an
optimal pricing policy.
In this section, I have tried to give
an inside about the formulation of the
pricing problems. Since there are pretty
mach variations of the above problem
formulation, it would be wrong to say that
the above one is a general formulation. It
is specific in the sense that, it takes into
account two pricing factors at a time.
There are others that consider only one
factor as Federgruen and Heching (1999),
Bitran and Mondschein (1997), etc.
5. Substitute and
Product Pricing:
The cross-elasticity can be either
positive or negative. If it is positive, the
two items are substitutes, a rise in the
price of Y raises the consumption of X. If
the cross-elasticity is negative, the items
are complements, a rise in price of Y
lowers the consumption of X.
Quantity of X demanded
X and Y are
complements
X and Y are
substitutes
Complementary
Price of Y
Pricing
of
substitute
and
complementary products is analyzed in a
separate section, since it will be the main
topic of my future studies. In this section,
the cross-price elasticity of demand will be
defined, some relationships between the
price and demand of both substitutable and
complementary products will be discussed
and finally an intended outline, which will
be certainly modified, for the future
studies will be provided.
As discussed before, one of the
main factors that affect the pricing
decisions is the price of complementary
and substitutable products. When a price
change on one item influences the sales
volume of another item, some degree of
cross-price elasticity of demand exists.
The demand for a product or
service X will usually depend not only on
its own price, P(X), but on prices of other
items, such as P(Y).This relationship is
known as cross-price elasticity of demand
and it is defined as follows:
Figure 5.1. Interrelated product or
service demand
Figure 5.1. illustrates the
relationship between the price of one
product and the demand of the other
product as they are substitutes and
complements.
Quantity of Y demanded
Quantity of X demanded
Cross-elasticity (X,Y) =
Figure 5.2. Perfect substitutes
quantity( X 2)  quantity( X 1) / quantity( X 1)
 price (Y 2)  pricce ( y1) / price (Y1)

Figure 5.2. illustrates how the
demands for substitutable products change
with respect to each other. As the demand
changeinqunatityofX
priceofY
*
changeinpriceofY
qunatityofX
14
for one product increases it is expected
that the demand for the other product to
decrease. What should be the strategy for
pricing the substitutable products?
The substitutable products are
characterized by the fact that small
changes in price ratios will lead to large
shifts in the relative quantities purchased.
Substitutes exist to serve to slightly
different market segments. If one offers
items with varying quality levels, price
differences should reflect the relationship
between the price and the value of the
product to the customer.
When the retailer makes price
changes to stimulate sales of one item, he
must also consider possible substitution
effect. If the price of one item is reduced,
sales will likely increase. However, sales
of the substitute item will suffer as buyers
substitute these items. Therefore, the
retailer should know which market
segments are most likely to respond to a
price change, and he should be sure to
estimate the effect of lost sales on the
other product when evaluating price
change effects.
Complements are characterized by
the fact that large changes in price ratios
will lead to only small shifts in the relative
quantities purchased. There is an increase
in the sales volume for all complements as
related items are reduced in price.
Montgomery (1988) states that Oxenfeldt
(1975) had pointed out the following
reasons for such behaviour:
1. Related value: When two
products or services are used in
conjugation with one another, purchase of
one item may lead to purchase of the
second.
2. Enhanced value: One product
or service may enhance the value or
increase the utilization of another.
3. Quality supplements: Items
designed for repair; maintenance or
operating assistance may enable a buyer to
obtain a high level of quality performance
4. Broader assortment: Products
or services totally unrelated in use may be
complementary if bought from the same
source. Shopping at only one store reduces
the buyer’s search cost.
There are two other important
concepts about the complementary
products: leader and bundling.
The prising of some products has
a very strong effect on a customer’s choice
of which store to patronize. If customers
purchase many other products once they
are in the store, sales of those products
increase the adjusted contribution margin
of the product that attracts customers to
the store. Consequently, it may be quite
reasonable to price a product so low. This
product(s) is(are) called loss leader(s).
Loss leaders are common in grocery
pricing. Supermarkets regularly take
losses on a few advertised items in order
to attract buyers to their stores because
those buyers will then purchase the
remainder of their needs at profitable
prices. The best loss leaders are those that
are frequently purchased and primarily by
price-sensitive customers.
Bundling involves offering special
prices to buyers purchasing the main items
plus one or more auxiliary items.
Generally, for a bundle of products lower
price that the sum of individual prices of
the products in the bundle is charged. The
retailer gains by selling more than one
Quantity of Y demanded
Quantity of X demanded
Figure 5.3. Perfect Complements
Figure 5.2. illustrates how the
demands for complementary products
change with respect to each other. As the
demand for one product increases it is
expected that the demand for the other
product to increase. What should be the
strategy for pricing the complementary
products?
15
product at a time. The price of the bundle
should be set such that the gain from the
sales should not be compensated by the
loss due to reduced price.
Although, I will not mention any
more about them, there are lots of things
to be said about the inventory management
and pricing policies of complementary and
substitutable products. Therefore my first
step toward the master thesis will be to
investigate this topic in detail. Then, I am
going to formulate the problem, which I
will intend to solve then. Most probably, I
will be concerned with finding the optimal
pricing policies of either complementary
or substitutable two type of product which
must be sold in a finite planning horizon
and they are available in limited quantities
at the beginning of the planning horizon.
In the formulation part, the market
segment, the degree of substitution
(complementation), etc. should be taken
into consideration. After formulating my
problem, I will try to get real life data in
order to evaluate the performance of my
algorithm. If the algorithm turned out to be
not applicable, I would try to adjust it so
as to capture the real world situations as
closely as possible.
profit maximization goals of a company.
However, the realization of these benefits
depends very much on the implementation
of the pricing strategies. The retailer must
first of all know about the most important
factors that he should consider in order to
determine his pricing policy. These factors
are the length of the planning horizon, the
initial inventory level, the distribution of
reservation prices, the behavior of his
competitors etc. Then, the retailer faces
with some tradeoffs while making pricing
decisions. Setting the prices high or low
has different positive and negative aspects.
These factors as well as some tradeoffs are
mentioned in the 3. Section of this report.
The retailer may want to use
already developed strategies in the
literature instead of developing a new one.
However, as I have not encountered yet,
he may not be able to find a study that
takes into consideration all of the factors
affecting the pricing decisions. Then, he
should decide on the factors that are more
important for his decision than other ones.
For example, the initial inventory level
can be the only factor that he wants to
include precisely on his formulations. In
order to reflect the other factors he may
adjust his parameters properly. In Section
4 of this term paper, I have included an
example for a pricing problem formulation
that considers the initial inventory level
and the length of the planning horizon
simultaneously. At that point, it can be
concluded that, the pricing literature needs
more studies that are able to incorporate
the other factors in the optimal pricing
problem formulations.
Finally, in Section 5 the topic that
is intended to be studied further is
mentioned:
complementary
and
substitutable product pricing. (You should
also refer to Section 4 for the definitions
and other important features of the topic.)
There are not much study in the literature
about
the
pricing
policies
of
complementary and substitutable products.
This topic is an important one since it is
the most common situation faced in the
real world. Almost all of the products have
substituted as well as complements.
Therefore, pricing decisions shouldn’t be
given in isolation but simultaneously for
these products.
6. Conclusion:
Pricing is a marketing decision
and is an art like most marketing
decisions. It depends as much on good
judgement as one the precise
calculations. We can see the
judgmental part of the pricing process
in the cases where the retailer decides
on the price of its product with respect
to
anticipated
behavior
the
competitors, anticipated changes in the
interest rates etc. However, the most
important part of the pricing process
relies on calculations. There are many
studies made in the literature that aim
to determine an optimal pricing policy.
These are discussed briefly in the 2.
Section of this report.
The importance of pricing lies on
the fact that, it is an easier yet riskier
(compared to other means as cost
minimization etc.) way to achieve the
16
Gallego G., Ryzin V.G., “A Multiproduct
Dynamic Pricing Problem and its
Applications
to
Network
Yield
Management”, Operations Research 45,
(1997), 24-41.
As a result, it can be said that this
paper is close to achieve its goals as to
form a base for my future studies.
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18