Download Optimal Pricing and Return Policies for Perishable Commodities

Optimal Pricing and Return Policies for Perishable
Commodities
B. A. Pasternack
Presenter:
Gökhan METAN
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Outline
i) Introduction
ii) Model
iii) Implications
iv) Examples
v) Conclusion
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Introduction
What the paper is all about?
 Pricing policies for a manufacturer that produceses
goods with short shelf or demand life.
Pricing Policy:
Specifies the price of the commodity
charged from the retailers, per unit credit for the returned goods,
and the percentage of purchased goods allowed to be returned for
this credit.
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Introduction
Question:
How would you set the price of the product for your
retailers, and what return policy would you impose?
How and what kind of decisions are made typically?
Price:
Return Policy:
i- Cost basis decisions
i- Full credit for all
unsold goods.
ii- “What market will
bear” approach
ii- No credit for
unsold goods.
No channel coordination!
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Introduction
Set a pricing policy
Profit
Purchase Decision
Customer Side
Profit
Price, demand, product availability
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Introduction
Assumptions about the model:
i- Single item is considered.
ii- Item has short shelf or demand life.
iii- Any retailer place only one order from the manufacturer.
iv- Goodwill cost is incurred partially by the retailer and
partially by the manufacturer. (when inventory is depleated)
v- Certain amount may be returned to the manufacturer for
partial credit and the remaining is disposed of by the retailer for
its salvage value. (when inventory remains beyond the
shelf/demand life)
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Introduction
Assumptions about the model:
Cont’d
vi- Manufacturing cost per item is independent of the production
quantity.
vii- All the retailers charge the same (fix) price for the product.
viii- Both the manufacturer and the retailers are profit
maximizers.
ix- Salvage value is same for manufacturer and the retailers.
x- No transfer mark-ups between retailers and the manufacturer.
(amount paid by the retailer = amount received by the
manufacturer)
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Introduction
Assumptions about the model:
Cont’d
xi- Demand at the retail level is stochastic.
xii- Manufacturer has control of the channel and is free to set the
pricing policy. Retailers decide to carry the commodity or not.
Objective:
To develop a pricing policy that optimizes the expected profit of
both the manufacturer and the retailers as well as to achieve the
channel coordination.
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Introduction
Methodology:
Single period inventory model (newsboy problem) is employed in
the analyses.
Interest:
Not finding the optimal ordering quantity!
What pricing policy for the manufacturer will be optimal ?
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Model
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Model
Manufacturing cost per item
Unit selling price by the retailer
Salvage value per unit
Manufacturing cost per item
Unit price paid by the retailer to
the manufacturer.
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Model
In the analyses we will consider two cases:
1) We will first assume such a
system that the retailers
belong to manufacturers own.
That is, they are company
stores.
2) In the second case, we will
consider indedendent retailers.
That is, the retailers determine
their order quantity.
This will enable us to determine the
optimal policy for the system as a
whole.
This will enable us to determine the
optimal policy for retailers where
they are independent.
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Model
1st CASE
Let the company produces Q units and sells directly to the
customers by its own retailers and EPT(Q) be the total expected
profit.
Total manufacturing
cost
Total Profit
Total Profit
Expected profit when
demand is less than
the production
quantity.
Total Salvage
Value for
unsold goods
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Total goodwill
cost for lost
demands
Expected profit when
demand is more than
the production
quantity.
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Model
Result
F(QT*)=(p+g2-c)/(p+g2-c3)
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Model
2nd CASE
Let the retailer orders Q units and EPR(Q) be the retailer’s
expected profit.
Retailer’s total
ordering cost
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Model
Q
ORDER
DEMAND
0
x
RQ
(1-R)Q
Retailer’s
revenue from
items sold
Credit
obtained for
unsold goods
from the
manufacturer
Total amount
obtained for
unsold goods
from their
salvage value
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Model
x
Q
ORDER
DEMAND
0
RQ
(1-R)Q
Retailer’s
revenue from
items sold
Credit
obtained for
unsold goods
from the
manufacturer
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Model
Q
ORDER
x
DEMAND
0
RQ
(1-R)Q
Total goodwill
cost of the
retailer.
Retailer’s
revenue from
items sold
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Model
Note that:
0
0
Q* is the order quantity of
independent retailer which
satisfies equation (7).
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Model
Now, the retailer orders Q* units and EPM(Q*) be the
manufacturer’s expected profit.
Profit obtained by
the sales of Q* units
to the retailer
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Model
Q*
ORDER
DEMAND
0
x
RQ*
(1-R)Q*
Total Credit paid for returned
unsold goods minus the total
salvage value obtained from these
items by the manufacturer
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Model
x
Q*
ORDER
DEMAND
0
RQ*
(1-R)Q*
Total Credit paid for returned
unsold goods minus the total
salvage value obtained from these
items by the manufacturer
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Model
Q*
ORDER
x
DEMAND
0
RQ*
(1-R)Q*
Total goodwill cost of
the manufacturer
(because of lost demand)
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Model
Now what we have on hand?
From Case-1 Analysis:
We know that the manufacturer wants to maximize the total
channel profit and hence wants:
QT* such that it satisfies F(QT*)=(p+g2-c)/(p+g2-c3)
From Case-2 Analysis:
We know that the independent retailer wants to maximize its
own profit and hence wants:
Q* such that it satisfies:
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Model
Hence set:
Q*=QT* such that it satisfies F(Q*)=F(QT*)=(p+g2-c)/(p+g2-c3)
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Results:
If the manufacturer sets these three parameters in such a way that
the previous equation is satisfied, the independent retailer should order
the same quantity from the manufacturer as would the manufacturer if
operating a company store.
 This results in maximum total profits to the retailer and
manufacturer, and the channel is said to be coordinated.
Model
The
manufacturer
has
the
control
over
the
parameters
c
1
Observations:
(cost of per unit order from the manufacturer), c2 (credit per
As
unique
solution to the
equation,
different
unit there
paid isbynothe
manufacturer
to previous
the retailer
for returned
values for these there decision variables result in different divisions of
goods) and R (percentage of the order quantity, Q, that can
expected profit between the manufacturer and the retailer.
be returned to the manufacturer for a credit of c2 per item).
 Therefore, the manufacturer’s pricing and return policy will
function as a risk sharing agreement between manufacturer and
retailer.
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Implications
Theorem 1. The policy of a manufacturer allowing unlimited
returns for full credit is system suboptimal.
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Implications
Theorem 2. The policy of a manufacturer allowing no
returns is system suboptimal.
Theorems 1 & 2 imply that “unlimited returns for full credit”
as well as “no returns” prevents channel coordination.
Theorem 3. A policy which allows for unlimited returns
(R=1) at partial credit (c2 <c1) will be system optimal for
appropriately chosen values of c1 and c2.
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Implications
If c1 and c2 are so chosen and the manufacturer allows for unlimited
returns, then the total expected profit for the retailer and manufacturer
are as follows:
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Implications
If the demand for the commodity follows a normal distribution (x ~ N(μ, σ))
then the previous equations become:
OBSERVATIONS:
c1 chosen at its low end (c1 = c + ε)  Manufacturer makes NO PROFIT
c1 chosen at its high end (c1 =p – ε)  Retailer makes NO PROFIT
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Implications
As c2 ↑ c1 also ↑
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Results & Suggestions:
Implications
The pricing should be set so that the average retail establishment captures at
least some portion of the gain from channel coordination.
R
E
A
S
O
N
If it can be demonstrated to the retailers that their profits will
improve as a result of price changes, then they should be more
willing to accept the new pricing plan.
Increasing the retailers’ profits should result in additional
distribution outlets being opened, resulting in an increase in
overall demand.
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Results & Suggestions:
Implications
A drawback!!!
Multi-retailer Environment  Manufacturer sets a single (uniform) pricing
policy for all retailers  Impacts on retailer profitability will be different
An easy but not feasible solution:
A different and retailer-specific pricing policy can be
A policy
total profit
determined and
set forthat
eachincreases
retailer retailers’
and this achieves
the does
not goal.
guarantee
to itincrease
all individual
retailer’s
manufacturer’s
In fact
is not defendable
under
the
profit. Act
Some(which
may faced
a decrease
in their
Robinson-Patman
is an with
act about
the competition
expectedinprofit
dueenvironment).
to the channel coordinated
and pricing actions
business
pricing policy.
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Results & Suggestions:
Implications
Another issue Goodwill Costs  Hard to Quantify  Vary among
different retailers  A uniform pricing policy for those retailer can not be
set  Fortunately, analyses show that when R=0 the retailers’ order
quantity is insensitive to small changes in goodwill cost.
Ensure
reasonable
rate of
return
$$$$$$
A pricing policy for
a new product!
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Desirable
enough
$$$
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Examples
Consider a product with:
Net retail price of $8.00
Manufacturing cost of $3.00
Salvage value of $1.00
Retailer goodwill cost is $3.00
Manufacturer goodwill cost is $2.00
Total goodwill cost is $5.00
(p=8).
(c=3)
(c3=1)
(g=3)
(g1=2)
(g2=g+g1=5)
Suppose that manufacturer charges $4.00 (c1=4) per item from the retailer
and not permit returns for unsold goods (R=0).
g=3, g1=2, g2=5, p=8, c=3 , c1=4, c3=1, R=0
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Examples
g=3, g1=2, g2=5, p=8, c=3 , c1=4, c3=1, R=0
Assume a retailer:
Demand ~ N(200, 50) and the retailer is a profit maximizer.
Q*=226
EPR(Q*)=$626.25
EPM(Q*)=$206.85
(1)
From Theorem-2, this cannot be optimal!
Manufacturer decides to allow unlimited returns to achieve channel
coordination.
Set R=1.
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Examples
g=3, g1=2, g2=5, p=8, c=3 , c1=4, c3=1, R=1
From
F(QT*)=(p+g2-c)/(p+g2-c3)
c1=$4.28
Q*=249
c2=$2.936
EPR(Q*)=$643.51
EPM(Q*)=$206.95
(2)
If all the gain is given to the retailer
Q*=249
c1=$4.37
c2=$3.044
EPR(Q*)=$626.86
EPM(Q*)=$223.61
(3)
If all the gain is given to the manufacturer
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Examples
c1=$4.32
c2=$2.984
EPR(Q*)=$636.11
EPM(Q*)=$214.35
(4)
Both Manuf. & Retailer benefit from the strategy
Now suppose this is the selected policy...
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Examples
Consider a second retailer:
Demand ~ N(200, 10) and the retailer is a profit maximizer.
Before channel coordination (c1=4, R=0)
Q*=205
EPR(Q*)=$765.25
EPM(Q*)=$201.05
(5)
After channel coordination (c1=4.32, R=1, c2=2.984)
Q*=210
EPR(Q*)=$716.02
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EPM(Q*)=$254.07
(6)
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Conclusion
It is possible for a manufacturer to set a pricing and return policy which
will ensure channel coordination.
For partial return case, the optimal values for the selling price to the
retailer and the return credit offered on the item will both be functions of
the individual retailer’s demand.  Since retailers have different demand
distributions  fixed price/return policies which allow for partial
returns cannot be optimal.
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Conclusion
Policy: Unlimited returns for partial credit  Optimal values for selling
price to the retailer and credit offered to the retailer can be determined
independent of the retailer’s demand distribution.  A range of optimal
values for selling price and return credits exist.  Choosing different
pairs result in different divisions of the profit.
As a result of channel coordination some retailers may face with a
decrease in their expected profits.
Since any manufacturer normally have a number of retailers, it is clear
that the policy with full returns for partial credits is the suitable one for
short-lived commodities
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THE END
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