2. Economies of Scale to Exploit Quantity Discounts
There are two types of quantity discounts
๏ Lot Size based quantity discount:
๏ Volume Based quantity discount:
๏ What motivates for discounts?
๏ผ All-unit quantity discounts
๏ผ Marginal unit quantity discounts
Based on quantity
ordered in a single lot
โข Improved coordination to increase total supply chain profits
โข Extraction of surplus by suppliers through price discrimination
Based on total
quantity over a given
period (regardless of
number of lots)
3. Coordination in Supply Chain
A supply chain is coordinated if the decisions the retailer and supplier make maximize total
supply chain profits.
Supplier
Retailer
Distributor
All stages try to
maximize their own
profit, independently
This may results in
lack of coordination
Action that maximizes
retailers profit may not
maximize total supply
chain profit
What should manufacturer do to
maximize total supply chain profit?
4. ๏ Quantity discounts (for commodity products):
When there is a large number of competitors in the market, the market sets the
price of that commodity and demand is fixed. (Ex. milk)
๏ Quantity discounts (for products for which the firm has market power):
When there are few competitors in the market, demand varies with price charged
by the retailer. (Ex. Herbal products)
โ Two Part Tariff
โ Volume based quantity discount
Coordination in Supply Chain
Manufacturer charges itโs entire profit as an up-
front franchise fee (ff) from the retailer and sets
its wholesale price as CR = CM
Based on total quantity over a given period
(regardless of number of lots)
5. Quantity discount for commodity products
The Impact of Locally Optimal Lot Sizes on Supply chain:
Problem No.1 Given Data: Demand (D) = 10,000 bottles/month
Data Related To Retailer
SR= Rs.100/Lot
IR = 0.2
CR = Rs.3
Data Related To Manufacturer
SM= Rs.250/Lot
IM = 0.2
CM = Rs.2/Unit
โ Evaluate the optimal lot size for retailer.
โ What is the Annual fulfillment and holding cost incurred by the
manufacturer as a result of retailerโs ordering policy?
Fixed order
placement,
transportation and
receiving cost
Price charged by
the manufacturer
Fixed order filling
cost
Production cost
8. Solution cont..
๏ In the above Example Retailer picks the lot size of 6,325 with an objective of minimizing only its own
cost.
๏ From a supply chain perspective, the optimal lot size should account for the fact that both the retailer
and the manufacturer incur costs associated with each replenishment lot.
๏ The Total supply chain cost using a lot size Q is obtained as follows:
๐ด๐๐๐ข๐๐ Cos๐ก ๐๐ ๐๐ข๐๐๐๐ฆ๐ถโ๐๐๐ =
๐ท
๐
โ ๐ ๐ +
๐
2
โ ๐ผ ๐ โ ๐ถ ๐ +
๐ท
๐
โ ๐ ๐ +
๐
2
โ ๐ผ ๐ โ CM
๐น๐๐ ๐๐๐ก๐๐๐๐ ๐๐๐ก ๐ ๐๐ง๐ ๐
โ
๐(๐๐๐ก๐๐ sup๐๐๐ฆ ๐โ๐๐๐ cos๐ก
๐๐
= 0
12. Summary:
When QR= 6,325
Without coordination
When Q*= 9,165
With coordination
Raise or Down in
Cost (After coordination)
Annual cost of
Retailer (Rs.)
3795 4059 Raise of Rs.264
Annual cost of
Manufacturer (Rs.)
6008 5106 Down of Rs. 902
Total supply chain
cost (Rs.)
9803 9165 Down of Rs. 638
Quantity discount for commodity products
So, manufacturer must offer retailer a suitable incentive to raise
itโs lot size to Q*=9,165 (as the total cost of retailer is raising by
Rs. 264 as he orders in lots of 9165)
13. Quantity discount for commodity products
Designing a suitable Lot size based quantity discount
Problem No.2: (Consider the data from previous problem)
Design a suitable quantity discount that gets retailer to order in lots of 9,165 units when it
aims to minimize only its own total costs.
Solution:
๏ CR = Rs.3/unit (CR: Price charged to retailer)
๏ Manufacturer should reduce the material cost by Rs 264/year (as retailerโs total cost
increased by Rs. 264/year when he orders in lots of 9165) for the sales of 1,20,000
units/year.
= 3 โ
264
1,20,000
โ Rs. 2.9978/unit
14. Quantity ordered by Retailer Unit price
If Q < 9165 units Rs. 3
If Q โฅ 9165 units Rs. 2.9978
Quantity discount for commodity products
Pricing Scheme:
Important points:
โข For commodity products for which price is set by the market, manufacturer with large fixed cost per lot
can use lot size based quantity discount to maximize total supply chain profit.
โข Lot size based discount, however, increase cycle inventory in the supply chain.
15. Problem: If manufacturer lowers itโs fixed cost per order from Rs. 250 to Rs. 100 & SM=
Rs.100/ order (no coordination in supply chain)
when QR= 6,325โถ ๐ด๐๐๐ข๐๐ ๐๐๐ ๐ก ๐๐ ๐ ๐๐ก๐๐๐๐๐ = ๐ ๐ . 3,795
Impact of lowering fixed cost per lot
๐ด๐๐๐ข๐๐ cos๐ก ๐๐ Manufacturer =
๐ท
๐ ๐
โ ๐ ๐ +
๐ ๐
2
โ ๐ผ ๐ โ CM
๐ด๐๐๐ข๐๐ cos๐ก ๐๐ Manufacturer =
1,20,000
6325
โ 100 +
6325
2
โ 0.2 โ 2 = ๐ ๐ . ๐๐๐๐
๐ด๐๐๐ข๐๐ Supply chain cos๐ก = Rs. 3795 + Rs. 3162 = Rs. ๐๐๐๐
From previous
example and not
affected by
change in SM
18. Summary:
No
coordination
(When SM=250)
Coordination
(When SM=250 )
No
coordination
(When SM=100)
Coordination
(When SM=100)
QR= 6325 Q*= 9165 QR= 6325 Q*= 6928
Total Supply
Chain Cost
Rs.9803 Rs. 9165 Rs.6957 Rs. 6929
Impact of lowering fixed cost per lot
All quantity discount can be removed if Sm is lowered
to Rs 100.
19. ๏ Here price at which the retailer sells the product influences demand.
Problem: Let annual demand faced by retailer is given by Demand Curve: (3,60,000 - 60,000p)
Case 1. Policy: (When No coordination in supply chain)
Quantity discount for products for which firm has market
power
p = price at which retailer
sells products
โข What should the manufacturer charge (CR) to the retailer?
โข What should the retailer charge (p) to the customer?
20. Solution: Profit at Retailer (ProfR) = (p - CR) (3,60,000 โ 60,000p)
Profit at Manufacturer (ProfM) = (CR - CM) (3,60,000 โ 60,000p)
Price p at which Retailer maximizes its profit is obtained by
Quantity discount for products for which firm has market
power
๐(Pr๐๐ ๐
๐๐
= 0
โ
๐[(๐ โ ๐ถ ๐ (3,60,000 โ 60000๐ ]
๐๐
= 0
โ 3,60,000 โ 60,000๐ + (๐ โ ๐ถ ๐ (โ60,000 = 0
โ ๐ = 3 +
๐ถ ๐
2
21. Solution cont..
ProfM=
ProfM=
To maximize ProfM
So
๐ถ ๐ โ ๐ถ ๐ (3,60,000 โ 60,000(3 +
๐ถ ๐
2
๐ถ ๐ โ 2 (1,80,000 โ 30,000๐ถ ๐
๐(Pr๐๐ ๐
๐๐ถ ๐
= 0
1,80,000 โ 30,000๐ถ ๐ + (CR โ 2 (โ30,000 = 0
๐ถ ๐ = Rs. 4
โ
โ
Where CM is
production cost
CM=Rs 2 per unit
๐ = 3 +
๐ถ ๐
2
โ ๐ = 3 +
4
2
โ ๐ = Rs. 5
Quantity discount for products for which firm has market
power
22. Summary: When decisions are made independently it is optimal (No Coordination)
Price charged by manufacturer (CR) Rs.4
Price charged by retailer (p) Rs. 5
๐๐๐ก๐๐ ๐๐๐๐๐๐ก ๐ท๐๐๐๐๐ = 3,60,000 โ 60,000p
3,60,000 โ 60,000 โ 5 = ๐๐, ๐๐๐ ๐๐๐๐๐
Pr๐๐ ๐ = (p โ CR) (3,60,000 โ 60,000p) โ 5 โ 4 (3,60,000 โ 60,000 โ 5 = ๐ ๐ . ๐๐, ๐๐๐
Pr๐๐ ๐ = ๐ถ ๐ โ 2 (1,80,000 โ 30,000๐ถ ๐ โ (4 โ 2 (1,80,000 โ 30,000 โ 4 = ๐ ๐ . ๐, ๐๐, ๐๐๐
๐๐๐ก๐๐ ๐๐ข๐๐๐๐ฆ ๐ถโ๐๐๐ ๐๐๐๐๐๐ก = 60,000 + 1,20,000 = ๐ ๐ . ๐, ๐๐, ๐๐๐
Quantity discount for products for which firm has market
power
23. Case 2. When There is coordination in supply chain: (Two stages coordinate their pricing decision to
maximize the supply chin profit
For optimal retail price
Pr๐๐SC = (p โ CM (3,60,000 โ 60,000p
๐(Pr๐๐ ๐๐ถ
๐๐
= 0
3,60,000 โ 60,000๐ + (๐ โ CM (โ60,000 = 0 ๐ = ๐๐ฌ. ๐/๐ฎ๐ง๐ข๐ญโโ
Quantity discount for products for which firm has market
power
๐๐๐ก๐๐ ๐๐๐๐๐๐ก ๐ท๐๐๐๐๐ = 3,60,000 โ 60,000p โ 3,60,000 โ 60,000 โ 4 = ๐, ๐๐, ๐๐๐ ๐๐๐๐๐
๐๐๐ก๐๐ ๐ ๐ข๐๐๐๐ฆ ๐โ๐๐๐ ๐๐๐๐๐๐ก (Pr๐๐ ๐๐ถ = (p โ CM (3,60,000 โ 60,000p โ (4 โ 2 (3,60,000 โ 60,000 โ 4
=Rs.2,40,000
CM=Rs 2/unit
24. Quantity discount for products for which firm has market
power
Summary:
๏ From summary table it is clear that when each stage of supply chain is setting its price independently
(i.e. no coordination) there is a loss of Rs. 6000 in supply chain profit.
๏ This phenomenon is called Double Marginalization.
๏ Double marginalization : Supply chain margin is divided into two stages but each stage makes its
pricing decision considering only its own local profit and this results in loss in profit.
Without
Coordination
With
Coordination
Loss due to lack
of coordination
Total supply chain
profit ProfitSC Rs. 1,80,000 Rs. 2,40,000 Rs. 6000
25. ๏ New pricing schemes to achieve coordinated solution and maximize supply chain profit (Even if
decisions are made independently)
Quantity discount for products for which firm has market
power
I. Two Part Tariff
II. Volume based quantity discount
26. Manufacturer charges itโs entire profit as an up-
front franchise fee (ff) and sets its wholesale
price as CR = CM
๏ Manufacturer can construct a two part tariff by which the retailer is charged an up-front franchise fee (ff )
๐๐ = Pr๐๐ ๐๐ถ โ Pr๐๐ ๐
From previous example
ProfSC = Rs. 2,40,000 (with coordination)
ProfR = Rs.60,000 (without coordination)
๐๐ = 2,40,000 โ 60,000
๐๐ = Rs. 1,80,000
Two part tariff constructed by manufacturer
๐๐ = Rs. 1,80,000
Material cost CR = CM =Rs. 2/unit
Two Part Tariff
27. ๏ Retail pricing decision is based on maximizing profit.
Optimal Retail price
๏ Retailer gets the maximum profit when
Now
Two Part Tariff (Analysis)
Pr๐๐ ๐ = (๐ โ ๐ถ ๐ (360000 โ 60000๐ โ ๐๐
Pr๐๐ ๐ = (๐ โ ๐ถM (360000 โ 60000๐ โ ๐๐
Since
CR = CM
๐ = 3 +
๐ถ ๐
2
As Derived in
previous example
๐ = 3 +
2
2
= Rs. 4/unit
Since
CM=Rs. 2/unit
๐๐๐ก๐๐ ๐๐๐๐๐๐ก ๐ท๐๐๐๐๐ = 360000 โ 60000๐ โ 3,60,000 โ 60,000 โ 4 = ๐, ๐๐, ๐๐๐ ๐ข๐๐๐ก๐
Pr๐๐ ๐ = (๐ โ ๐ถM (360000 โ 60000๐ โ ๐๐ โ 4 โ 2 360000 โ 60000 โ 4 โ 1,80,000 = Rs. ๐๐, ๐๐๐
Pr๐๐M = ๐, ๐๐, ๐๐๐
Charged by manufacturer as an up-front
(Franchise fee)
๐(Pr๐๐ ๐
๐๐
= 0 โ
28. Pr๐๐SC = 60,000 + 1,80,000 = Rs. 2,40,000
Without coordination Two part tariff
Rs.1,80,000 Rs. 2,40,000Pr๐๐SC
Same as what we got when
supply chain is coordinated
Two Part Tariff (Analysis)
29. Problem: Total demand Dcoord = 1,20,000 units, Retail price (p) = Rs. 4/unit
๏ Manufacturer want to design a volume based quantity discount scheme that gets the retailer to buy
(sell) 1,20,000 units/year.
๏ Pricing scheme must be such that
Volume based quantity discount
From previous example when supply chain
stages are coordinated
Pr๐๐R = At least Rs. 60,000
Pr๐๐M = At least Rs. 1,20,000 From previous example
when supply chain stages
was not coordinated
30. ๏ Analysis: Several schemes can be designed, one such scheme is when
D < 1,20,000 CR = Rs.4/unit
CR = Rs.3.50/unitD๐๐๐๐๐ โฅ 1,20,000
Pr๐๐ ๐ = (๐ โ ๐ถ ๐ (360000 โ 60000๐ โ (4 โ 3.5 (3,60,000 โ 60,000 โ 4 = ๐ ๐ . 60,000
Pr๐๐ ๐ = (๐ โ ๐ถM (360000 โ 60000๐ โ (3.5 โ 2 (1,20,000 = ๐ ๐ . 1,80,000
๐๐๐ก๐๐ ๐๐ข๐๐๐๐ฆ ๐ถโ๐๐๐ ๐๐๐๐๐๐ก (๐๐๐๐SC = 60,000 + 1,80,000 = ๐ ๐ . 2,40,000
Non coordinated Volume based
ProfSC Rs. 1,80,000 Rs. 2,40,000
Volume based quantity discount
Same as what we got when
supply chain is coordinated
31. Lot-size-based vs. volume based quantity discount
Lot-size-based quantity discount Volume based quantity discount
1. It is based on quantity purchased per lot. 1. It is based on rate of purchase or volume
purchased on average per specified time
period.
2. It tend to increase cycle inventory in the
supply chain
2. It is compatible with small lots that reduces
cycle inventory
3. It makes sense only when the manufacturer
incurs high fixed cost per period.
3. In all other instances it is better to have
volume based quantity discount.
32. Hockey Stick Phenomenon:
๏ In volume based discount orders from the retailer peak toward the end of a financial horizon, this is
referred to as the hockey stick phenomenon.
๏ As demand from retailer increases dramatically toward the end of a period, similar to the way a hockey
stick bends upward toward the end of the stick.
๏ Solution to hockey stick phenomenon : Base the volume discounts on a rolling horizon.
Volume based Quantity discount
For example, each week the manufacturer may offer retailer the volume
discount based on sales over the last 12 weeks.
33. Price Discrimination to Maximize Supplier Profits
Price discrimination is the practice whereby a firm charges differential prices to different segment of
customers to maximize profits.
๏ The goal of supplier is to price so as to maximize itโs profit, by dividing its customer into segments.
Example: In Airlines, passengers travelling on the same plane often pay different
prices for their seats.
34. Problem: A contract manufacturer has identified two customer segments for its production capacity.
Production cost : c = Rs. 10/unit
(i) What price should the contract manufacturer charge each segment if its goal is to maximize profits?
(ii) If the contract manufacturer were to charge a single price over both segments, what should it be?
(iii) How much increase in profits does differential pricing provide?
Price Discrimination to Maximize Supplier Profits
Demand curve
First segment of customers ๐1 = 5000 โ 20๐1
Second segment of customers ๐2 = 5000 โ 40๐2
35. Total profit made
(with capacity constraint)
If there is no capacity constraint , for segment i the supplier attempts to maximize
To find the optimal price for each segment
Price Discrimination to Maximize Supplier Profits
๐๐๐ฅ
๐=1
๐
๐๐ โ ๐ (๐ด๐ โ ๐ต๐ ๐๐
Profit made by
supplier per unit
๐๐ โ ๐ (๐ด๐ โ ๐ต๐ ๐๐
]๐[(๐๐ โ ๐ (๐ด๐ โ ๐ต๐ ๐๐
๐๐๐
= 0
๐ด๐ โ ๐ต๐ ๐๐ + (๐๐ โ c (โ๐ต๐ = 0 โ ๐๐ =
๐ด๐
2๐ต๐
+
๐
2
Optimal price for
each segment
Demand curve
for segment i
36. Solution:
(i) Without capacity constraints, the differential prices to be charged each segment are given by
Equation
Demand from two segments:
Price Discrimination to Maximize Supplier Profits
๐๐ =
๐ด๐
2๐ต๐
+
๐
2
๐1 =
๐ด1
2๐ต1
+
๐
2
๐2 =
๐ด2
2๐ต2
+
๐
2
โ
โ ๐1 =
5000
2 โ 20
+
10
2
๐2 =
5000
2 โ 40
+
10
2
โ
โ
๐1 = Rs. 130
๐2 = Rs. 67.50
๐1 = 5000 โ 20P1 โ 5000 โ 20 โ 130 โ ๐1 = 2,400 units
๐2 = 5000 โ 40๐2 โ 5000 โ 40 โ 67.50 โ ๐2 = 2,300 units
37. Total profit of supplier :
(ii) If the contract manufacturer charges the same price p to both segments, he is attempting to maximize
Optimal price
๐1 โ ๐1 + (๐2 โ ๐2 โ [๐(๐1 + ๐2
2400 โ 130 + (2300 โ 67.50 โ [10(2400 + 2300
๐๐๐ก๐๐ ๐๐๐๐๐๐ก = ๐ ๐ . 4,20,250
Price Discrimination to Maximize Supplier Profits
๐ โ 10 5000 โ 20๐ + (๐ โ 10 (5000 โ 40๐
= ๐ โ 10 10000 โ 60๐
๐ =
10000
2 โ 60
+
10
2
โ ๐ = Rs. 88.33
Solution cont..
38. Demand for two customers
Total profit =
(iii) Increase in profit due to differential pricing
Price Discrimination to Maximize Supplier Profits
๐1 = 5000 โ 20 โ 88.33 โ ๐1 = 3,323.40
๐2 = 5000 โ 40 โ 88.33 โ ๐2 = 1,466.80
(๐ โ ๐ (๐1 + ๐2
= (88.33 โ 10 (3323.40 + 1466.80
= ๐ ๐ . 3,68,166.67
= 4,20,250 โ 3,68,166.67
= Rs. 52083.33
Conclusion: Setting a fixed price for all segment of customers or for all units will not maximize profits for
manufacturer.