Supply Chain Management: Strategy,
Planning, and Operation
Seventh Edition, Global Edition
Chapter 11
Managing Economies of
Scale in a Supply Chain
Cycle Inventory
Copyright © 2019 Pearson Education, Ltd.
Learning Objectives (1 of 2)
11.1 Describe the role of cycle inventory in a supply chain.
11.2 Choose the optimal lot size given fixed ordering costs
in a supply chain.
11.3 Evaluate how aggregation is best implemented to
reduce cycle inventory in a supply chain.
11.4 Understand the impact of quantity discounts on lot
size and cycle inventory.
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Learning Objectives (2 of 2)
11.5 Devise appropriate discounting schemes for a supply
chain.
11.6 Understand the impact of trade promotions on lot size
and cycle inventory.
11.7 Develop replenishment policies to improve
synchronization in multiechelon supply chains.
11.8 Identify managerial levers that reduce lot size and
cycle inventory in a supply chain without increasing cost.
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Role of Cycle Inventory in a Supply
Chain (1 of 8)
• Lot or batch size is the quantity that a stage of a supply
chain either produces or purchases at a time
• Cycle inventory is the average inventory in a supply
chain due to either production or purchases in lot sizes
that are larger than those demanded by the customer
Q: Quantity in a lot or batch size
D: Demand per unit time
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Inventory Profile
Figure 11-1 Inventory Profile of Jeans at Jean-Mart
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Role of Cycle Inventory in a Supply
Chain (2 of 8)
lot size Q
Cycle inventory 

2
2
average inventory
Average flow time 
average flow rate
Average flow time
cycle inventory
resulting from cycle 
demand
inventory
Q

2D
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Role of Cycle Inventory in a Supply
Chain (3 of 8)
For lot sizes of 1,000 pairs of jeans and daily demand of
100 pairs of jeans
Average flow time
Q
1,000
resulting from cycle 

2D 2  100
inventory
 5 days
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Role of Cycle Inventory in a Supply
Chain (4 of 8)
• Lower cycle inventory
– Decreases vulnerability to demand changes
– Lowers working capital requirements
– Lowers inventory holding costs
• Cycle inventory is held to
– Take advantage of economies of scale
– Reduce costs in the supply chain
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Role of Cycle Inventory in a Supply
Chain (5 of 8)
• Average price paid per unit purchased is a key cost in
the lot-sizing decision
Material cost = C
• Fixed ordering cost includes all costs that do not vary
with the size of the order but are incurred each time an
order is placed
Fixed ordering cost = S
• Holding cost is the cost of carrying one unit in inventory
for a specified period of time Holding cost = H = hC
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Role of Cycle Inventory in a Supply
Chain (6 of 8)
• Following costs considered in lot sizing decisions
Average price per unit purchased, $C unit
Fixed ordering cost incurred per lot, $S lot
Holding cost incurred per unit per year,
$H / unit / year  hC
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Role of Cycle Inventory in a Supply
Chain (7 of 8)
• Primary role of cycle inventory is to allow different stages
to purchase product in lot sizes that minimize the sum of
material, ordering, and holding costs
• Ideally, cycle inventory decisions should consider costs
across the entire supply chain
• In practice, each stage generally makes its own supply
chain decisions
• Increases total cycle inventory and total costs in the
supply chain
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Role of Cycle Inventory in a Supply
Chain (8 of 8)
• Economies of scale exploited in three typical situations
1. A fixed cost is incurred each time an order is placed
or produced
2. The supplier offers price discounts based on the
quantity purchased per lot
3. The supplier offers short-term price discounts or holds
trade promotions
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Summary of Learning Objective 1
Cycle inventory builds up in a supply chain because
product is produced or purchased in large lots to lower the
sum of material, ordering, and holding costs by exploiting
economies of scale. Opportunities to exploit economies of
scale arise if a fixed cost is incurred each time an order is
placed or produced, the supplier offers price discounts
based on the quantity purchased per lot, or the supplier
offers short-term price discounts. A reduction in cycle
inventory improves a supply chain’s ability to match supply
with demand.
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Economies of Scale to Exploit Fixed Costs
• Lot sizing for a single product (EOQ)
D = Annual demand of the product
S = Fixed cost incurred per order
C = Cost per unit
h = Holding cost per year as a fraction of product cost
• Basic assumptions
– Demand is steady at D units per unit time
– No shortages are allowed
– Replenishment lead time is fixed
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Estimating Cycle Inventory Related Costs
in Practice (1 of 3)
• Inventory Holding Cost
– Cost of capital
WACC 
E
D
(Rf    MRP) 
Rb (1  t)
DE
DE
Where
E = amount of equity
D = amount of debt
Rf = risk-free rate of return
β = the firm’s beta
MRP = market risk premium
Rb = rate at which the firm can borrow money
t = tax rate
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Estimating Cycle Inventory Related Costs
in Practice (2 of 3)
• Inventory Holding Cost
– Obsolescence (or spoilage) cost
– Handling cost
– Occupancy cost
– Miscellaneous costs
 Theft, security, damage, tax, insurance
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Estimating Cycle Inventory Related Costs
in Practice (3 of 3)
• Ordering Cost
– Buyer time
– Transportation costs
– Receiving costs
– Other costs
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Lot Sizing for a Single Product (Economic
Order Quantity)
• Basic assumptions
1. Demand is steady at D units per unit time.
2. No shortages are allowed—that is, all demand must
be supplied from stock
3. Replenishment lead time is fixed (initially assumed to
be zero)
• Minimize
– Annual material cost
– Annual ordering cost
– Annual holding cost
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Lot Sizing for a Single Product (1 of 3)
Annual material cost  CD
D
Number of orders per year 
Q
D
Annual ordering cost    S
Q 
Q 
Q 
Annual holding cost    H    hC
2
2
D
Q 
Total annual cost, TC    S    hC  CD
2
Q 
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Lot Sizing for a Single Product (2 of 3)
Figure 11-2 Effect of Lot Size on Costs at Best Buy
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Lot Sizing for a Single Product (3 of 3)
• The economic order quantity (EOQ)
Optimal lot size, Q* 
2DS
hC
• The optimal ordering frequency
n* 
D
DhC

Q*
2S
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EOQ Example (1 of 3)
Annual demand, D  1,000  12  12,000units
Order cost per lot, S = $4,000
Unit cost per computer, C = $500
Holding cost per year as a fraction of unit cost, h = 0.2
Optimal order size  Q* 
2  12,000  4,000
 980
0.2  500
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EOQ Example (2 of 3)
Cycle inventory 
Q * 980

 490
2
2
D 12,000
Number of orders per year 

 12.24
Q*
980
D
Q* 
Annual ordering and holding cost 
S
hC  $97,980

Q*
 2 
Average flow time 
Q*
490

 0.041  0.49 month
2D 12,000
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Key Point (1 of 3)
Total ordering and holding costs are relatively stable
around the economic order quantity. A firm is often better
served by ordering a convenient lot size close to the EOQ
rather than the precise EOQ.
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Key Point (2 of 3)
If demand increases by a factor of k, the optimal lot size
increases by a factor of k .
The number of orders placed per year should also
increase by a factor of k .
Flow time attributed to cycle inventory should decrease by
a factor of k .
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EOQ Example (3 of 3)
• Lot size reduced to Q = 200 units
Annual inventory - related costs 
D
Q 
S    hC  $250,000
Q
2
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Lot Size and Ordering Cost
• If the lot size Q* = 200, how much should the ordering
cost be reduced?
Desired lot size, Q* = 200
Annual demand, D  1,000  12  12,000units
Unit cost per computer, C = $500
Holding cost per year as a fraction of inventory value,
h = 0.2
hC(Q*)2 0.2  500  2002
S

 $166.7
2D
2  12,000
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Key Point (3 of 3)
To reduce the optimal lot size by a factor of k, the fixed
order cost S must be reduced by a factor of k 2 .
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Production Lot Sizing
• The entire lot does not arrive at the same time
• Production occurs at a specified rate P
• Inventory builds up at a rate of P−D
• Inventory depleted at a rate of D
QP 
Annual setup cost
2DS
(1  D P )hC
Annual holding cost
 D 
 P S
Q 
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Lot Sizing with Capacity Constraint
• If order size is constrained to K units
and Q > K,
– Compare the cost of ordering K units and the EOQ
– Optimal order size is the minimum of EOQ and
capacity K
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Summary of Learning Objective 2
In deciding on the optimal lot size, the supply chain goal is
to minimize the total cost—the order cost, holding cost, and
material cost. As lot size increases, so does the annual
holding cost. However, the annual order cost and, in some
instances, the annual material cost decrease with an
increase in lot size. The EOQ balances the three costs to
obtain the optimal lot size. The higher the order and
transportation cost, the higher the lot size and cycle
inventory. The optimal lot size can be decreased if the fixed
cost associated with each lot is reduced.
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Aggregating Multiple Products in a
Single Order
• Savings in transportation costs
– Reduces fixed cost for each product
– Lot size for each product can be reduced
– Cycle inventory is reduced
• Single delivery from multiple suppliers or single truck
delivering to multiple retailers
• Reduce receiving and loading costs to reduce cycle
inventory
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Lot Sizing with Multiple Products or
Customers (1 of 2)
• Ordering, transportation, and receiving costs grow with
the variety of products or pickup points
• Lot sizes and ordering policy that minimize total cost
Di: Annual demand for product i
S: Order cost incurred each time an order is placed,
independent of the variety of products in the order
si: Additional order cost incurred if product i is included
in the order
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Lot Sizing with Multiple Products or
Customers (2 of 2)
• Three approaches
1. Each product manager orders his or her model
independently
2. The product managers jointly order every product in
each lot
3. Product managers order jointly but not every order
contains every product; that is, each lot contains a
selected subset of the products
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Multiple Products Ordered and Delivered
Independently (1 of 2)
Demand
DL  12,000 yr , DM  1,200 yr , DH  120 yr
Common order cost
S = $4,000
Product-specific order cost
sL  $1,000, sM  $1,000, sH  $1,000
Holding cost
h = 0.2
Unit cost
CL  $500, CM  $500, CH  $500
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Multiple Products Ordered and Delivered
Independently (2 of 2)
Table 11-1 Lot Sizes and Costs for Independent Ordering
Blank
Litepro
Medpro
Heavypro
Demand per year
12,000
1,200
120
Fixed cost/order
$5,000
$5,000
$5,000
Optimal order size
1,095
346
110
Cycle inventory
548
173
55
$54,772
$17,321
$5,477
year
11.011.0
per year
3.5 3.5
per year
year
1.1year
year
1.1 per
Annual ordering cost
$54,772
$17,321
$5,477
Average flow time
2.4 weeks
7.5 weeks
23.7 weeks
Annual cost
$109,544
$34,642
$10,954
Annual holding cost
Order frequency
Total annual cost = $155,140
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Lots Ordered and Delivered Jointly
S *  S  sL  sM  sH
Annual order cost = S * n
DL hCL DM hCM DH hCH
Annual holding cost 


2n
2n
2n
DL hCL DM hCM DH hCH
Total annual cost 


S*n
2n
2n
2n
DL hCL  DM hCM  DH hCH
n* 
2S *
D hC

n* 
k
i 1
i
i
2S *
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Products Ordered and Delivered
Jointly (1 of 2)
S *  S  sA  sB  sC  $7,000 per order
12,000  100  1,200  100  120  100
n* 
 9.75
2  7,000
Annual order cost  9.75  7,000  $68,250
Annual ordering
and holding cost = $61,512 + $6,151 + $615 + $68,250
= $136,528
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Products Ordered and Delivered
Jointly (2 of 2)
Table 11-2 Lot Sizes and Costs for Joint Ordering at Best Buy
Blank
Litepro
Medpro
Heavypro
Demand per year (D)
12,000
1,200
120
Order frequency (n∗)
9.75
per year
year
9.75
9.75
peryear
year
9.75
9.75
peryear
year
9.75
1,230
123
12.3
615
61.5
6.15
$61,512
$6,151
$615
2.67 weeks
2.67 weeks
2.67 weeks
Optimal order size (D/n∗)
Cycle inventory
Annual holding cost
Average flow time
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Aggregation with Capacity Constraint (1 of 3)
• W.W. Grainger example
Demand per product, Di = 10,000
Holding cost, h = 0.2
Unit cost per product, Ci = $50
Common order cost, S = $500
Supplier-specific order cost, si = $100
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Aggregation with Capacity Constraint (2 of 3)
S   S  s1  s2  s3  s4  $900 per order
D hC
4  10,000  0.2  50

n 

 14.91
4

i 1
1
2S 
1
2  900
900
Annual order cost  14.91
 $3,355
4
Annual holding
hCi Q
671

 0.2  50 
 $3,355
cost per supplier
2
2
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Aggregation with Capacity Constraint (3 of 3)
Total required capacity per truck  4  671  2,684 units
Truck capacity = 2,500 units
2,500
 625
Order quantity from each supplier 
4
10,000
Order frequency increased to
 16
625
Annual order cost per supplier increases to $3,600
Annual holding cost per supplier decreases to $3,125
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Lots Ordered and Delivered Jointly for a
Selected Subset (1 of 3)
Step 1: Identify the most frequently ordered product
assuming each product is ordered independently
ni 
hCi Di
2(S  si )
Step 2: For all products i  i  , evaluate the ordering
frequency
ni 
hCi Di
2si
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Lots Ordered and Delivered Jointly for a
Selected Subset (2 of 3)
Step 3: For all i  i  , evaluate the frequency of product i
relative to the most frequently ordered product i* to be mi
mi  n ni 
Step 4: Recalculate the ordering frequency of the most
frequently ordered product i* to be n
hC m D

n
2 S   s / m 
l
i 1
i
i
l
i 1 i
i
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Lots Ordered and Delivered Jointly for a
Selected Subset (3 of 3)
Step 5: Evaluate an order frequency of ni  n mi and the
total cost of such an ordering policy
 Di 
TC  nS   ni si   
 hC1
i 1
i 1  2ni 
l
l
Tailored aggregation – higher-demand products ordered
more frequently and lower-demand products ordered less
frequently
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Ordered and Delivered Jointly – Frequency
Varies by Order (1 of 4)
• Applying Step 1
nL 
hCLDL
 11.0
2(S  sL )
Thus
n  11.0
nM 
hCM DM
 3.5
2(S  sM )
nH 
hCH DH
 1.1
2(S  sH )
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Ordered and Delivered Jointly – Frequency
Varies by Order (2 of 4)
• Applying Step 2
nM 
hCM DM
 7.7 and nH 
2sM
hCH DH
 2.4
2sH
• Applying Step 3
 n  11.0 
 n  11.0 
mM     
 2 and mH     
5


 nM   7.7 
 nH   2.4 
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Ordered and Delivered Jointly – Frequency
Varies by Order (3 of 4)
• Applying Step 4
n = 11.47
• Applying Step 5
nL  11.47 / yr
nM  11.47 / 2  5.74 / yr
nH  11.47 / 5  2.29 / yr
Annual order cost
nS  nLsL  nM sM  nH sH  $65,383.50
Total annual cost
$130,767
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Ordered and Delivered Jointly – Frequency
Varies by Order (4 of 4)
Table 11-3 Lot Sizes and Costs for Ordering Policy Using Heuristic
Blank
Litepro
Medpro
Heavypro
Demand per year (D)
12,000
1,200
120
2.292.29
per year
Order frequency (n∗)
Optimal order size (D/n∗)
Cycle inventory
Annual holding cost
Average flow time
year 5.745.74
year
11.4711.47
per year
per year
1,046
209
52
523
104.5
26
$52,307
$10,461
$2,615
2.27 weeks
4.53 weeks
11.35 weeks
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Summary of Learning Objective 3
A key to reducing lot size without increasing costs is
reducing the fixed cost associated with each lot. This may
be achieved by aggregating lots across multiple products,
customers, or suppliers. Complete aggregation, where all
products are included in each order, is very effective when
product-specific order costs are small. If product-specific
order costs are large, tailored aggregation, where only a
subset of products is included in each order, is more
effective.
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Economies of Scale to Exploit Quantity
Discounts
• Lot size-based discount – discounts based on quantity
ordered in a single lot
• Volume based discount – discount is based on total
quantity purchased over a given period
• Two common schemes
– All-unit quantity discounts
– Marginal unit quantity discount or multi-block tariffs
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Quantity Discounts
• Two basic questions
1. What is the optimal purchasing decision for a buyer
seeking to maximize profits? How does this decision
affect the supply chain in terms of lot sizes, cycle
inventories, and flow times?
2. Under what conditions should a supplier offer quantity
discounts? What are appropriate pricing schedules
that a supplier seeking to maximize profits should
offer?
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All-Unit Quantity Discounts (1 of 6)
• Pricing schedule has specified quantity break points
q0 , q1,
, qr , where q0  0
• If an order is placed that is at least as large as qi but
smaller than qi 1, then each unit has an average unit
cost of Ci
• Unit cost generally decreases as the quantity increases,
i.e., C0  C1 
 Cr
• Objective is to decide on a lot size that will minimize the
sum of material, order, and holding costs
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All-Unit Quantity Discounts (2 of 6)
Figure 11-3 Average Unit Cost with All Unit Quantity Discounts
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All-Unit Quantity Discounts (3 of 6)
Step 1: Evaluate the optimal lot size for each price Ci ,0  i  r
as follows
Qi 
2DS
hCi
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All-Unit Quantity Discounts (4 of 6)
Step 2: We next select the order quantity Q*i for each price Ci
1. qi  Qi  qi 1
2. Qi  qi
3. Qi  qi 1
• Case 3 can be ignored as it is considered for Qi +1
*
q

Q

q
,
then
set
Q
• For Case 1 if i
i
i 1
i  Qi
• If
Qi  qi , then a discount is not possible

• Set Q i  qi
to qualify for the discounted price of Ci
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All-Unit Quantity Discounts (5 of 6)
Step 3: Calculate the total annual cost of ordering Qi units
D
 Qi* 
Total annual cost, TCi   *  S    hCi  DCi
 2 
 Qi 
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All-Unit Quantity Discounts (6 of 6)
Step 4: Select Qi* with the lowest total cost TCi
• Cutoff price

1
DS h
C *   DCr 
 qr Cr  2hDSCr 
D
qr
2

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All-Unit Quantity Discount Example (1 of 3)
Order Quantity
Unit Price
0–4,999
$3.00
5,000–9,999
$2.96
10,000 or more
$2.92
q0 = 0, q1 = 5,000, q2 = 10,000
C0 = $3.00, C1 = $2.96, C2 = $2.92
D  120,000 year, S  $100 lot, h  0.2
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All-Unit Quantity Discount Example (2 of 3)
Step 1
Q0 
2DS
 6,325; Q1 
hC0
2DS
 6,367; Q2 
hC1
2DS
 6,411
hC2
Step 2
Ignore i = 0 because Q0 = 6,325 > q1 = 5,000
For i = 1, 2
Q1*  Q1  6,367; Q2*  q2  10,000
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All-Unit Quantity Discount Example (3 of 3)
Step 3
D 
 Q1* 
TC1   *  S  
 hC1  DC1  $358,969; TC2  $354,520
 Q1 
 2 
Lowest total cost is for i = 2
Order Q *2 = 10,000 bottles per lot at $2.92 per bottle
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Marginal Unit Quantity Discounts (1 of 6)
• Multi-block tariffs – the marginal cost of a unit that
decreases at a breakpoint
For each value of i, 0  i  r , let Vi be the cost of
ordering qi units
Vi  C0 (q1  q0 )  C1 (q2  q1 )  ...  Ci –1 (qi  qi –1 )
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Marginal Unit Quantity Discounts (2 of 6)
Figure 11-4 Marginal Unit Cost with Marginal Unit Quantity Discount
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Marginal Unit Quantity Discounts (3 of 6)
Material cost of each order Q is Vi  Q  qi  Ci
D
Annual order cost    S
Q 
Annual holding cost  Vi  (Q  qi )C i  h / 2
Annual materials cost 
D
Vi  (Q  qi )Ci 

Q
D
Total annual cost    S  Vi  (Q  qi )C i  h / 2
Q 

D
Vi  (Q  qi )Ci 

Q
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Marginal Unit Quantity Discounts (4 of 6)
Step 1: Evaluate the optimal lot size for each price Ci
Optimal lot size for Ci is Qi 
2D(S  Vi  qi Ci )
hCi
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Marginal Unit Quantity Discounts (5 of 6)
Step 2: Select the order quantity Qi* for each price Ci
1. If qi  Qi  qi 1 then set Qi*  Qi
2. If Qi  qi then set Qi*  qi
3. If Qi  qi 1 then set Qi*  qi 1
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Marginal Unit Quantity Discounts (6 of 6)
Step 3: Calculate the total annual cost of ordering Qi*
D 
D
*
TCi   *  S  Vi  (Qi  qi )C i  h / 2  * Vi  (Qi*  qi )Ci 
Qi
 Qi 
Step 4: Select the order size Qi* with the lowest total
cost TCi
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Marginal Unit Quantity Discount
Example (1 of 3)
• Original data now a marginal discount
Order Quantity
Unit Price
0−4,999
$3.00
5,000−9,999
$2.96
10,000 or more
$2.92
q0 = 0, q1 = 5,000, q2 = 10,000
C0 = $3.00, C1 = $2.96, C2 = $2.92
D  120,000 year, S  $100 lot, h  0.2
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Marginal Unit Quantity Discount
Example (2 of 3)
V0  0; V1  3(5,000 – 0)  $15,000
V2  3(5,000 – 0)  2.96(10,000 – 5,000)  $29,800
Step 1
Q0 
2D(S  V0  q0C0 )
 6,325
hC0
Q1 
2D(S  V1  q1C1 )
 11,028
hC1
Q2 
2D(S  V2  q2C2 )
 16,961
hC2
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Marginal Unit Quantity Discount
Example (3 of 3)
Step 2
Q0*  q1  5,000 because Q0  6,324  5,000
Q1*  q2  10,000; Q2  Q2  16,961
Step 3
D 
D
TC0   *  S  V0  (Q0*  q0 )C 0  h / 2  * V0  (Q0*  q0 )C0   $363,900
Q0
 Q0 
D 
D
TC1   *  S  V1  (Q1*  q1 )C 1  h / 2  * V1  (Q1*  q1 )C1   $361,780
Q1
 Q1 
D 
D
TC2   *  S  V2  (Q2*  q2 )C 2  h / 2  * V2  (Q2*  q2 )C2   $360,365
Q2
 Q2 
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Summary of Learning Objective 4
Lot-size–based quantity discounts increase the lot size and
cycle inventory within the supply chain because they
encourage buyers to purchase in larger quantities to take
advantage of the decrease in price. The relative increase in
cycle inventory because of quantity discounts increases as
the buyer reduces fixed costs per order.
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Why Quantity Discounts?
• Quantity discounts can increase the supply chain surplus
for the following two main reasons
1. Improved coordination to increase total supply chain
profits
2. Extraction of surplus through price discrimination
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Quantity Discounts for Commodity Products
D = 120,000 bottles/year, SR = $100, hR = 0.2, CR = $3 SM
= $250, hM = 0.2, CM = $2
2  120,000  100
QR 
 6,325
0.2  3
 D 
 QR 
Annual cost for DO  
hR CR  $3,795
 SR  

 2 
 QR 
2DSR

hR CR
 D 
 QR 
Annual cost for manufacturer  
S

hM CM  $6,008
 M 

 2 
 QR 
Annual supply chain cost
(DO and manufacturer)
 $6,008  $3,795  $9,803
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Locally Optimal Lot Sizes
Annual cost for
DO and manufacturer
D
Q 
D
Q 
   SR    hR CR    SM    hM CM
Q 
2
Q 
2
Q* 
2D(SR  SM )
 9,165
hR CR  hM CM
 D 
Q * 
Annual cost for DO  
S

hR CR  $4,059
R



Q * 
 2 
 D 
Q * 
Annual cost for manufacturer  
S

hM CM  $5,106
M



Q * 
 2 
Annual supply chain cost
DO and manufacturer 
 $5,106  $4,059  $9,165
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Designing a Suitable Lot Size-Based
Quantity Discount
• Design a suitable quantity discount that gets DO to order
in lots of 9,165 units when its aims to minimize only its
own total costs
• Manufacturer needs to offer an incentive of at least $264
per year to DO in terms of decreased material cost if DO
orders in lots of 9,165 units
• Appropriate quantity discount is $3 if DO orders in lots
smaller than 9,165 units and $2.9978 for orders of 9,165
or more
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Quantity Discounts When Firm Has
Market Power (1 of 3)
Demand curve = 360,000−60,000p
Production cost = CM = $2 per bottle
ProfR  ( p  CR )(360,000  60,000 p )
ProfM  (CR  CM )(360,000  60,000 p )
CR
p to maxim ize ProfR p  3 
2

CR  

ProfM  (CR  CM )  360,000  60,000  3 

2



 (CR  2)(180,000  30,000CR )
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Quantity Discounts When Firm Has
Market Power (2 of 3)
CR = $4 per bottle, p = $5 per bottle
Total market demand = 360,000 − 60,000p = 60,000
ProfR   5  4  360,000  60,000  5   $60,000
ProfM   4  2  360,000  60,000  5   $120,000
ProfSC   p  CM  360,000  60,000 p 
Coordinated retail price
CM
2
p 3
 3   $4
2
2
ProfSC   $4  $2   120,000  $240,000
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Quantity Discounts When Firm Has
Market Power (3 of 3)
Prices coordinated at p = $4
Market demand = 360,000 − 60,000p = 120,000 bottles
Total supply chain profit
ProfSC   $4  $2   120,000  $240,000
Prices set independently, supply chain loses
$240,000 − $180,000 = $60,000
Double marginalization – supply chain margin divided
between two stages
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Two-Part Tariff
• Manufacturer charges its entire profit as an up-front
franchise fee ff
• Sells to the retailer at cost
• Retail pricing decision is based on maximizing its profits
• Effectively maximizes the coordinated supply chain profit
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Volume-Based Quantity Discounts
• Design a volume-based discount scheme that gets the
retailer to purchase and sell the quantity sold when the
two stages coordinate their actions
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Lessons from Discounting Schemes (1 of 2)
• Quantity discounts play a role in supply chain
coordination and improved supply chain profits
• Discount schemes that are optimal are volume based and
not lot size based unless the manufacturer has large
fixed costs associated with each lot
• Even in the presence of large fixed costs for the
manufacturer, a two-part tariff or volume-based discount,
with the manufacturer passing on some of the fixed cost
to the retailer, optimally coordinates the supply chain and
maximizes profits
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Lessons from Discounting Schemes (2 of 2)
• Lot size–based discounts tend to raise the cycle
inventory in the supply chain
• Volume-based discounts are compatible with small lots
that reduce cycle inventory
• Retailers will tend to increase the size of the lot toward
the end of the evaluation period, the hockey stick
phenomenon
• With multiple retailers with different demand curves
optimal discount continues to be volume based with the
average price charged to the retailers decreasing as the
rate of purchase increases
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Price Discrimination to Maximize
Supplier Profits
• Firm charges differential prices to maximize profits
• Setting a fixed price for all units does not maximize profits
for the manufacturer
• Manufacturer can obtain maximum profits by pricing each
unit differently based on customers’ marginal willingness
to pay at each quantity
• Quantity discounts are one mechanism for price
discrimination because customers pay different prices
based on the quantity purchased
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Summary of Learning Objective 5
Quantity discounts are justified to increase total supply
chain profits when independent lot-sizing decisions in a
supply chain lead to suboptimal solutions from an overall
supply chain perspective. If suppliers have large fixed
costs, suitable lot-size–based quantity discounts can be
justified because they help increase supply chain profits.
For products for which the firm has market power, two-part
tariffs or volume-based quantity discounts can be used to
achieve coordination in the supply chain and maximize
supply chain profits. Volume-based discounts are more
effective than lot-size–based discounts in increasing supply
chain profits without increasing lot size and cycle inventory.
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Short-Term Discounting: Trade
Promotions (1 of 2)
• Trade promotions are price discounts for a limited
period of time
• Key goals
1. Induce retailers to use price discounts, displays, or
advertising to spur sales
2. Shift inventory from the manufacturer to the retailer
and the customer
3. Defend a brand against competition
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Short-Term Discounting: Trade
Promotions (2 of 2)
• Impact on the behavior of the retailer and supply chain
performance
• Retailer has two primary options
1. Pass through some or all of the promotion to
customers to spur sales
2. Pass through very little of the promotion to customers
but purchase in greater quantity during the promotion
period to exploit the temporary reduction in price
(forward buy)
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Forward Buying Inventory Profile
Figure 11-5 Inventory Profile for Forward Buying
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Forward Buy (1 of 2)
• Costs to be considered – material cost, holding cost, and
order cost
• Three assumptions
1. The discount is offered once, with no future discounts
2. The retailer takes no action to influence customer
demand
3. Analyze a period over which the demand is an integer
multiple of Q*
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Forward Buy (2 of 2)
• Optimal order quantity
dD
CQ *
Q 

(C – d )h C – d
d
• Retailers are often aware of the timing of the next
promotion
Forward buy  Q d  Q *
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Impact of Trade Promotions on Lot
Sizes (1 of 2)
Q *  6,325 bottles,C  $3 per bottle
d  $0.15, D  120,000, h  0.2
Q* 6,324
Cycle inventory at DO 

 3,162.50 bottles
2
2
Q * 6,324
Average flow time 

 0.3162 months
2D  2D 
Qd 
dD
CQ *

(C – d )h C – d
0.15  120,000
3  6,325


 38,236
(3.00 – 0.15)  0.20 3.00 – 0.15
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Impact of Trade Promotions on Lot
Sizes (2 of 2)
• With trade promotions
Cycle inventory at DO
Qd
38,236


 19, 118bottles
2
2
Qd
38,236
Average flow time 

2D  20,000 
 1.9118 months
Forward buy  Q d – Q*  38,236 – 6,325  31,911 bottles
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How Much of a Discount Should the
Retailer Pass through?
• Profits for the retailer
ProfR = (300,000 − 60,000p)p − (300,000 − 60,000p)CR
• Optimal price
p = (300,000 + 60,000CR ) / 120,000
• Demand with no promotion
DR = 30,000 − 60,000p = 60,000
• Optimal price with discount
p = (300,000 + 60,000  2.85) / 120,000 = $3.925
• Demand with promotion
DR = 300,000 − 60,000p = 64,500
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Trade Promotions (1 of 2)
• Trade promotions generally increase cycle inventory
in a supply chain and hurt performance
• Counter measures
– EDLP (every day low pricing)
– Discount applies to items sold to customers
(sell-through) not the quantity purchased by the
retailer (sell-in)
– Scanner-based promotions
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Trade Promotions (2 of 2)
• Trade promotions may make sense
– When deal elasticity and holding costs are high
– With strong brands
– As a competitive response
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Summary of Learning Objective 6
Faced with a short-term discount, it is optimal for retailers to
pass through only a fraction of the discount to the customer,
keeping the rest for themselves. Simultaneously, it is optimal for
retailers to increase the purchase lot size and forward buy for
future periods. Thus, trade promotions often lead to an increase
of cycle inventory in a supply chain without a significant increase
in customer demand. This generally results in reduced supply
chain profits unless the trade promotion reduces demand
fluctuations. Trade promotions may be justified as a competitive
necessity or a one-time discount to eliminate built up inventory at
the supplier. Trade promotions may also be justified for products
where consumer demand is very sensitive to price discounts.
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Managing Multiechelon Cycle Inventory (1 of 2)
• Multiechelon supply chains have multiple stages with
possibly many players at each stage
• Lack of coordination in lot sizing decisions across the
supply chain results in high costs and more cycle
inventory than required
• The goal is to decrease total costs by coordinating
orders across the supply chain
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Managing Multiechelon Cycle Inventory (2 of 2)
Figure 11-6 Inventory Profile at Retailer and Manufacturer with No
Synchronization
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Integer Replenishment Policy (1 of 4)
• Divide all parties within a stage into groups such that all parties
within a group order from the same supplier and have the
same reorder interval
• Set reorder intervals across stages such that the receipt of a
replenishment order at any stage is synchronized with the
shipment of a replenishment order to at least one of its
customers
• For customers with a longer reorder interval than the supplier,
make the customer’s reorder interval an integer multiple of the
supplier’s interval and synchronize replenishment at the two
stages to facilitate cross-docking
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Integer Replenishment Policy (2 of 4)
• For customers with a shorter reorder interval than the supplier,
make the supplier’s reorder interval an integer multiple of the
customer’s interval and synchronize replenishment at the two
stages to facilitate cross-docking
• The relative frequency of reordering depends on the setup
cost, holding cost, and demand at different parties
• These polices make the most sense for supply chains in which
cycle inventories are large and demand is relatively
predictable
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Integer Replenishment Policy (3 of 4)
Figure 11-7 Illustration of an Integer Replenishment Policy
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Integer Replenishment Policy (4 of 4)
Figure 11-8 A Multiechelon Distribution Supply Chain
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Summary of Learning Objective 7
Integer replenishment policies can be synchronized in
multiechelon supply chains to keep cycle inventory and
costs low. Under such policies, the reorder interval at any
stage is an integer multiple of a base reorder interval.
Synchronized integer replenishment policies facilitate a
high level of cross-docking across the supply chain.
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Managerial Levers to Reduce Cycle
Inventory (1 of 4)
• Three factors drive lot sizing decisions
– Fixed costs associated with production or
purchasing
– Quantity discounts offered by suppliers
– Short-term price discounts offered by suppliers
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Managerial Levers to Reduce Cycle
Inventory (2 of 4)
• If buildup is due to large lots associated with fixed costs
– reduce fixed costs
– Decrease changeover times
• If buildup is due to transportation – facilitate aggregation
– Coordinating orders
– Using intermediate locations to aggregate from
multiple suppliers
– Use milk runs for pickup and delivery
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Managerial Levers to Reduce Cycle
Inventory (3 of 4)
• If buildup is due to order placement and receiving –
employ appropriate technologies
– Electronic order placement
– Advanced shipping notices
– RFID
• If buildup is due to lot sizing decisions – check
supplier’s fixed costs
– Reduce fixed costs
– Employ volume-based discounts
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Managerial Levers to Reduce Cycle
Inventory (4 of 4)
• If buildup is due to short-term discounts – limit forward
buying
– EDLP
– Link discount to sell-through rather than sell-in
– Limit quantity purchased
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Summary of Learning Objective 8
• The key managerial levers for reducing lot size, and
thus cycle inventory, in the supply chain without
increasing cost are the following:
• Reduce fixed ordering and transportation costs
incurred per order.
• Implement volume-based discounting schemes rather
than individual lot-size–based discounting schemes.
• Eliminate or reduce trade promotions and encourage
EDLP. Base trade promotions on sell-through rather
than sell-in to the retailer.
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