supply chain management

1. Managing Economies of Scale in
the Supply Chain: Cycle
Inventory

2. Role of Inventory in the Supply Chain
Improve Matching of Supply
and Demand
Improved Forecasting
Reduce Material Flow Time
Reduce Waiting Time
Reduce Buffer Inventory
Economies of Scale
Supply / Demand
Variability
Seasonal
Variability
Cycle Inventory Safety Inventory
Figure Error! No text of
Seasonal Inventory

3. Supply
Sources:
plants
vendors
ports
Regional
Warehouses:
stocking
points
Field
Warehouses:
stocking
points
Customers,
demand
centers
sinks
Production/
purchase
costs
Inventory &
warehousing
costs
Transportation
costs
Inventory &
warehousing
costs
Transportation
costs

4. Inventory
 Where do we hold inventory?
◦ Suppliers and manufacturers
◦ warehouses and distribution centers
◦ retailers
 Types of Inventory
◦ WIP
◦ raw materials
◦ finished goods
 Why do we hold inventory?
◦ Economies of scale
◦ Uncertainty in supply and demand

5. Goals:
Reduce Cost, Improve Service
 By effectively managing inventory:
◦ Xerox eliminated $700 million inventory from its
supply chain
◦ Wal-Mart became the largest retail company
utilizing efficient inventory management
◦ GM has reduced parts inventory and transportation
costs by 26% annually

6. Goals:
Reduce Cost, Improve Service
 By not managing inventory successfully
◦ In 1994, “IBM continues to struggle with shortages
in their ThinkPad line” (WSJ, Oct 7, 1994)
◦ In 1993, “Liz Claiborne said its unexpected earning
decline is the consequence of higher than
anticipated excess inventory” (WSJ, July 15, 1993)
◦ In 1993, “Dell Computers predicts a loss; Stock
plunges. Dell acknowledged that the company was
sharply off in its forecast of demand, resulting in
inventory write downs” (WSJ, August 1993)

7. Understanding Inventory
 The inventory policy is affected by:
◦ Demand Characteristics
◦ Lead Time
◦ Number of Products
◦ Objectives
 Service level
 Minimize costs
◦ Cost Structure

8. Cost Structure
 Order costs
◦ Fixed
◦ Variable
 Holding Costs
◦ Insurance
◦ Maintenance and Handling
◦ Taxes
◦ Opportunity Costs
◦ Obsolescence

9. Role of Cycle Inventory
in a Supply Chain
 Lot, or batch size: quantity that a supply chain stage
either produces or orders at a given time.
 Cycle inventory is held primarily to take advantage of
economies of scale in the supply chain and reduce
cost within a supply chain.
 Cycle inventory: average inventory that builds up in
the supply chain because a supply chain stage either
produces or purchases in lots that are larger than
those demanded by the customer
◦ Q = lot or batch size of an order
◦ D = demand per unit time

10. Case of jeans at Jean Mart, a department
store
 Inventory profile: plot of the inventory level over time
 It is assumed here that the demand is stable (while
considering safety inventory, it is not so)
 Cycle inventory = Q/2 (depends directly on lot size)
 Average flow time = Average inventory / Average flow
rate (Little’s Law) = average length of time that
elapses between the time material enters the supply
chain to the point at which it exits.
 But, for any supply chain, average flow rate equals
demand
 Thus, average flow time from cycle inventory =
Q/(2D)

11. Role of Cycle Inventory in a Supply Chain
Q = 1000 units
D = 100 units/day
It takes 10 days for the entire lot to be sold
Cycle inventory = Q/2 = 1000/2 = 500 = Avg inventory level
from cycle inventory
Avg flow time = Q/2D = 1000/(2)(100) = 5 days
Thus, jeans spend in the supply chain an average time of 5
days
 Therefore, cycle inventory adds 5 days to the time a unit
spends in the supply chain
 Lower cycle inventory is better because:
◦ Average flow time is lower. The larger the cycle inventory, the
longer is the lag time between when a product is produced and
when it is sold. A lower level of cycle inventory is always desirable,
because long time lags leave a firm vulnerable to demand changes
in the marketplace.
◦ Working capital requirements are lower
◦ Lower inventory holding costs

12. Role of Cycle Inventory
in a Supply Chain
 For this we first identify supply chain costs that are influenced by lot
size.
 Supply chain costs influenced by lot size:
◦ Material cost = C (average price paid per unit purchased, increasing
lot size might result in availing of price discounts and thus reduce
material cost , $ per unit)
◦ Fixed ordering cost = S (such as administrative cost, trucking cost,
labour cost, all costs that do not vary with the size of the order but
are incurred every time an order is placed, e.g., $400 per truck, if a
lot of 100 pairs, transportation cost will be $4/pair, whereas 1000
pairs means $0.40/pair, thus increasing the lot size decreases the
fixed ordering cost per unit purchased, $ per lot)
◦ Holding cost = H = hC (a combination of the cost of capital, cost of
physically storing the inventory, and the cost that results from the
product being obsolete, reducing lot size and cycle inventory,
reduces the holding cost, H: $ per unit per year, h = cost of holding
$1 in inventory for one year)

13. Role of Cycle Inventory
in a Supply Chain
 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, but in practice, each stage generally
makes its own supply chain decisions. This
increases total cycle inventory and total
costs in the supply chain

14. Economies of Scale
to Exploit Fixed Costs
 How do you decide whether to go shopping at a
convenience store or at Sam’s Club?
 When we need only a small quantity, we go to the nearby
convenience store because the benefit of a low fixed cost
outweighs the cost of the convenience store’s higher
prices.
 When we are buying a large quantity, however, we go to
Sam’s Club (located far away), where the lower prices
over the larger quantity purchased more than make up
for the increase in fixed cost.

15. Economies of Scale
to Exploit Fixed Costs: different ways
 Lot sizing for a single product (EOQ)
 Aggregating multiple products in a single
order
 Lot sizing with multiple products or customers
◦ Lots are ordered and delivered
independently for each product
◦ Lots are ordered and delivered jointly for all
products
◦ Lots are ordered and delivered jointly for a
subset of products

16. Lot sizing for a single product (EOQ)
 The Purchasing Manager of Best Buy
places a replenishment order for a new lot
of Q number of HP computers. Including the
cost of transportation, Best Buy incurs a
fixed cost of $S per order.
 The purchasing manager must decide on
the number of computers to order from HP
in a lot.
 We assume the following inputs:

17. Economies of Scale
to Exploit Fixed Costs
Annual demand = D
C = cost per unit
H = holding cost per year as a fraction of product cost
If no discount is available, the holding cost per unit per year, H =
hC
Number of orders per year = D/Q
Three costs to decide on the lot size:
Annual material cost = CD (purchase price is independent of lot
size)
Annual order cost = (D/Q)S
Annual holding cost = (Q/2)H = (Q/2)hC (where average
inventory or cycle inventory = Q/2)
Total annual cost = TC = CD + (D/Q)S + (Q/2)hC

18. Fixed Costs: Optimal Lot Size
and Reorder Interval (EOQ)
D: Annual demand
D: Monthly demand = D/12
S: Setup or Order Cost
C: Cost per unit
h: Holding cost per year as a fraction
of product cost
H: Holding cost per unit per year
Q: Lot Size (the optimal lot size that
minimizes total cost = Q*, known
as Economic Order Quantity, EOQ)
T: Reorder interval
n* = optimal ordering frequency
AFT = average flow time
Material cost is constant and therefore
is not considered in this model
D
Q
AFT
D
Q
DH
S
T
S
DH
n
H
DS
Q
hC
H
2
/
*
/
*
2
2
*
2
*







19. Example 1
Demand, D = 12,000 computers per year
d = 1000 computers/month
Unit cost, C = $500
Holding cost fraction, h = 0.2 (holding cost of 20%)
Fixed cost, S = $4,000/order
Q* = Sqrt[(2)(12000)(4000)/(0.2)(500)] = 980 computers
Cycle inventory = Q*/2 = 490
Average flow time = average time each computer spends in
inventory before it is sold = Q*/2d = 980/(2)(1000) = 0.49
month
Reorder interval, T = 0.98 month
No. of reorders per year = D/Q* = 12.24

20. Example 1 (continued)
Annual ordering and holding cost =
= (12000/980)(4000) + (980/2)(0.2)(500) = $97,980
Suppose lot size is reduced to Q=200, which would reduce flow time:
Annual ordering and holding cost =
= (12000/200)(4000) + (200/2)(0.2)(500) = $250,000
To make it economically feasible to reduce lot size, the fixed cost
associated with each lot would have to be reduced. Thus, if the fixed
cost associated with each lot is reduced to $1000, the optimal lot size
reduces to 490.
Further, using a lot size of 1,100 (instead of 980), increases annual cost
to $98,636. Even though the order size is more than 10% larger than
the optimal order size Q*, the total cost increases by only 0.6%.
Thus, total ordering and holding costs are relatively stable around the
EOQ, that is, relatively insensitive to Q around Q*.
Moreover, if demand increases by a factor k, the optimal lot size
increases by a factor sqrt k. The number of orders placed per year
should also increase by a factor sqrt k. However, flow time attributed
to cycle inventory should decrease by a factor sqrt k.

21. Example 2 (Relationship between desired lot
size and order cost)
If desired lot size = Q* = 200 units, what would S have
to be?
D = 12000 units
C = $500
h = 0.2
Use EOQ equation and solve for S:
S = [hC(Q*)2]/2D = [(0.2)(500)(200)2]/(2)(12000) =
$166.67
Thus, to reduce optimal lot size by a factor of k, the fixed
order cost must be reduced by a factor of k2

22. Key Points from EOQ Model
 In deciding the optimal lot size, the tradeoff is between
setup (order) cost and holding cost.
 If demand increases by a factor of 4, it is optimal to
increase batch size by a factor of 2 and produce (order)
twice as often. Cycle inventory (in days of demand) should
decrease as demand increases.
 If lot size is to be reduced, one has to reduce fixed order
cost. To reduce lot size by a factor of 2, order cost has to
be reduced by a factor of 4.

23. Example: Aggregating Multiple Products in a
Single Order
 Suppose there are 4 computer products in the previous example:
Deskpro, Litepro, Medpro, and Heavpro
 Assume demand for each is 1000 units per month
 If each product is ordered separately:
◦ Q* = 980 units for each product
◦ Total cycle inventory = 4(Q/2) = (4)(980)/2 = 1960 units
 Aggregate orders of all four products:
◦ Combined Q* = 1960 units
◦ For each product: Q* = 1960/4 = 490
◦ Cycle inventory for each product is reduced to 490/2 = 245
◦ Total cycle inventory = 1960/2 = 980 units
◦ Thus, lot size for each product, average flow time, inventory
holding costs will be reduced

24. Aggregating Multiple Products
in a Single Order
 Transportation is a significant contributor to the fixed cost per order.
 Can, therefore, possibly combine shipments of different products from the
same supplier
◦ same overall fixed cost
◦ shared over more than one product
◦ effective fixed cost is reduced for each product
◦ lot size for each product can be reduced
 Can also have a single delivery coming from multiple suppliers (allowing
fixed transportation cost to be spread across multiple suppliers) or a
single truck delivering to multiple retailers (allowing fixed transportation
cost to be spread across multiple retailers).
 Aggregating across products, retailers, or suppliers in a single order
allows for a reduction in lot size for individual products because fixed
ordering and transportation costs are now spread across multiple
products, retailers, or suppliers.
 Wal-Mart achieves the above through cross-docking, but we cannot
ignore receiving or loading costs – importance of Advanced Shipping
Notices (ASN) and RFID technology.

25. Three models of Store Manager: Best Buy with multiple
models of computers (Litepro (L), Medpro (M), and
Heavypro (H))
 If each product manager orders his model independently
(no aggregation – high cost).
 The product managers jointly order every product in each
lot (weakness – low demand products are aggregated
with high demand products in each order, resulting in
high costs if the product-specific order costs for the low
demand products is large).
 Product managers order jointly but not every order
contains every product; that is, each lot contains a
selected subsets of the products.
 Let us consider all the models.

26. Lot Sizing with Multiple
products or Customers
 In practice, the fixed ordering cost is dependent at least in part
on the variety associated with an order of multiple models
◦ A portion of the cost is related to transportation
(independent of variety)
◦ A portion of the cost is related to loading and receiving (not
independent of variety)
 Three scenarios:
◦ Lots are ordered and delivered independently for each
product
◦ Lots are ordered and delivered jointly for all three models
◦ Lots are ordered and delivered jointly for a selected subset
of models

27. Lot Sizing with Multiple Products
 Demand per year
◦ DL = 12,000; DM = 1,200; DH = 120
 Common transportation cost, S = $4,000
 Product specific order cost (for each model
ordered and delivered on the same truck, an
additional fixed cost of $1000 is incurred for
receiving and storage)
◦ sL = $1,000; sM = $1,000; sH = $1,000
 Holding cost, h = 0.2
 Unit cost
◦ CL = $500; CM = $500; CH = $500

28. Delivery Options
 First model: No Aggregation: Each product ordered separately.
Because each model of the computer is ordered and delivered
independently, a separate truck delivers each model. Thus, a
fixed ordering cost of $4000 + $1000 = $5000 is incurred for
each product delivery. Annual ordering cost = ((S + sL) + (S + sM)
+ (S + sH)) x n (ordering frequency).
 Second model: Complete Aggregation: All products delivered on
each truck. All three models are included each time an order is
placed. So the annual ordering cost here is (S* x n) = (S + sL +
sM + sH) x n.
 Third model: Tailored Aggregation: Lots are ordered and
delivered jointly for a selected subsets of the products on each
truck
 Aggregate across products, supply points or delivery points.

29. No Aggregation: Order Each Product Independently
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
Annual holding
cost
$54,772 $17,321 $5,477
Order frequency 11.0 / year 3.5 / year 1.1 / year
Annual ordering
cost
$55,000 #17,500 $5,500
Average flow
time
2.4 weeks 7.5 weeks 23.7 weeks
Annual cost $109,772 $34,821 $10,977
Total cost = $155,570

30. Aggregation: Order All Products Jointly
S* = S + sL + sM + sH = 4000+1000+1000+1000 = $7000
n* = Sqrt[(DLhCL+ DMhCM+ DHhCH)/2S*]
= 9.75 (formula obtained by minimizing total annual cost),
where hCL = hCM = hCH = 20% of $500 = $100
Annual order cost = 9.75 x $7000 = $68, 250
QL = DL/n* = 12000/9.75 = 1230
QM = DM/n* = 1200/9.75 = 123
QH = DH/n* = 120/9.75 = 12.3
Cycle inventory = Q/2
Average flow time (in weeks) = (Q/2)/(weekly demand)

31. Complete Aggregation:
Order All Products Jointly
Litepro Medpro Heavypro
Demand per year
(D)
12,000 1,200 120
Order frequency
(n*)
9.75/year 9.75/year 9.75/year
Optimal order
size (D/n*)
1,230 123 12.3
Cycle inventory 615 61.5 6.15
Annual holding
cost
$61,512 $6,151 $615
Average flow
time
2.67 weeks 2.67 weeks 2.67 weeks
Annual order cost = 9.75 × $7,000 = $68,250
Annual total cost = $136,528 (down from
$155,570, by about 13 per cent)

32. Case of W.W. Grainger: Aggregating four suppliers
(each supplier, one product) per truck
 Di = 10,000
 h = 0.2
 Ci = $50
 Common order cost = S = $500
 Supplier-specific order cost = $100
 Combined order cost = S* =
($500+$100+$100+$100+$100) =$900
 n* = Sqrt[(Σ DihCi, i=1,..k)/2S*] = 14.91 (k = 4 here)
 Annual order cost per supplier = 14.91 x (900/4) =
$3,354
 Quantity ordered from each supplier = Q =
10,000/14.91 = 671 units per order
 Annual holding cost per supplier =(h CiQ)/2 =
(0.2x50x671)/2 = $3,355
 Thus, total capacity per truck = 4 x 671 = 2,684

33. Case of W.W. Grainger: Aggregating four suppliers
(each supplier, one product) per truck: Introducing
Capacity constraint
 Compare the total load for the optimal n* with truck
capacity. If the optimal load exceeds the truck
capacity, n* is increased until the load equals the
truck capacity. Further, by applying the formula n* =
Sqrt[(SUM DihCi, i=1,..k)/2S*] for different values of k,
we can also find the optimal number of items or
suppliers to be aggregated in a single delivery.
 Thus, if truck capacity limit is 2500 units, the order
frequency must be increased to ensure that the order
quantity from each supplier is 2,500/4 = 625.
 Thus, W.W. Grainger should increase the order
frequency to 10,000/625 = 16.
 This would increase the annual cost order cost per
supplier to $3,600 and decrease the annual holding
cost per supplier to #3,125.

34. Tailored aggregation
 The first step is to identify the product that is to be
ordered most frequently, assuming each product is
ordered independently.
 For each successive product, we then identify orders
in which it is included. Assumption: each product is
included in the order at regular intervals.
 Once we have identified the most frequently ordered
model, for each successive product i, we identify the
frequency mi, where model i is ordered every mi
deliveries.
 Each product i has an annual demand Di, a unit cost
Ci, and a product specific order cost si. The common
order cost is S.
 Using the same Best Buy data, product managers
have decided to order jointly, but to be selective
about which models they include in each order.

35. Calculations: Tailored aggregation
 nL = sqrt ((DLhCL)/2(S+ sL)) = 11.0; similarly, nM = 3.5
and nH = 1.1 (L is most frequently ordered model, 11
times a year). (Put 1bar).
 The frequency with which M and H are included in L
order are given as follows:
 nM = sqrt ((DMhCM/2 sM)) = 7.7 and nH = 2.4 (Put 2
bars)
 mM = nL/ nM (2 bars) = 11.0/7.7 = 1.4 (= 2) and
similarly, mH = 4.5 (= 5)
 Therefore, L is included in every order, M in every 2nd
order and H in every 5th order.
 Recalculate nL = n = sqrt ((DLhCLmL + DMhCM mM +
DHhCH mH)/2(S + sL/mL + sM/ mM + sH/ mH)) = 11.47

36. Calculations: Tailored aggregation
 Thus, recalculated nM = 11.47/2 = 5.74/year and nH
= 11.47/5 = 2.29/year
 Thus, L will be ordered 11.47 times, L, 5.74 times,
and H, 2.29 times/year.
 The annual holding cost of this policy = (((DL/2 nL)
hCL) + ((DM/2 nM) hCM) + ((DH/2 nH) hCH) =
$65,385.5
 The annual order cost = nS + nL sL + nM sM + nH sH,
(n = nL)
 For each, order size = D/n, cycle inventory = D/2n
 Total (annual order + holding) cost = $130,767

37. Lessons from Aggregation
 Aggregation allows a firm to lower lot size without increasing
cost
 Complete aggregation is effective if product specific fixed cost
is a small fraction of joint fixed cost (all customers, all
products, all trips).
 Tailored aggregation is effective if product specific fixed cost is
a large fraction of joint fixed cost. Here, larger customers get
more frequent deliveries. Tailored aggregation differentiates
between high volume and low volume items, orders low
volume items less frequently, and is suitable when product
specific order cost is high. For instance, the total cost in the
last example was $130,767. Tailored aggregation results in a
cost reduction of $5,761 (about 4%) compared to the joint
ordering of all models. The cost reduction results because
each model specific fixed cost of $1,000 is not incurred with
every order.
 On the transportation end, the product-specific order costs can
be reduced by locating supply points or delivery points close
to one another.

38. Economies of Scale to
Exploit Quantity Discounts
 All-unit quantity discounts
 Marginal unit quantity discounts
 Why quantity discounts?
◦ Improved coordination to increase total supply chain
profits. A supply chain is coordinated if the decision
the retailer and supplier make maximize total supply
chain profits. However, in reality, each stage has a
separate owner and considers its own costs in an
effort to maximize its own profit. Thus, the question is
how can a manufacturer use appropriate quantity
discount to ensure that coordination results even if
the retailer is acting to maximize its own profits?
◦ Price discrimination to maximize supplier profits
through extraction of surplus

39. Quantity Discounts
 Commodity products - Lot size based: a discount is
lot-sized based if the pricing schedule offers
discounts based on the quantity ordered in a single
lot.
◦ All units
◦ Marginal unit, also known as multi-block tariffs. In
this case, the pricing schedule contains specified
break points q0, q1, q2, …qr. If an order size of q is
placed, the first q1-q0 units are priced at C0, the
next q2-q1 are priced at C1, and so on, C0>C1>C2…
 Products with demand curve - Volume based: a discount is
volume-based if the discount is based on the total quantity
purchased over a given period, regardless of the number of lots
purchased over that period.
 How should buyer react?
 What are appropriate discounting schemes?

40. All-Unit Quantity Discounts
 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
 The unit cost generally decreases as the quantity
increases, i.e., C0>C1>…>Cr
 The objective for the company (a retailer in our
example) is to decide on a lot size that will minimize
the sum of material, order, and holding costs

41. All-Unit Quantity Discount Procedure (different from
what is in the textbook)
Step 1: Calculate the EOQ for the lowest price. If it is
feasible (i.e., this order quantity is in the range for that
price), then stop. This is the optimal lot size. Calculate
TC for this lot size.
Step 2: If the EOQ is not feasible, calculate the TC for this
price and the smallest quantity for that price.
Step 3: Calculate the EOQ for the next lowest price. If it is
feasible, stop and calculate the TC for that quantity and
price.
Step 4: Compare the TC for Steps 2 and 3. Choose the
quantity corresponding to the lowest TC.
Step 5: If the EOQ in Step 3 is not feasible, repeat Steps
2, 3, and 4 until a feasible EOQ is found.

42. All-Unit Quantity Discounts: Example
Cost/Unit
$3
$2.96
$2.92
Order Quantity
5,000 10,000
Order Quantity
5,000 10,000
Total Material Cost

43. All-Unit Quantity Discount: Example
Order quantity Unit Price
0-5000 $3.00
5001-10000 $2.96
Over 10000 $2.92
q0 = 0, q1 = 5001, q2 = 10001
C0 = $3.00, C1 = $2.96, C2 = $2.92
D = 120000 units/year, S = $100/lot, h =
0.2

44. All-Unit Quantity Discount: Example
Step 1: Calculate Q2* = Sqrt[(2DS)/hC2]
= Sqrt[(2)(120000)(100)/(0.2)(2.92)] = 6410
Not feasible (6410 < 10001)
Calculate TC2 using C2 = $2.92 and q2 = 10001
TC2 =
(120000/10001)(100)+(10001/2)(0.2)(2.92)+(120000)(2.9
2)
= $354,520
Step 2: Calculate Q1* = Sqrt[(2DS)/hC1]
=Sqrt[(2)(120000)(100)/(0.2)(2.96)] = 6367
Feasible (5000<6367<10000)  Stop
TC1 =
(120000/6367)(100)+(6367/2)(0.2)(2.96)+(120000)(2.96)
= $358,969
TC2 < TC1  The optimal order quantity Q* is q2 = 10001

45. All-Unit Quantity Discounts
 If all units are sold for $3 (no discount), Q0* = 6,324 units. Since
6,324>5000, we should set q1 = 5001 for getting it at $2.96 per unit,
and TC0 = $359,080. However, the optimal quantity to order is
10,001 with discounts. Thus, the quantity discount is an incentive to
order more.
 Suppose fixed order cost were reduced to $4 (from $100)
◦ Without discount, Q0* would be reduced to 1265 units, that is, if
fixed cost of ordering is reduced, lot size reduces sharply.
◦ With discount, optimal lot size would still be 10001 units
◦ Thus, the average inventory (flow time) increases.
 What is the effect of such a discount schedule?
◦ Retailers are encouraged to increase the size of their orders
◦ Average inventory (cycle inventory) in the supply chain is
increased
◦ Average flow time is increased
◦ Is an all-unit quantity discount an advantage in the supply chain?

46. All unit quantity discount vs. marginal unit
quantity discount
◦ The marginal unit quantity discount
results in a larger lot size than an all-
unit quantity discount.
◦ As the lot size is increased beyond the
last break point, the material cost
continues to decline.
◦ Quantity discounts often contribute
more to cycle inventory.
◦ So, why quantity discounts?

47. Why Quantity Discounts?
 Improved coordination in the supply
chain
◦ Commodity products: for commodity
products such as milk, a competitive
market exists, and costs are driven down to
the product’s marginal cost. In this case,
the market sets the price and the firm’s
objective is to lower costs.
◦ Products with demand curve
 2-part tariffs
 Volume discounts

48. Commodity products case
 A retail company DO sells a commodity product
(vitamins). Do incurs a fixed order placement,
transportation, and receiving cost of $100 every time it
places an order with the manufacturer, plus a holding
cost of 20%. The manufacturer charges $3 per bottle of
vitamins.
 Every time DO places an order, the manufacturer has to
process, pack, and ship the order. The manufacturer
incurs a fixed order filling cost of $250, production cost of
$2 per bottle, plus a holding cost of 20%.

49. Coordination for
Commodity Products
 D = 120,000 bottles/year
 SR = $100, hR = 0.2, CR = $3
 SS = $250, hS = 0.2, CS = $2
Retailer’s (DO) optimal lot size (EOQ) = 6,324 bottles. Annual
holding + ordering costs of Retailer = $3,795; Annual order cost
at manufacturer = (120,000/6,324) x 250 = $4,744, annual
holding cost of supplier = (6,324/2) x 2 x 0.2 = $1,265, thus total
supplier cost = $6,009
Therefore, supply chain cost = $3,795 + $6,009 = $9,804
A lot size-based quantity discount is appropriate in this case.
When the lot size increases, manufacturer’s cost relatively
decreases due to large lot size, but order and holding costs
(cycle inventory increases) increase for the retailer although the
total supply chain cost also decreases. Therefore, the
manufacturer must induce the retailer to buy in larger quantity,
by sharing some benefits with the retailer.
Q* for the manufacturer = sqrt ((2 x 120,000 x 250)/0.2 x 2)) =
9,165. Thus, if the supplier offers each bottle for $2.9978 for all
orders in lots of 9,165 or more. The manufacturer’s and the total
supply chain profit increases by $638, by offering quantity
discount of $264, when DO has an incentive to order in lots of
9,165.

50. Coordination for
Commodity Products
 What can the supplier do to decrease supply chain costs?
◦ Coordinated lot size: 9,165; Retailer cost = $4,059; Supplier
cost = $5,106; Supply chain cost = $9,165
 Effective pricing schemes
◦ All-unit quantity discount
 $3 for lots below 9,165
 $2.9978 for lots of 9,165 or more
◦ Pass some fixed cost to retailer (enough that he raises order
size from 6,324 to 9,165)
On the contrary, for a low enough set-up or order cost (fixed cost
per order reduces from $250 to $100), the manufacturer gains
very little from using a lot size-based quantity discount; it makes
sense for him to eliminate all quantity discounts. This brings out
the importance of marketing and sales on the one hand, and
operations, on the other hand, working in close coordination.

51. Quantity Discounts When
Firm Has Market Power
 A new vitamin pill whose properties are highly valued
has been introduced into the market by the
manufacturer. It can be thus be argued that the price
at which DO sells this drug influences demand.
Assume that the annual demand faced by DO is
given by the demand curve 360,000 – 60,000p,
where p is the price DO sells this drug. The
manufacturer incurs a cost CS = $2 per bottle.
 The manufacturer must decide what to charge DO,
and DO, in turn, must decide on the price to charge
the customer.

52. Quantity Discounts When
Firm Has Market Power
 No inventory related costs
 Demand curve
360,000 - 60,000p
What are the optimal prices and profits in the following situations?
◦ The two stages coordinate the pricing decision
 Price = $4, Profit = $240,000, Demand = 120,000
◦ The two stages make the pricing decision independently
 Price = $5, Profit = $180,000, Demand = 60,000

53. Quantity Discounts When
Firm Has Market Power
 Independent decision-making: it is optimal for DO
to sell the drug at $5 per bottle (= p) and for the
manufacturer to charge CR = $4 per bottle .
 Total market demand = 360,000 – 60,000p =
60,000
 ProfitR = p(360,000 – 60,000p) - (360,000 –
60,000p) x $4
 = ($5 x 60,000) – ($4 x $60,000) = $60,000
 ProfitM = ($4 x 60,000) – ($2 x 60,000) = $120,000
 Thus, the total supply chain profit in this case =
$60,000 + $120,000 = $180,000

54. Double marginalization
 If the two stages coordinate pricing, p = $4, and let CR = $3.25 per
bottle, market demand is 120,000, the total supply chain profit =
120,000 x ($4 - $2) = $240,000 = ProfitR + ProfitM = (120,000 x (4 –
3.25)) + (120,000 x (3.25-2))
 We can thus realize that if each stage sets its price independently,
the supply chain thus loses $240,000 - $180,000 = $60,000 in
profit.
 This phenomenon is referred to as double marginalization.
 Double marginalization leads to a loss of profit because the supply
chain margin is divided between two stages but each stage makes
its decision considering only its local margin.
 There are two pricing schemes that the manufacturer may use to
achieve the coordinated solution and maximize supply chain profits
even though the retailer firm DO acts in a way that maximizes its
own profit: two-part tariff and volume-based quantity discounts.

55. Two-Part Tariffs
 Design a two-part tariff that achieves the
coordinated solution: the manufacturer
charges its entire profit as an up-front
franchise fee and then sells to the retailer at
its cost price.
 In the case here, the manufacturer charges
DO a franchise fee of $180,000 (its profit)
and material cost of CS = CR = $2 per bottle.
DO maximizes its profit if p = $4 per bottle. It
has annual sales of 360,000 – 60,000p =
120,000 and profits of $60,000 = ([120,000 x
$4] – [(120,000 x 2) + 180,000)]).

56. Volume Discounts
 Design a volume discount scheme that achieves the
coordinated solution. We recall that 120,000 bottles are
sold per year when the supply chain is coordinated.
 The manufacturer must offer DO a volume discount to
encourage DO to purchase this quantity. The
manufacturer thus offers a price CR = $4 per bottle if the
quantity purchased by DO is less than 120,000 and CR =
$3.50 per bottle if the volume is 120,000 or higher.
 It is then optimal for DO to order 120,000 units and offer
them at $4 per bottle to the customers. The total profit
earned by DO is (360,000-60,000p) x (p – CR) = $60,000.
 The total profit earned by the manufacturer is 120,000 x
(CR - $2) = $180,000, the total supply chain profit
remaining unchanged.

57. Impact of inventory costs
◦ For products for which a firm has market power, lot
size-based discounts are not optimal for the supply
chain even in the presence of inventory costs
(order and holding).
◦ In such a setting, a two-part tariff or volume-based
discount, with the supplier passing on some fixed
costs with above pricing to the retailer, is needed
for the supply chain to be coordinated and
maximize profits, given the assumption that
customer demand decreases when the retailer
increases price.

58. Lessons from Discounting Schemes
 Lot size-based discounts increase lot size and cycle
inventory in the supply chain.
 Lot size-based discounts are justified to achieve
coordination for commodity products. Lot-sized discounts
are based on quantity purchased per lot, not the rate of
purchase.
 Volume-based discounts are based on the rate of
purchase or volume purchased on average per year or
month.
 Volume-based discounts are compatible with small lots
that reduce cycle inventory.
 Lot size-based discounts make sense only when the
manufacturer incurs a very high fixed cost per order.
 Volume based discounts with some fixed cost passed on
to retailer are more effective in general
◦ Volume based discounts are better over rolling horizon,
for instance, each week the manufacturer may offer DO
the volume discount based on sales over the last 12
weeks.

59. Short-Term Discounting: Trade Promotions
 Trade promotions are price discounts for a limited period of
time (also may require specific actions from retailers, such
as displays, advertising, etc.)
 Key goals for promotions from a manufacturer’s
perspective:
◦ Induce retailers to use price discounts, displays, advertising to
increase sales
◦ Shift inventory from the manufacturer to the retailer and customer
◦ Defend a brand against competition
◦ Goals are not always achieved by a trade promotion
 What is the impact on the behavior of the retailer and on the
performance of the supply chain?
 Retailer has two primary options in response to a promotion:
◦ Pass through some or all of the promotion to customers to spur sales
◦ Purchase in greater quantity during promotion period to take
advantage of temporary price reduction, but pass through very little of
savings to customers

60. Short-Term Discounting: Trade Promotions
 The first action lowers the price of the product for the
end customer, leading to increased purchases and
thus increased sales for the entire supply chain.
 The second action does not increase purchases by
the customer but increases the amount of inventory
held at the retailer increasing the cycle inventory and
the flow time within the supply chain.
 A forward buy occurs in the latter case helping
reduce the retailer’s cost of goods after the
promotion ends but it usually increases demand
variability and can decrease supply chain profitability.