Supply Chain Management
Lecture 18
Outline
• Today
– Chapter 10
• 3e: Sections 1, 2 (up to page 273), 6
• 4e: Sections 1, 2, 3 (up to page 260)
• Thursday
– Finish Chapter 10
– Start with Chapter 11
Staples Visit
• Date
– Friday April 2
• Location
– Staples fulfillment Center
– Brighton, CO
• Subject
– Lunch and Learn
Guest Lecture
• Date
– Tuesday April 20
• Speaker
– Paul Dodge (Senior Vice President – Supply Chain)
• Subject
– Today’s Supply Chain
The Importance of Inventory
• Firms can reduce costs by reducing inventory, but
customers become dissatisfied when an item is
out of stock
The objective of inventory management is to
strike a balance between inventory investment
and customer service
Inventory Decisions
• How much to order?
– Order quantity or lot size (Q)
• When to order?
– Order frequency (n)
Find an inventory policy that is optimal with
respect to some criteria (usually cost)
Inventory Profile
Average demand D
Inventory
Lot size Q
Q/2
0
Time
Cycle
Average flow time =
Average inventory
= Q/2D
Average demand
Average inventory due
to cycle inventory Q/2
Q
The Role of Cycle Inventory in a Supply
Chain
• What is cycle inventory?
– 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 customers
• What is lot size or batch size?
– Lot or batch size is the quantity that a stage of a supply
chain either produces of purchases at a time
Inventory
Inventory Profile
Q
Q/2
Time
Inventory
0
Q
Q/2
0
Time
Why Order in Large/Small Lots?
• Fixed ordering cost: S (cost incurred per order/lot)
– Increase the lot size to decrease the fixed ordering cost per unit
• Holding cost: H (cost of carrying one unit in inventory)
– Decrease the lot size to decrease holding cost
• Material cost: C (cost per unit)
Lot size Q is chosen by trading off holding
costs against fixed ordering costs
Convenience store
Sam's Club
Fixed cost
Low
High
Material cost
High
Low
Cost Influenced by Lot Size
Annual Cost
Holding Cost
Ordering Cost
Material Cost
Order Quantity
Material Cost (C)
• Material cost ($/unit)
– The average price paid per unit
Supply Chain Cost Influenced by Lot
Size
Annual Cost
CD
Material Cost
Order Quantity
Holding Cost (H)
• Holding cost ($/unit/year)
– Cost of carrying one unit in inventory for a specified
period of time
Category
Warehousing/occupancy cost
Handling costs
Obsolescence cost
Cost of capital
Miscellaneous cost
Total holding cost
% of
Inventory Value
6%
3%
3%
11%
3%
26%
Supply Chain Cost Influenced by Lot
Size
Annual Cost
(Q/2)H
Holding Cost
Material Cost
Order Quantity
Ordering Cost (S)
• Ordering cost ($/lot)
– Fixed cost incurred each time an order is placed
(does not vary with the size of the order)
• Buyer time (order placement)
• Transportation cost
• Receiving cost
1000 Orders = $400,000
1 Order = $ 400
Purchase Order
Description Qty.
Microwave 1000
Order
quantity
PurchaseOrder
Order
Purchase
Purchase Order
Description
Qty.
Purchase
Order
Description
Qty.
Description
Qty.1
Microwave
Description
Qty.
Microwave 11
Microwave
Microwave
1
Supply Chain Cost Influenced by Lot
Size
Annual Cost
(D/Q)S
Holding Cost
Ordering Cost
Material Cost
Order Quantity
Supply Chain Cost Influenced by Lot
Size
Annual Cost
CD + (D/Q)S + (Q/2)H
Total Cost Curve
Holding Cost
Ordering Cost
Optimal
Order Quantity (Q*)
Material Cost
Order Quantity
Economic Order Quantity (EOQ)
• Optimal order quantity
2 D  S
EOQ
Q* 
hC
H
Example: Economic Order Quantity
• Example 10-1
– Demand for the Deskpro computer at Best Buy is 1,000
units per month. Best Buy incurs a fixed order
placement, transportation, and receiving cost of $4,000
each time an order is placed. Each computer costs
Best Buy $500 and the retailer has an annual holding
cost of 20 percent.
D
S
C
h
= 1,000 x 12 = 12,000
= $4,000
= $500
= 0.2
Example: Economic Order Quantity
• Example 10-1
D = 12,000
S = 4,000
C = 500
h = 0.2
2 D  S
EOQ
Q* 
hC
H
Q* = sqrt((2DS)/(hC))
= sqrt((2 x 12,000 x 4,000)/(0.2 x 500))
= 980
Example: Economic Order Quantity
• Example 10-1
D = 12,000
S = 4,000
C = 500
h = 0.2
Q* = 980
Order frequency = D/Q
= 12,000 / 980 = 12.24
Cycle inventory = Q/2
= 980 / 2 = 490
Average flow time = Q/(2D)
= 980 / (2 x 12,000) = 0.041
Example: Economic Order Quantity
• Example 10-1
D = 12,000
S = 4,000
C = 500
h = 0.2
Q* = 980
Annual ordering and holding cost
= (D/Q*)S + (Q*/2)hC
= $48,990 + $48,990
= $97,980
What if Q = 1,000
What if Q = 900
What if Q = 200
cost = $98,000
cost = $98,333
cost = $250,000
Summary
Description
Formula
Optimal order quantity Q* sqrt((2DS)/H)
Order frequency
n
D/Q
Cycle inventory
Q/2
Average flow time
(Avg inventory)/(Avg demand)
Order cost
(D/Q)S
Holding cost
(Q/2)H
Material cost
CD
Key Points from EOQ Model
1. Total ordering and holding costs are relatively
stable around the economic order quantity
2. If demand increases by a factor k, the optimal lot
size increases by a factor k
3. To reduce the optimal lot size by a factor of k,
the fixed order cost S must be reduced by a
factor k2
2 D  S
EOQ
Q* 
hC
H
Example: Economic Order Quantity
• Example 10-2
– The store manager at Best Buy would like to reduce
the optimal lot size from 980 to 200. For this lot size
reduction to be optimal, the store manager wants to
evaluate how much the order cost per lot should be
reduced (currently $4,000)
Q* = sqrt((2DS)/(hC))
200 = sqrt((2 x 12,000 x S)/(0.2 x 500))
S = (hC(Q*)2)/2D
= (0.2 x 500 x 2002)/(2 x 12,000) = $166.7
Example: Economic Order Quantity
• How can the store manager reduce the fixed
ordering cost?
– Aggregate multiple products in a single order
• Can possibly combine shipments of different products from the
same supplier
• Can also have a single delivery coming from multiple suppliers
Aggregating Multiple Products in a
Single Order
• Example 10-1 (continued)
– Assume Best Buy sells 4 different models of Deskpro
each with demand of 1,000 units per month (all costs
are same)
– 4 single orders
• Q* for each model equals 980
• Annual order and holding cost equal 97,980 x 4 = $391,920
– 1 aggregate order
• D = 12,000 x 4 = 48,000
• Q* = sqrt((2 x 48,000 x 4,000)/(0.2 x 500))
= 1,960 (= 490 for each model)
• Annual order and holding cost = (D/Q)S + (Q/2)hC
= ((48,000/1,960) x 4,000) + (1,960/2) x 0.2 x 500
= $244,918
Lot Sizing with Multiple Products or
Customers
• Ordering cost has two components
– Common (to all products)
– Individual (to each product)
• Example
– It is cheaper for Wal-Mart to receive a truck containing
a single product than a truck containing many different
products
• Inventory and restocking effort is much less for a single product
Lot Sizing with Multiple Products or
Customers
• Multiple products
– Independent orders
• No aggregation: Each product ordered separately
1
2
3
– Joint order of all products
• Complete aggregation: All products delivered on each truck
1 2 3
1 2 3
1 2 3
– Joint order of a subset of products
• Tailored aggregation: Selected subsets of products on each truck
1
1 2
Which option will likely have the lowest cost?
1 2 3