supply chain management lecture 18. outline today –chapter 10 3e: sections 1, 2 (up to page 273),...
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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
Inventory
Time
Q
Q/2
0
Cycle
Lot
size
Q
Average demand D
Average inventory due
to cycle inventory Q/2
Average inventoryAverage demand
Average flow time = = Q/2D
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 Profile
Q/2
Q/2
Inventory
Time
Q
0
Inventory
Time
Q
0
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
Fixed cost Material costConvenience store Low HighSam's Club High Low
Cost Influenced by Lot Size
Order Quantity
Annual Cost
Holding CostHolding Cost
Ordering CostOrdering Cost Material CostMaterial Cost
Material Cost (C)
• Material cost ($/unit)– The average price paid per unit
Supply Chain Cost Influenced by Lot Size
Order QuantityOrder Quantity
Annual CostAnnual Cost
Material CostMaterial CostCD
Holding Cost (H)
• Holding cost ($/unit/year)– Cost of carrying one unit in inventory for a specified
period of time
Warehousing/occupancy cost 6%
Handling costs 3%
Obsolescence cost 3%
Cost of capital 11%
Miscellaneous cost 3%
Total holding costTotal holding cost 26%26%
% of % of Category Category Inventory ValueInventory Value
Supply Chain Cost Influenced by Lot Size
Order QuantityOrder Quantity
Annual CostAnnual Cost
Holding CostHolding Cost
Material CostMaterial Cost
(Q/2)H
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
Purchase Order
Description Qty.Microwave 1
Purchase Order
Description Qty.Microwave 1
Purchase Order
Description Qty.Microwave 1
Purchase Order
Description Qty.Microwave 1
1 Order = $ 4001 Order = $ 4001000 Orders = $400,0001000 Orders = $400,000
Order Order quantityquantity
Purchase Order
Description Qty.Microwave 1000
Supply Chain Cost Influenced by Lot Size
Order QuantityOrder Quantity
Annual CostAnnual Cost
Holding CostHolding Cost
Ordering CostOrdering Cost Material CostMaterial Cost
(D/Q)S
Supply Chain Cost Influenced by Lot Size
Order QuantityOrder Quantity
Annual CostAnnual Cost
Holding CostHolding Cost
Total Cost CurveTotal Cost Curve
Ordering CostOrdering Cost Material CostMaterial Cost
Optimal Optimal Order Quantity (Q*)Order Quantity (Q*)
CD + (D/Q)S + (Q/2)H
Economic Order Quantity (EOQ)
• Optimal order quantity
H
SDEOQ
2
hCQ*
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.
= 1,000 x 12 = 12,000DSCh
= $4,000= $500= 0.2
Example: Economic Order Quantity
• Example 10-1
D = 12,000S = 4,000 C = 500h = 0.2
Q* = sqrt((2DS)/(hC))= sqrt((2 x 12,000 x 4,000)/(0.2 x 500))= 980
H
SDEOQ
2hC
Q*
Example: Economic Order Quantity
• Example 10-1
D = 12,000S = 4,000 C = 500h = 0.2Q* = 980
Order frequency
Cycle inventory
Average flow time
= D/Q= 12,000 / 980 = 12.24
= Q/2= 980 / 2 = 490
= Q/(2D)= 980 / (2 x 12,000) = 0.041
Example: Economic Order Quantity
• Example 10-1
D = 12,000S = 4,000 C = 500h = 0.2Q* = 980
Annual ordering and holding cost
= (D/Q*)S + (Q*/2)hC
What if Q = 1,000
What if Q = 900
What if Q = 200
cost = $98,000
cost = $98,333
cost = $250,000
= $48,990 + $48,990= $97,980
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
H
SDEOQ
2hC
Q*
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
– Joint order of all products• Complete aggregation: All products delivered on each
truck
– Joint order of a subset of products• Tailored aggregation: Selected subsets of products on
each truck
1 2 3
1 2 3
1 1 1
1 2 3 1 2 3
2 32
Which option will likely have the lowest cost?