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MS3121 Fundamentals of Business Logistics
Management
Every management mistake ends up in
inventory.
Michael C. Bergerac
Former Chief Executive

Revlon, Inc.
Topic 7 Inventory Policy Decisions Part I
Fundamentals
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Inventory Decisions in Strategy
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What are Inventories?

• Finished product held for sale
• Goods in warehouses
• Work in process
• Goods in transit
• Staff hired to meet service needs
• Any owned or financially controlled raw
  material, work in process, and/or finished good
  or service held in anticipation of a sale but
  not yet sold

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Where are Inventories?
9-4
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Reasons for Inventories

• Improve customer service
• Provides immediacy in product availability
• Encourage production, purchase, and
  transportation economies
• Allows for long production runs
• Takes advantage of price-quantity discounts
• Allows for transport economies from larger
  shipment sizes
• Act as a hedge against price changes
• Allows purchasing to take place under most
  favorable price terms
• Protect against uncertainties in demand and lead
  times
• Provides a measure of safety to keep operations
  running when demand levels and lead times
  cannot be known for sure
• Act as a hedge against contingencies
• Buffers against such events as strikes, fires,
  and disruptions in supply

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Reasons Against Inventories

• They consume capital resources that might be put
  to better use elsewhere in the firm
• They too often mask quality problems that would
  more immediately be solved without their
  presence
• They divert managements attention away from
  careful planning and control of the supply and
  distribution channels by promoting an insular
  attitude about channel management

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Types of Inventories

• Pipeline
• Inventories in transit
• Speculative
• Goods purchased in anticipation of price
  increases
• Regular/Cyclical/Seasonal
• Inventories held to meet normal operating needs
• Safety
• Extra stocks held in anticipation of demand and
  lead time uncertainties
• Obsolete/Dead Stock
• Inventories that are of little or no value due to
  being out of date, spoiled, damaged, etc.

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Regular/Cyclical/Seasonal inventory

• Also called cycle inventory/stock
• Accumulated stock that will not be used or sold
  immediately.
• Price discounts
• Transportation discounts
• Production economics

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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 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
• Cycle inventory Q/2 (depends directly on lot
  size)

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Role of Cycle Inventory in a Supply Chain

• Q 1000 units
• d 100 units/day
• Cycle inventory Q/2 1000/2 500
• Avg inventory level from cycle inventory500

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Nature of Demand

• Perpetual demand
• Continues well into the foreseeable future
• Seasonal demand
• Varies with regular peaks and valleys throughout
  the year
• Lumpy demand
• Highly variable (? Mean ?3?)
• Regular demand
• Not highly variable (lt Mean ?3?)
• Terminating demand
• Demand goes to 0 in foreseeable future
• Derived demand
• Demand is determined from the demand of another
  item of which it is a part

Accurately forecasting demand is singly the most
important factor in good inventory management
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Inventory Management Objectives
Good inventory management is a careful balancing
act between stock availability and the cost of
holding inventory.

• Service objectives
• Setting stocking levels so that there is only a
  specified probability of running out of stock
• Cost objectives
• Balancing conflicting costs to find the most
  economical replenishment quantities and timing

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Inventorys Conflicting Cost Patterns
Total cost
Minimum cost reorder quantity
Cost
Carrying cost
Procurement cost
Stockout cost
Replenishment quantity
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Costs Relevant to Inventory Management

• Carrying costs
• Cost for holding the inventory over time
• The primary cost is the cost of money tied up in
  inventory, but also includes obsolescence,
  insurance, personal property taxes, and
  storage costs
• Typically, costs range from the cost of short
  term capital to about 40/year. The average is
  about 25/year of the item value in inventory.

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Inventory Costs Inventory Carrying Cost

• Capital Cost
• Opportunity cost associated with investing in
  inventory, or any asset.
• What is the implicit value of having capital tied
  up in inventory, instead of some other worthwhile
  project?
• Minimum ROI expected from any asset.
• Debate on inventory valuation at fully allocated
  or variable costs only.

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Inventory Costs Inventory Carrying Cost

• Storage Space Cost
• Handling costs, rents, utilities.
• Logistics develops a cost formula for storage
  space costs based on cost behaviors.
• Public space mostly variable.
• Private space a mix of fixed and variable.

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Inventory Costs Inventory Carrying Cost

• Inventory Service Cost
• Insurance and taxes on stored goods.
• Varies according to the value of the goods.
• Inventory Risk Cost
• Largely beyond the control of the firm.
• Due to obsolescence, damage, theft, employee
  pilferage.

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Example of Carrying Cost Components for Computer
Hard Disks
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Relevant Costs (Contd)

• Procurement costs / Setup costs / Order costs
• Cost of preparing the order
• Cost of order transmission
• Cost of production setup if appropriate
• Cost of materials handling or processing at the
  receiving dock
• Price of the goods

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Inventory Costs Expected Stockout
Cost

• Cost of not having product available when a
  customer wants it.
• Includes backorder costs (special order).
• Losing one item profit by substituting a
  competing firms product.
• Losing a customer permanently if customer finds
  they prefer the substituted product and/or
  company.

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Inventory Costs Expected Stockout
Cost

• Possible to handle this by adding safety stock.
• In a manufacturing firm, a stockout may result in
  lost hours of production until the item is
  restocked.

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Stockouts Four possible outcomes

• Customers wait
• Back orders
• Lost sales
• Lost customers

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Expected Costs of Stockouts
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Inventory Management Philosophies

• Pull
• Demand driven
• Draws inventory into the stocking location
• Decentralized network
• Build to order / ship to order
• Quick response to demand, no economies of scale
• Push
• Supply driven
• Allocates production to stocking locations based
  on overall demand
• Encourages economies of scale in production
• Relies on forecasting

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Pull vs. Push Inventory Philosophies
PULL - Replenish inventory with
PUSH - Allocate supply to each
order sizes based on specific needs
warehouse based on the forecast
of each warehouse
for each warehouse
Demand
Warehouse 1
Q
1
A
1
Demand
A
Q
2
2
Plant
Warehouse 2
A
3
Q
3
A Allocation quantity to each warehouse
Demand
Q Requested replenishment quantity
by each warehouse
Warehouse 3
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Push Inventory Control

• Steps
• Forecast demand
• Find inventory on hand
• Establish stock availability level
• Estimate safety stock level
• Calculate net inventory requirement (demand
  inventory on-hand safety stock requirement)
• Apportion the excess inventory based on the
  forecasted demand

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Push Inventory Control
Example Tuna Production A tuna packer allocate
its products to three field warehouses on a
monthly basis. The current production run is
125000 lb. Information to facilitate inventory
decision for the upcoming month is given below.
Allocate the tuna production to the 3 warehouses.
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Reorder Point Control (Contd)
Assume monthly demand follows a normal
distribution
Monthly Demand for WH1
P90
Total requirement
z
S2000
Mean 10000 lb.
Z 1.96 from standard normal distribution
table Total requirement with a product
availability level of 90 should be 10000 1.28
2000 12560
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Push Inventory Control
Example Tuna Production
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Pull inventory control

• Fixed order quantity approach under certainty
• Fixed order quantity approach under uncertainty
• Uncertain demand
• Uncertain lead time
• Uncertain lead time demand

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Fixed order quantity approach (conditional of
certainty)

• Application
• Single product
• Fixed demand
• Fixed lead time
• No stockout cost
• Only inventory carrying cost and ordering cost
  are considered
• Also called Single Product Two-bin System

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Fixed order quantity approach (conditional of
certainty)
Annual demand D Number of orders per year
D/Q Inventory holding cost as a of unit price
I Ordering/procurement cost per unit S Annual
ordering/procurement cost (D/Q)S Annual holding
cost (Q/2)IC d demand rate, in time units LT
average lead time, in time units Average flow
time from cycle inventory Q/(2d) Total annual
cost TC TC Ordering cost Carrying cost
(D/Q)S (Q/2)IC
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Fixed order quantity approach (conditional of
certainty)
Objective Minimizing TC
Approach Develop a simple control system by
finding the replenishment quantity (Q) and the
reorder point (ROP).
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Fixed order quantity approach (conditional of
certainty)
Inventory Level
Q
Reorder point, R
Lead time
Lead time
0
Time
Order Placed
Order Placed
Order Received
Order Received
9-22
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Fixed order quantity approach (conditional of
certainty)
Suppose a company has weekly demand of 50 units.
Order cost is 10USD per order. Inventory
carrying cost is 10 per year. Product price is
5USD per unit. Lead time is 3 weeks. Find the
economic order quantity and corresponding
re-order point.
D S I C LT d
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Fixed order quantity approach (conditional of
certainty)
Using differential calculus, the optimal value
for Q will be
Famous EOQ formula
The reorder point is ROP d(LT) 3(50)
150 units
Rule When the inventory level drops to 150 units
(ROP) then reorder 322 units (Q).
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Fixed order quantity approach (conditional of
certainty)

• Cycle inventory Q/2 322/2 161 Avg
  inventory level from cycle inventory
• Avg flow time Q/2d 322/(250) 3.22 ? 4 days
• Cycle inventory adds 4 days to the time a unit
  spends in the supply chain
• Lower cycle inventory is better because
• Average flow time is lower
• Working capital requirements are lower
• Lower inventory holding costs

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Fixed order quantity approach (conditional of
uncertainty)

• Re-order point method
• Demand during lead time is uncertain, and follows
  a normal distribution
• Safety stock should be established
• EOQ is estimated by the basic formula
• Reorder point is estimated as
• ROP d LT z Sd
• where z is found from the Z-table
  corresponding to the given in-stock probability,
  Sd is the standard deviation of demand during
  lead time.

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Reorder Point Control for a Single Item
Quantity on hand
Q
Place order
Q
DDLT
ROP
Receive order
P
0
Stockout
LT
LT
Time
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Reorder Point Control for a Single Item
Actual on hand
Inventory level
Q
ROP
Safety stock
0
Time
LT
LT
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Reorder Point Control (Contd)
Finding the reorder point requires an
understanding of the demand-during-lead-time
distribution
DDLT
P
Week 3
Week 2
Week 1



sd10
sd10
sd10
z
S17.3
d 100
d 100
d 100
X 300
ROP
Weekly demand is normally distributed with a mean
of d 100 and a standard deviation of sd
10 Lead time is 3 weeks
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Fixed order quantity approach (conditional of
uncertainty)
Re-order point method example
Company A collected the following data for one
product held in inventory
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Fixed order quantity approach (conditional of
uncertainty)
Re-order point method example
EOQ
Average inventory level (AIL) cycle inventory
(regular stock) safety stock
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Fixed order quantity approach (conditional of
uncertainty)
Re-order point method example
Total relevant cost order cost cycle stock
carrying cost safety stock carrying cost
stockout cost
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Customer Service Level
For individual items The service level (stock
availability) actually achieved by inventory
control methods is not best represented by the
probability (P) of a stockout during the lead
time. It is more accurate to compute it as
follows.
Using data from the reorder point under
uncertainty example, the service level would be
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Fixed order quantity approach (conditional of
uncertainty)
Re-order point method example
Service level (SL)
Note Higher than P
That is, the demand of the product can be met
94.8 of the time.
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Customer Service Level (Contd)
This actual level is higher than P 0.75 that
was used to set the inventory level. The reason
is that there are periods of time when the stock
level is above the reorder point and there is no
risk of being out of stock.
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