Post on 20-Jan-2015
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Chapter 12
Inventory Management
McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved.
Inventory
• Inventory– A stock or store of goods
• Independent demand items– Items that are ready to be sold or used
12-2
Types of Inventory
• Raw materials and purchased parts• Work-in-process• Finished goods inventories or merchandise• Maintenance and repairs (MRO) inventory, tools and
supplies• Goods-in-transit to warehouses or customers (pipeline
inventory)
12-3
Inventory Functions
• Inventories serve a number of functions such as:1. To meet anticipated customer demand
2. To smooth production requirements
3. To decouple operations
4. To protect against stockouts
5. To take advantage of order cycles
6. To hedge against price increases
7. To permit operations
8. To take advantage of quantity discounts
12-4
Inventory Management
• Management has two basic functions concerning inventory:1. Establish a system for tracking items in inventory
2. Make decisions about• When to order
• How much to order
12-5
Effective Inventory Management
• Requires:1. A system keep track of inventory
2. A reliable forecast of demand
3. Knowledge of lead time and lead time variability
4. Reasonable estimates of• holding costs• ordering costs• shortage costs
5. A classification system for inventory items
12-6
Inventory Counting Systems
• Periodic System– Physical count of items in inventory made at periodic
intervals
• Perpetual Inventory System– System that keeps track of removals from inventory
continuously, thus monitoring current levels of each item• Two-bin system
– Two containers of inventory; reorder
when the first is empty
12-7
Inventory Counting Technologies
• Universal product code (UPC)– Bar code printed on a label that has information about
the item to which it is attached
• Radio frequency identification (RFID) tags– A technology that uses radio waves to identify objects,
such as goods in supply chains
12-8
Demand Forecasts and Lead Time
• Forecasts– Inventories are necessary to satisfy customer demands, so it is
important to have a reliable estimates of the amount and timing of demand
• Lead time– Time interval between ordering and receiving the order
• Point-of-sale (POS) systems– A system that electronically records actual sales– Such demand information is very useful for enhancing
forecasting and inventory management
12-9
ABC Classification System
• A-B-C approach– Classifying inventory according to some measure of importance, and
allocating control efforts accordingly
– A items (very important)
• 10 to 20 percent of the number of items in inventory and about 60 to 70 percent of the annual dollar value
– B items (moderately important)
– C items (least important)
• 50 to 60 percent of the number
of items in inventory but only
about 10 to 15 percent of the
annual dollar value
Annual $ value of items
High
LowFew ManyNumber of Items
AA
CCBB
12-10
Cycle Counting
• Cycle counting– A physical count of items in inventory
• Cycle counting management– How much accuracy is needed?
• A items: ± 0.2 percent
• B items: ± 1 percent
• C items: ± 5 percent
– When should cycle counting be performed?
– Who should do it?
12-11
How Much to Order: EOQ Models
• The basic economic order quantity model• The economic production quantity model• The quantity discount model
12-12
Basic EOQ Model
• The basic EOQ model is used to find a fixed order quantity that will minimize total annual inventory costs
• Assumptions– Only one product is involved
– Annual demand requirements are known
– Demand is even throughout the year
– Lead time does not vary
– Each order is received in a single delivery
– There are no quantity discounts
12-13
The Inventory Cycle
Profile of Inventory Level Over Time
Quantityon hand
Q
Receive order
Placeorder
Receive order
Placeorder
Receive order
Lead time
Reorderpoint
Usagerate
Time
12-14
Total Annual Cost
cost Ordering
yearper unit in usually Demand,
unitper cost (carrying) Holding
unitsin quantity Order
where
2
Cost Ordering AnnualCost Holding AnnualCost Total
S
D
H
Q
SQ
DH
Q
12-15
Goal: Total Cost Minimization
Order Quantity (Q)
The Total-Cost Curve is U-Shaped
Ordering Costs
Q*
An
nu
al C
ost
(optimal order quantity)
Holding Costs
SQ
DH
QTC
2
12-16
Deriving EOQ
• Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.
• The total cost curve reaches its minimum where the carrying and ordering costs are equal.
cost holdingunit per annual
cost)der demand)(or annual(22* H
DSQ
12-17
Economic Production Quantity (EPQ)
• Assumptions– Only one product is involved
– Annual demand requirements are known
– Usage rate is constant
– Usage occurs continually, but production occurs periodically
– The production rate is constant
– Lead time does not vary
– There are no quantity discounts
12-18
EPQ: Inventory Profile
Q
Q*
Imax
Productionand usage
Productionand usage
Productionand usage
Usageonly
Usageonly
Cumulativeproduction
Amounton hand
Time
12-19
EPQ – Total Cost
rate Usage
ratedelivery or Production
inventory Maximum
where
2
Cost SetupCost CarryingTC
max
max
u
p
upp
Q
I
SQ
DH
I
12-20
EPQ
up
p
H
DSQp
2*
12-21
Quantity Discount Model
• Quantity discount– Price reduction offered to customers for placing large
orders
priceUnit
where
2
Cost PurchasingCost OrderingCost CarryingCost Total
P
PDSQ
DH
Q
12-22
Quantity Discounts
12-23
Quantity Discounts
12-24
When to Reorder
• Reorder point– When the quantity on hand of an item drops to this amount, the
item is reordered.– Determinants of the reorder point
1. The rate of demand
2. The lead time
3. The extent of demand and/or lead time variability
4. The degree of stockout risk acceptable to management
12-25
Reorder Point: Under Certainty
) as units timesame(in timeLeadLT
per week) day,per period,per (units rate Demand
where
LTROP
d
d
d
12-26
Reorder Point: Under Uncertainty
• Demand or lead time uncertainty creates the possibility that demand will be greater than available supply
• To reduce the likelihood of a stockout, it becomes necessary to carry safety stock– Safety stock
• Stock that is held in excess of expected demand due to variable demand and/or lead time
StockSafety timelead during
demand Expected ROP
12-27
Safety Stock
LT Time
Expected demandduring lead time
Maximum probable demandduring lead time
ROP
Qu
an
tity
Safety stock
12-28
Safety Stock?
• As the amount of safety stock carried increases, the risk of stockout decreases.– This improves customer service level
• Service level– The probability that demand will not exceed supply during lead
time– Service level = 100% - Stockout risk
12-29
How Much Safety Stock?
• The amount of safety stock that is appropriate for a given situation depends upon:1. The average demand rate and average lead time
2. Demand and lead time variability
3. The desired service level
demand timelead ofdeviation standard The
deviations standard ofNumber
where
timelead duringdemand Expected
ROP
dLT
dLT
z
z
12-30
Reorder Point
ROP
Risk ofstockoutService level
Expecteddemand
Safetystock
0 z
Quantity
z-scale
The ROP based on a normalDistribution of lead time demand
12-31
Reorder Point: Demand Uncertainty
) as units time(same timeLead LT
) as units time(same periodper demand of stddev. The
per week) day,(per periodper demand Average
deviations standard ofNumber
where
LT ROP
d
d
d
z
zd
d
d
LT :Note ddLT 12-32
Reorder Point: Lead Time Uncertainty
) as units time(same timelead Average LT
) as units time(same timelead of stddev. The
per week) day,(per periodper Demand
deviations standard ofNumber
where
LT ROP
LT
LT
d
d
d
z
zdd
12-33
How Much to Order: FOI
• Fixed-order-interval (FOI) model– Orders are placed at fixed time intervals
• Reasons for using the FOI model– Supplier’s policy may encourage its use– Grouping orders from the same supplier can produce savings in
shipping costs– Some circumstances do not lend themselves to continuously
monitoring inventory position
12-34
Fixed-Quantity vs. Fixed-Interval Ordering
12-35
FOI Model
order of at timeposition Inventory
levelinventory Target
order Amount to
where
Order of Timeat PositionInventory
LevelInventoryTarget
Order toAmount
IP
T
Q
IPTQ
12-36
FOI Model
orders)between timeof(length intervalOrder OI
where
LTOILT OI
dzdT
interest of frame-Time*
* D
QOI
OI* represents the optimal time between orders. Time-frame of interest is an appropriate period (e.g., days or weeks). This is usually based on the time-frame expressed by the average demand rate, d-bar.
12-37
Single-Period Model
• Single-period model– Model for ordering perishables and other items with limited
useful lives– Shortage cost
• Generally, the unrealized profit per unit
• Cshortage = Cs = Revenue per unit – Cost per unit
– Excess cost• Different between purchase cost and salvage value of items
left over at the end of the period
• Cexcess = Ce = Cost per unit – Salvage value per unit
12-38
Single-Period Model
• The goal of the single-period model is to identify the order quantity that will minimize the long-run excess and shortage costs
• Two categories of problem:– Demand can be characterized by a continuous distribution– Demand can be characterized by a discrete distribution
12-39
Stocking Levels
Service level
So Balance Point
Quantity
Cs Ce
So =OptimumStocking Quantity
unitper cost excess
unitper cost shortage
where
level Service
e
s
es
s
C
C
CC
C
12-40