Chapter 9
Inventory Management
Copyright 2011 John Wiley & Sons, Inc.
9-1
Lecture Outline
• Basics of Inventory Management
• Inventory Systems
• Fixed-Order Quantity System
• Fixed-Time Period Systems
• Independent vs. Dependent
Demand
• Managing Supply Chain Inventory
Copyright 2011 John Wiley & Sons, Inc.
9-2
What is Inventory?
Inventory is quantities of goods in stock
• Manufacturing Inventory
–
–
–
–
raw materials
component parts
work-in-process (WIP)
finished goods
• Service Inventory
– involves all activities carried out in
advance of the customer’s arrival
Copyright 2011 John Wiley & Sons, Inc.
9-3
Inventory Policy
Inventory policy addresses two questions
concerning replenishment of inventory:
• When to order?
• How much to Order?
Copyright 2011 John Wiley & Sons, Inc.
9-4
Reasons for Carrying Inventory
• Protect Against Lead Time Demand
• Maintain Independence of Operations
• Balance Supply and Demand
• Buffer Uncertainty
• Economic Purchase Orders
Copyright 2011 John Wiley & Sons, Inc.
9-5
Types of Inventory
• Cycle Stock
– inventory for immediate use
– typically produced in batches (production cycle)
• Safety Stock
– extra inventory carried for uncertainties in
supply and demand
– also called buffer stock
• Anticipation Inventory
– inventory carried in anticipation of events
– smooth out the flow of products in supply chain
– also called seasonal or hedge inventory
Copyright 2011 John Wiley & Sons, Inc.
9-6
Types of Inventory Continued
• Pipeline Inventory
– inventory in transit
– exists because points of supply and
demand are not the same
– also called transportation inventory
• Maintenance, Repair and Operating
Items (MRO)
– inventories not directly related to product
creation
Copyright 2011 John Wiley & Sons, Inc.
9-7
Inventory Costs
• Holding Cost
– costs that vary with the amount of inventory held
– typically described as a % of inventory value
– also called carrying cost
• Ordering Cost
– costs involved in placing an order
– sometimes called setup cost
– inversely related to holding cost
• Shortage Cost
– occur when we run out of stock
Copyright 2011 John Wiley & Sons, Inc.
9-8
Inventory Systems
Inventory systems answer the questions:
when to order and how much to order
There are two categories:
• Fixed-Order Quantity System
– an order of fixed quantity, Q, is placed when
inventory drops to a reorder point, ROP
• Fixed-Time Period System
– inventory is checked in fixed time periods, T,
and the quantity ordered varies
Copyright 2011 John Wiley & Sons, Inc.
9-9
Fixed-Order Quantity System
– assumes a constant demand rate of d
– the inventory position, IP, is reduced by a rate
of d
– order placed when the reorder point, ROP is
reached
– when inventory is received, the IP is increased
by the order quantity, Q
Copyright 2011 John Wiley & Sons, Inc.
9-10
Fixed-Order Quantity System
Continued
– there is a lead time, L, during which we have
to wait for the order
– inventory is checked on a continual basis
– Q is computed as the economic order
quantity, EOQ
Copyright 2011 John Wiley & Sons, Inc.
9-11
Fixed-Order Quantity System
Copyright 2011 John Wiley & Sons, Inc.
9-12
Fixed-Time Period System
– inventory levels checked in fixed time periods, T
– a target inventory level, R, is restored when order
received
– sometimes called Periodic Review System
– quantity ordered varies:
Q = R – IP
where: Q = order quantity
R = target inventory level
IP = inventory position
Copyright 2011 John Wiley & Sons, Inc.
9-13
Fixed-Time Period System
Copyright 2011 John Wiley & Sons, Inc.
9-14
Compare Inventory Systems
Copyright 2011 John Wiley & Sons, Inc.
9-15
Fixed-Order Quantity System
There are two main variables to calculate in
the Fixed-Order Quantity System:
• Order Quantity (Q)
– EOQ is the most Economic Order
Quantity
• Reorder Point (ROP)
Assume:
– demand (d), lead time (L), holding cost (H),
stock-out cost (S), and unit price (C) are constant
Copyright 2011 John Wiley & Sons, Inc.
9-16
Economic Order Quantity (EOQ)
The EOQ minimizes the total annual inventory cost
Total Cost = Purchase + Ordering + Holding
cost
cost
cost
TC = DC + (D/Q)S + (Q/2)H
where: TC = Total cost
C = Unit cost
S = Ordering cost
Copyright 2011 John Wiley & Sons, Inc.
D = Annual demand
Q = Order quantity
H = Holding cost
9-17
EOQ Continued
TC = DC + (D/Q)S + (Q/2)H
• Notice: DC = Annual purchase cost
D/Q = # orders placed per year
Annual ordering cost = # orders/yr x cost/order
Q/2 = average inventory level
Annual holding cost = avg. inventory x cost/unit
Copyright 2011 John Wiley & Sons, Inc.
9-18
EOQ Continued
Copyright 2011 John Wiley & Sons, Inc.
9-19
Solving for EOQ
The EOQ can be found by taking the derivative
of TC with respect to Q and set = 0
• Total Cost Equation: TC = DC + (D/Q)S + (Q/2)H
•
1st
Derivative:
TC
 DS H
0 2  0
dQ
2
Q
• Solve for Q optimal: EOQ  2 D S
H
Copyright 2011 John Wiley & Sons, Inc.
9-20
EOQ Example
Given: Demand = 1000 items per month
Holding Cost = 15% of product cost
Ordering Cost = $300 per order
Product Cost = $60 per unit
• EOQ
2 DS

H
2(12,000)(300)
 894.5  895
(0.15)( 60)
• Orders per year D  12,000  13.4
Q
895
• Annual Holding Cost  Q  H   895  9  $4028
2
Copyright 2011 John Wiley & Sons, Inc.
 2 
9-21
Reorder Point (ROP)
The ROP provides enough inventory to
ensure that demand is covered during the
lead time (L)
ROP = Demand during Lead Time = dL
Given: Lead time = 1 week
d = 250 items/week
ROP = dL = (1) x (250) = 250 items
 order is placed when inventory level = 250 items
Copyright 2011 John Wiley & Sons, Inc.
9-22
Safety Stock
• Safety stock is inventory carried in addition to
the demand during lead time
• It is common to carry safety stock when demand
(d) or lead time (L) are not constant
ROP = demand during lead time + safety stock
ROP = dL + ZkσL
– value of Z for a particular service level (k)
– service level = probability of being in stock
– σL = standard deviation of demand over the lead time
Copyright 2011 John Wiley & Sons, Inc.
9-23
Safety Stock Example
Given: Desired service level = 95%
Demand = 1000 items per month
Lead time = 1 week
σL2 = 64
Determine the Reorder Point
ROP = dL + ZkσL
ROP = (250)(1 week )  1.645 64  263.16
Copyright 2011 John Wiley & Sons, Inc.
9-24
Economic Production Quantity (EPQ)
• Recall that EOQ assumes the entire order, Q,
arrives at once at the end of the lead time
• When produced items are delivered to the
operation during completion of the order, it is
called economic production quantity (EPQ)
– sometimes called the production rate model
– maximum inventory position (and therefore
average inventory) are less than with EOQ
– Q and ROP calculated differently
Copyright 2011 John Wiley & Sons, Inc.
9-25
EPQ
Copyright 2011 John Wiley & Sons, Inc.
9-26
Calculating EPQ
Annual Total Cost:
 Imax
D
TC  DC    S  
Q
 2
Imax

H

Q
 Q  d  
p
where: Imax = maximum inventory
p = daily production rate
d = average daily demand rate
Copyright 2011 John Wiley & Sons, Inc.
9-27
Calculating EPQ Continued
Substitute Imax into Annual Total Cost:

d
D
TC  DC    S   p   Q H
2p 
Q

Use calculus to solve for EPQ:
2D S
EPQ 
 d
H 1  
 p
Copyright 2011 John Wiley & Sons, Inc.
9-28
EPQ Example
A manufacturer uses 50,000 wheels per year.
The manufacturer produces its own wheels at
a rate of 600 per day. Carrying cost per
wheel is $1/year and setup cost for a
production run is $45. The plant operates
250 days per year.
What is EPQ and Imax?
Copyright 2011 John Wiley & Sons, Inc.
9-29
EPQ Example Continued
2D S
EPQ 

 d
H 1  
 p
Imax
2(50,000)( 45)
 2,598
 200 
11 

 600 
Q
 2598 
 Q  d    2598  200
  1,732
 600 
p
Copyright 2011 John Wiley & Sons, Inc.
9-30
Fixed-Time Period Systems
An order is placed after a set time interval, T,
to bring inventory up to the target inventory
level
Q = R - IP
where: Q = order quantity
R = target inventory level
IP = inventory position at time T
Q
T can be set for a particular Q: T 
d
Copyright 2011 John Wiley & Sons, Inc.
9-31
Computing Target Inventory
Target inventory should cover:
– demand during lead time, L
– demand during review period, T
– safety stock
R = demand during L + demand during T + safety stock
R  dL  dT  Zk t
LT
t
where t = interval over which standard deviation is given
Copyright 2011 John Wiley & Sons, Inc.
9-32
Fixed-Time Period Example
Given: T = 14 days
d = 30 units per day
L = 7 days
σday = 10 units
no more than 2 stockouts/year
calculate k =
26  2
 0.9231
26
R  dL  dT  Zk t
LT
t
7  14
R  (30)(7)  (30)(14)  1.426(10)
 692
1
Copyright 2011 John Wiley & Sons, Inc.
9-33
Independent vs. Dependent Demand
Inventory policy is based on the type of demand
• Independent Demand
– demand for a finished product
• Dependent Demand
– demand for components parts or subassemblies
– order quantities computed with Material
Requirements Planning (MRP)
– relationship between independent and dependent
demand is shown in a bill of materials (BOM)
Copyright 2011 John Wiley & Sons, Inc.
9-34
Bill of Materials
Copyright 2011 John Wiley & Sons, Inc.
9-35
Managing Supply Chain Inventory
In addition to the quantitative models, there
are a number of practical implications to
consider:
• ABC Inventory Classification
• Practical Considerations of EOQ
• Measuring Inventory Performance
• Vendor Managed Inventory
Copyright 2011 John Wiley & Sons, Inc.
9-36
ABC Inventory Classification
ABC system classifies inventory based on its
degree of importance
Steps:
1. Determine annual usage or sales for each item
2. Determine % of total usage or sales for each item
3. Rank items from highest to lowest %
4. Classify items into groups:
A: highest value, B: moderate value, C: least valuable
Copyright 2011 John Wiley & Sons, Inc.
9-37
ABC Inventory Classification
Copyright 2011 John Wiley & Sons, Inc.
9-38
Practical Considerations of EOQ
• Lumpy Demand
– can use Periodic Order Quantity (POQ) when
demand is not uniform
• EOQ Adjustments
– total cost changes little on either side of the EOQ
 managers can adjust to accommodate needs
• Capacity Constraints
– storage capacity and costs should be considered
when ordering large quantities
Copyright 2011 John Wiley & Sons, Inc.
9-39
Measuring Inventory Performance
Common metrics for inventory:
• Units
– # units available
• Dollars
– dollars tied up in inventory
• Weeks of Supply
– (avg. on-hand inventory) / (avg. weekly usage)
• Inventory Turns
– (cost of good sold) / (avg. inventory value)
Copyright 2011 John Wiley & Sons, Inc.
9-40
Average Inventory Example
Given a fixed-order quantity model with:
Annual Demand (D) = 1,000 units
Order Quantity (Q) = 250 units
Safety Stock (SS) = 50 units
• Average Inventory = Q/2 + SS
= 250/2 + 50 = 175 units
• Inventory Turn = D/(Q/2 + SS)
= 1,000/175 = 5.71 turns per year
Copyright 2011 John Wiley & Sons, Inc.
9-41
Vendor Managed Inventory (VMI)
VMI arrangements have the vendor
responsible for managing the inventory
located at a customer’s facility
The vendor:
– stocks inventory
– places replenishment orders
– arranges the display
– typically owns inventory until purchased
– is required to work closely with customer
Copyright 2011 John Wiley & Sons, Inc.
9-42
Review
1. Reasons to carry inventory include protecting
against lead time demand, maintaining
independence, buffering against uncertainty.
2. Inventory types include: cycle stock, safety
stock, anticipation, pipeline, and MRO.
3. 3 inventory costs: holding, ordering, & shortage.
4. a. Inventory systems answer: when to order
and how much to order.
Copyright 2011 John Wiley & Sons, Inc.
9-43
Review Continued
4. b. Two most common systems are: fixed-order
quantity and fixed-time period.
5. Fixed-order quantity systems have a reorder
point (ROP). The basic system utilizes the
economic order quantity (EOQ), and when
production feeds demand, it utilizes the
economic production quantity (EPQ).
6. In fixed-time period systems the time between
orders, T, is constant, and the order quantity
varies. Orders bring the IP to a target level, R.
Copyright 2011 John Wiley & Sons, Inc.
9-44
Review Continued
7. Independent demand is for a finished product
and dependent demand is for components.
8. ABC classification defines the degree of
importance for inventory.
9. The most common ways to measure
inventory are in units, dollars, weeks of
supply, and inventory returns.
10.Vendor managed inventory (VMI) is where the
vendor is responsible for the inventory
located at a customer’s facility.
Copyright 2011 John Wiley & Sons, Inc.
9-45
Copyright 2011 John Wiley & Sons, Inc.
All rights reserved. Reproduction or translation of
this work beyond that permitted in section 117 of the
1976 United States Copyright Act without express
permission of the copyright owner is unlawful.
Request for further information should be addressed
to the Permission Department, John Wiley & Sons,
Inc. The purchaser may make back-up copies for
his/her own use only and not for distribution or
resale. The Publisher assumes no responsibility for
errors, omissions, or damages caused by the use of
these programs or from the use of the information
herein.
9-46