Inventory-Management Group 7.pptx

Inventory Management
Learning Block 1
Introduction to Inventory Management

Course Agenda
1. Introduction to Inventory Management
2. Monitoring and Analyzing Inventory
3. Inventory Control
4. Inventory Management and Forecasting
5. Managing Inventory in the Supply Chain
6. Inventory Performance Measurement and Financial Implications
2

Learning Block Agenda
• Understand the role and importance of inventory
• Discuss the main reasons for carrying inventory
• Describe the main approaches to managing inventory
• Outline how inventory items can be classified
• Explain the key roles and responsibilities for managing inventory at distribution
centers (DCs)

Description
• A function in the overall supply chain process of an organization
• Inventory is often obtained by suppliers in the form of raw materials and other goods
and materials through the procurement department
• Inventory also includes work in the process and finished products from
manufacturing operations

Key Elements
The importance and
use of inventory in
the supply chain.
Exposure to the
different types of
inventory.
Techniques for
effectively managing
and controlling
inventory levels.
The relationship
between forecasting
and inventory
management.
Financial impacts of
inventory
assessment.

Introductory Management
• Companies are increasingly looking to provide improved customer
service levels at reduced costs; the amount, type, and cost of
inventory within a company has direct impacts on both service
levels and the profitability associated with those service levels.

Unit 1: Inventory Basics
Inventory Includes:
• Raw Materials
• Work in Progress (WIP)
• Finished goods
• Merchandise
• Spare parts
• Other operating
supplies
Inventories may be
found in:
• Factories
• Warehouses
• Retail Stores
• Other type of storage
facilities

Balancing Supply and
Demand
Greatest Challenges for
managing inventories
• Ideally, an organization
would have sufficient
inventory to satisfy
customer demands for
products without losing
any revenue due to
insufficient stock.
• An organization does not
want to have too much
inventory on hand,
because it costs too much
money to both acquire
and hold inventory.

• Inventory management involves striking a balance between three classes of costs:
• Acquisition costs are incurred during purchase order (PO) preparation and processing and
during receiving and inspecting purchase items
• Carrying costs are incurred in maintaining a stock of goods in storage
• Stockout costs (also called shortage costs) are incurred when an item is out of stock

LearningBlock 1: Introductory Management
Insufficient Inventory
A complete lack
or limited amount
of components
and raw materials
to assemble
products
Equipment
downtime due to
the lack of spare
parts
Loss of Sales

• Acquisition Costs
• Include the purchase price paid and associated administrative costs.
• Costs associated with placing the PO for those materials or services, including the labor
cost to create, review, and transmit the order.
• The labor costs to receive and pay for ordered items.

• Carrying Costs
• There are costs associated with carrying items, such as building like warehouses, utilities,
systems to track inventory, and labor to manage those inventory tracking systems.
• Purchasing large quantities of product may require a form to utilize funds from loans or
the issuance of stock.
• The cost of using borrowed funds

• Stockout Costs
Backorder Costs
• These are incurred when a firm must
place an order with its suppliers for a
rush shipment to meet customers or
internal manufacturing needs; rush
shipments typically incur higher
handling and transportation costs
Lost Costumers
• if costumers are not willing to
wait for a backorder, they may
decide to take their business
elsewhere, leading to reduce
revenue for the firm.

The Necessity of Inventory
• Firms hold inventory to meet the needs of their customers
• Customers may be external to the firm of employees of other departments within
the firm who requires a certain product, material, or part.

The Necessity of Inventory
• Firms hold inventories as means of dealing with uncertainty in the supply chain.
• This uncertainty comes from chronic
• supplier manufacturing delays
• late deliveries
• poor quality
• damaged and incorrect deliveries
• other issues that arise in the supply chain

AppropriateReasonstoCarryInventory
• A manufacturing company requires
inventory of raw materials and
components to create finished products
and meet its production and other
schedules.
• Retailers could not operate without
inventories of finished goods; without
inventory, customers would be looking at
empty shelves.
• Personnel throughout the supply chain
need to manage inventory on a daily basis
• Ex. Retail store managers must know the
exact number of items they carry on
display and in storage to fill costumer
orders, place orders when inventory is
low, and control theft and losses due to
error.

ProblematicReasonsforCarryingInventory
• Ordering inventory is often used
to compensate for supply chain
problems, which leads to excess
inventory.
• Instead of addressing the root
causes of problems, companies
mask them with high inventories

ProblematicReasonsforCarryingInventory
• Examples of supply chain problems include
 Poor demand planning, poor forecasting, and high forecasting error
 Product theft
 Poor supplier performance (inaccurate lead time, late delivery, poor quality,
etc.)
 Poor production yields that require greater inputs for the desired output
 Poor or non-existent inventory planning and tracking systems
 Poor inventory counting systems that reduce stock accuracy
 Large-quantity purchases to obtain lower unit prices that are outweighed
by higher carrying costs
 Inattention to obsolete inventory disposition; obsolete stock no longer has
value

Inventory Carrying Locations
• Inventories of raw materials, components,
semi-finished products, maintenance
items, and repair items are often held at
supplier facilities or at the buying
company’s warehouse and other facilities.
• Inventories of finished or
intermediate (semi-finished or
processed) goods may be found at
locations such as manufacturing
facilities, warehouses, DC’s
(distribution centers), retail
locations or point-of-sale (POS)
locations.

Unit 3: Functional Types of Inventory

Functional Types of Inventory
• Different types of inventory have unique functions or purposes and may be managed
differently depending on where the inventory is held and its role in the supply chain.
• Cycle Stock
• In-process stock
• Safety tock
• Maintenance, Repair, and
Operations (MRO) Inventory
• Seasonal stock
• Promotional stock
• Speculative stock (hedge
stock)

• Cycle stock: inventory that is depleted through normal use or sale; firms hold cycle
stock in DC’s and retail stores in anticipation of customer orders or to respond to
normal consumption demands.
• In-process stock: good being manufactured or in between manufacturing processes
(also known as WIP or semi-finished goods)
• Safety stock (buffer stock): Held to protect against uncertainties in the supply chain.
These uncertainties include chronic supplier manufacturing delays, changes in
demand rate (the rate of demand for stock that can vary over time), and variances in
lead-time length.

• Seasonal stock: Stock held in advance of the season when the firm
expects to sell it. Industries that typically require significant
seasonal stock include apparel, sporting goods, and specialty
holiday.
• Promotional stock: Stock held to respond quickly to marketing
promotions or price incentives a firm plans to offer its customers,
including holiday promotions.

• Speculative stock (hedge stock): most commonly associated with companies
involved in manufacturing or assembly. This type of inventory is held to protect
against expected and possible price increases or constrained availability.

• Maintenance, Repair, and Operations
(MRO) Inventory: Parts and materials
that exist primarily to ensure a plant
or manufacturing facility and its
equipment are safe, reliable, and
optimally available for production
purposes. Service parts help ensure
that key pieces of equipment continue
to function effectively.

Managing Inventory
• According to Scott (2015), inventory
management is a means of controlling
and managing the flow of products into,
within, and out of an organization.
• Effective inventory management means
using a variety of different inventory
management tools and techniques
(which is covered in Learning Block 2).
• The central goal of inventory
management is to optimize levels of
inventory so there is the right amount of
inventory in place to meet customer
needs, while ensuring the company is
not overinvesting in inventory.

Managing Inventory
• Although the key principles of
inventory management are the
same across all industries, the
areas that need to be
emphasized vary from sector to
sector.
• Key areas of responsibility for
inventory management:
• Demand Planning
• Deciding How Much Inventory
to Hold
• Counting Inventory
• Tracking and Controlling
Inventory

Managing Inventory
• Demand Planning: A key element of
inventory planning is to estimate the
amount of inventory required over a
set time period to meet customer
needs.
• Various forecasting, planning tools,
and techniques are used for demand
planning and are covered in Learning
Block 4.
• Accurate demand planning prevents
both oversupply and undersupply of
inventory.

Managing Inventory
• Deciding How Much Inventory to Hold:
Rightsizing the inventory is dependent on
the specific industry. Retailers may want a
one- or two-month supply on hand, while
food businesses will want to have much
less inventory because of their products’
limited shelf life, especially fresh foods, to
minimize loss and spoilage.
• Companies carrying maintenance spares
may carry inventory for months or even
years until demand arises. Several tools,
techniques, and strategies exist for
determining how much inventory to hold,
which is outlined in Learning Block 2.

Managing Inventory
• Counting Inventory: For inventory
control purposes, it is necessary to
compare the on-hand levels with
inventory records by performing a
physical count of all items.
• Inventory counts are usually done
either by counting the entire
inventory at one time, known as a
physical inventory, or by counting
items at varying times on a
prescheduled basis, which is called
cycle counting (counting inventory is
covered in Learning Block 3).

Managing Inventory
• Tracking and Controlling Inventory:
Once a company has acquired inventory,
suitable tracking and control methods
must be implemented.
• Accurate tracking of inventory is
essential to ensuring where inventory is
in the supply chain, how much inventory
is moving in and out of the company, and
how much inventory is being held at any
one point in time.
• Inventory control involves counting and
monitoring inventory items, recording
the stocking and retrieval of items,
identifying and verifying storage
locations, recording changes to
inventory, and anticipating inventory
needs (inventory control is covered in
Learning Block 3).

Managing Inventory
1. How inventory items can be classified
(ABC analysis)
2. How accurate inventory records can
be maintained

ABC Analysis
▶ Divides inventory into three classes based on annual dollar
volume
▶ Class A - high annual dollar volume
▶ Class B - medium annual dollar volume
▶ Class C - low annual dollar volume
▶ Used to establish policies that focus on the few critical parts and
not the many trivial ones

ABC Analysis
ABC Calculation
(1) (2) (3) (4) (5) (6) (7)
ITEM
STOCK
NUMBER
PERCENT
OF
NUMBER
OF ITEMS
STOCKED
ANNUAL
VOLUME
(UNITS) x
UNIT
COST =
ANNUAL
DOLLAR
VOLUME
PERCENT
OF ANNUAL
DOLLAR
VOLUME CLASS
#10286 20% 1,000 $ 90.00 $ 90,000 38.8% A
#11526 500 154.00 77,000 33.2% A
#12760 1,550 17.00 26,350 11.3% B
#10867 30% 350 42.86 15,001 6.4% B
#10500 1,000 12.50 12,500 5.4% B
#12572 600 $ 14.17 $ 8,502 3.7% C
#14075 2,000 .60 1,200 .5% C
#01036 50% 100 8.50 850 .4% C
#01307 1,200 .42 504 .2% C
#10572 250 .60 150 .1% C
8,550 $232,057 100.0%
72%
23%
5%

ABC Analysis
A Items
B Items
| | | | | | | | | |
10 20 30 40 50 60 70 80 90 100
Percentage
of
annual
dollar
usage
80 –
70 –
60 –
50 –
40 –
30 –
20 –
10 –
0 –
Percentage of inventory items
Figure 12.2
C Items

ABC Analysis
▶ Other criteria than annual dollar volume may be used
▶ High shortage or holding cost
▶ Anticipated engineering changes
▶ Delivery problems
▶ Quality problems

ABC Analysis
▶ Policies employed may include
1. More emphasis on supplier development for A items
2. Tighter physical inventory control for A items
3. More care in forecasting A items

Record Accuracy
► Accurate records are a critical
ingredient in production and
inventory systems
► Periodic systems require regular
checks of inventory
► Two-bin system
► Perpetual inventory tracks receipts
and subtractions on a continuing basis
► May be semi-automated

Record Accuracy
► Incoming and outgoing
record keeping must be
accurate
► Stockrooms should be secure
► Necessary to make precise decisions
about ordering, scheduling, and
shipping

Cycle Counting
• Items are counted and records updated on a periodic basis
• Often used with ABC analysis
• Has several advantages
1. Eliminates shutdowns and interruptions
2. Eliminates annual inventory adjustment
3. Trained personnel audit inventory accuracy
4. Allows causes of errors to be identified and corrected
5. Maintains accurate inventory records

Cycle Counting Example
5,000 items in inventory, 500 A items, 1,750 B items, 2,750 C
items
Policy is to count A items every month (20 working days), B items
every quarter (60 days), and C items every six months (120 days)
ITEM
CLASS QUANTITY
CYCLE
COUNTING
POLICY
NUMBER OF ITEMS
COUNTED PER DAY
A 500 Each month 500/20 = 25/day
B 1,750 Each quarter 1,750/60 = 29/day
C 2,750 Every 6 months 2,750/120 = 23/day
77/day

Control of Service Inventories
• Can be a critical component
of profitability
• Losses may come from
shrinkage or pilferage
• Applicable techniques include
1. Good personnel selection, training, and discipline
2. Tight control of incoming shipments
3. Effective control of all goods leaving facility

Inventory Models
▶ Independent demand - the demand for item is independent of
the demand for any other item in inventory
▶ Dependent demand - the demand for item is dependent upon
the demand for some other item in the inventory

Inventory Models
▶ Holding costs - the costs of holding or “carrying” inventory over
time
▶ Ordering costs - the costs of placing an order and receiving
goods
▶ Setup costs - cost to prepare a machine or process for
manufacturing an order
▶ May be highly correlated with setup time

Holding Costs
TABLE 12.1 Determining Inventory Holding Costs
CATEGORY
COST (AND RANGE) AS A
PERCENT OF INVENTORY
VALUE
Housing costs (building rent or depreciation,
operating costs, taxes, insurance)
6% (3 - 10%)
Material handling costs (equipment lease or
depreciation, power, operating cost)
3% (1 - 3.5%)
Labor cost (receiving, warehousing, security) 3% (3 - 5%)
Investment costs (borrowing costs, taxes, and
insurance on inventory)
11% (6 - 24%)
Pilferage, space, and obsolescence (much higher in
industries undergoing rapid change like PCs and cell
phones)
3% (2 - 5%)
Overall carrying cost 26%

Inventory Models for Independent
Demand
Need to determine when and how much to
order
1. Basic economic order quantity
(EOQ) model
2. Production order quantity model
3. Quantity discount model

Basic EOQ Model
1. Demand is known, constant, and independent
2. Lead time is known and constant
3. Receipt of inventory is instantaneous and
complete
4. Quantity discounts are not possible
5. Only variable costs are setup (or ordering)
and holding
6. Stockouts can be completely avoided
Important assumptions

Inventory Usage Over Time
Figure 12.3
Order
quantity = Q
(maximum
inventory
level)
Usage rate
Average
inventory
on hand
Q
2
Minimum
inventory
Inventory
level
Time
0
Total order received

Minimizing Costs
Objective is to minimize total costs
Table 12.4(c)
Annual
cost
Order quantity
Total cost of
holding and
setup (order)
Holding cost
Setup (order) cost
Minimum
total cost
Optimal order
quantity (Q*)

Minimizing Costs
▶ By minimizing the sum of setup (or ordering) and holding costs,
total costs are minimized
▶ Optimal order size Q* will minimize total cost
▶ A reduction in either cost reduces the total cost
▶ Optimal order quantity occurs when holding cost and setup cost
are equal

Minimizing Costs
Q = Number of pieces per order
Q* = Optimal number of pieces per order (EOQ)
D = Annual demand in units for the inventory item
S = Setup or ordering cost for each order
H = Holding or carrying cost per unit per year
Annual setup cost = (Number of orders placed per year)
x (Setup or order cost per order)
Annual demand
Number of units in each order
Setup or order
cost per order
=
=
D
Q
æ
è
ç
ö
ø
÷S
Annual setup cost =
D
Q
S

Minimizing Costs
Annual holding cost = (Average inventory level)
x (Holding cost per unit per year)
Order quantity
2
(Holding cost per unit per year)
=
=
Q
2
æ
è
ç
ö
ø
÷H
Annual setup cost =
D
Q
S
Annual holding cost =
Q
2
H

Minimizing Costs
D
Q
S =
Q
2
æ
è
ç
ö
ø
÷H
Optimal order quantity is found when annual setup
cost equals annual holding cost
Solving for Q* 2DS = Q2
H
Q2
=
2DS
H
Q*
=
2DS
H
Annual setup cost =
D
Q
S
Annual holding cost =
Q
2
H

An EOQ Example
Determine optimal number of needles to order
D = 1,000 units
S = $10 per order
H = $.50 per unit per year
Q*
=
2DS
H
Q*
=
2(1,000)(10)
0.50
= 40,000 = 200 units

An EOQ Example
Determine expected number of orders
D = 1,000 units Q* = 200 units
S = $10 per order
N = = 5 orders per year
1,000
200
= N = =
Expected
number of
orders
Demand
Order quantity
D
Q*

An EOQ Example
Determine optimal time between orders
S = $10 per order N = 5 orders/year
T = = 50 days between orders
250
5
= T =
Expected
time between
orders
Number of working days per year
Expected number of orders

An EOQ Example
Determine the total annual cost
H = $.50 per unit per year T = 50 days
Total annual cost = Setup cost + Holding cost
TC =
D
Q
S +
Q
2
H
=
1,000
200
($10)+
200
2
($.50)
= (5)($10)+(100)($.50)
= $50+$50 = $100

The EOQ Model
When including actual cost of material P
Total annual cost = Setup cost + Holding cost + Product cost
TC =
D
Q
S +
Q
2
H + PD

Robust Model
▶ The EOQ model is robust
▶ It works even if all parameters and assumptions are not
met
▶ The total cost curve is relatively flat in the area of the
EOQ

An EOQ Example
Determine optimal number of needles to order
H = $.50 per unit per year T = 50 days
TC =
D
Q
S +
Q
2
H
=
1,500
200
($10)+
200
2
($.50)
= $75+$50 = $125
1,500 units
=
1,500
244.9
($10)+
244.9
2
($.50)
= 6.125($10)+122.45($.50)
= $61.25+$61.22 = $122.47
Only 2% less than
the total cost of
$125 when the
order quantity was
200

Reorder Points
• EOQ answers the “how much” question
• The reorder point (ROP) tells “when” to order
• Lead time (L) is the time between placing and
receiving an order
ROP =
Lead time for a new
order in days
Demand
per day
= d x L
d =
D
Number of working days in a year

Reorder Point Curve
Q*
ROP
(units)
Inventory
level
(units)
Time (days)
Figure 12.5
Lead time = L
Slope = units/day = d
Resupply takes place as order arrives

Reorder Point Example
Demand = 8,000 iPods per year
250 working day year
Lead time for orders is 3 working days, may take 4
ROP = d x L
d =
D
Number of working days in a year
= 8,000/250 = 32 units
= 32 units per day x 3 days = 96 units
= 32 units per day x 4 days = 128 units

Production Order Quantity Model
1. Used when inventory builds up over a period of time
after an order is placed
2. Used when units are produced and sold
simultaneously
Inventory
level
Time
Demand part of cycle with
no production (only usage)
Part of inventory cycle during which
production (and usage) is taking place
t
Maximum
inventory
Figure 12.6

Q = Number of pieces per order p = Daily production rate
H = Holding cost per unit per year d = Daily demand/usage rate
t = Length of the production run in days
= (Average inventory level) x
Annual inventory
holding cost
Holding cost
per unit per year
= (Maximum inventory level)/2
Annual inventory
level
= –
Maximum
inventory level
Total produced during
the production run
Total used during
the production run
= pt – dt

= –
Maximum
inventory level
Total produced during
the production run
Total used during
the production run
= pt – dt
However, Q = total produced = pt ; thus t = Q/p
Maximum
inventory level = p – d = Q 1 –
Q
p
Q
p
d
p
Holding cost = (H) = 1 – H
d
p
Q
2
Maximum inventory level
2

Setup cost = (D / Q)S
Holding cost = 1
2
HQ 1- d p
( )
é
ë
ù
û
D
Q
S = 1
2
HQ 1- d p
( )
é
ë
ù
û
Q2
=
2DS
H 1- d p
( )
é
ë
ù
û
Qp
*
=
2DS
H 1- d p
( )
é
ë
ù
û

Production Order Quantity Example
D = 1,000 units p = 8 units per day
S = $10 d = 4 units per day
H = $0.50 per unit per year
Qp
*
=
2DS
H 1- d p
( )
é
ë
ù
û
Qp
*
=
2(1,000)(10)
0.50 1-(4 8)
é
ë
ù
û
=
20,000
0.50(1 2)
= 80,000
= 282.8 hubcaps, or 283 hubcaps

When annual data are used the equation becomes
Note:
d = 4 = =
D
Number of days the plant is in operation
1,000
250
Qp
*
=
2DS
H 1-
Annual demand rate
Annual production rate
æ
è
ç
ö
ø
÷

Quantity Discount Models
▶Reduced prices are often available when larger
quantities are purchased
▶Trade-off is between reduced product cost and
increased holding cost
TABLE 12.2 A Quantity Discount Schedule
DISCOUNT
NUMBER DISCOUNT QUANTITY DISCOUNT (%)
DISCOUNT
PRICE (P)
1 0 to 999 no discount $5.00
2 1,000 to 1,999 4 $4.80
3 2,000 and over 5 $4.75

Q*
=
2DS
IP
Total annual cost = Setup cost + Holding cost + Product cost
TC =
D
Q
S +
Q
2
H + PD
where Q = Quantity ordered P = Price per unit
D = Annual demand in units H = Holding cost per unit per year
S = Ordering or setup cost per order
Because unit price varies, holding cost (H) is
expressed as a percent (I) of unit price (P)

Steps in analyzing a quantity discount
1. For each discount, calculate Q*
2. If Q* for a discount doesn’t qualify, choose
the lowest possible quantity to get the
discount
3. Compute the total cost for each Q* or
adjusted value from Step 2
4. Select the Q* that gives the lowest total
cost

1,000 2,000
Total
cost
$
0
Order quantity
Q* for discount 2 is below the allowable range at point a and
must be adjusted upward to 1,000 units at point b
a
b
1st price
break
2nd price
break
Total cost
curve for
discount 1
Total cost curve for discount 2
Total cost curve for discount 3
Figure 12.7

Quantity Discount Example
Calculate Q* for every discount
Q1* = = 700 cars/order
2(5,000)(49)
(.2)(5.00)
2(5,000)(49)
(.2)(4.80)
2(5,000)(49)
(.2)(4.75)
Q*
=
2DS
IP

Calculate Q* for every discount
2(5,000)(49)
(.2)(5.00)
2(5,000)(49)
(.2)(4.80)
2(5,000)(49)
(.2)(4.75)
Q*
=
2DS
IP
1,000 — adjusted
2,000 — adjusted

TABLE 12.3 Total Cost Computations for Wohl’s Discount Store
DISCOUNT
NUMBER
UNIT
PRICE
ORDER
QUANTITY
ANNUAL
PRODUCT
COST
ANNUAL
ORDERING
COST
ANNUAL
HOLDING
COST TOTAL
1 $5.00 700 $25,000 $350 $350 $25,700
2 $4.80 1,000 $24,000 $245 $480 $24,725
3 $4.75 2,000 $23.750 $122.50 $950 $24,822.50
Choose the price and quantity that gives the
lowest total cost
Buy 1,000 units at $4.80 per unit

Probabilistic Models and
Safety Stock
▶Used when demand is not constant or certain
▶Use safety stock to achieve a desired service
level and avoid stockouts
ROP = d x L + ss
Annual stockout costs = the sum of the units short x the
probability x the stockout cost/unit
x the number of orders per year

Safety Stock Example
NUMBER OF UNITS PROBABILITY
30 .2
40 .2
ROP  50 .3
60 .2
70 .1
1.0
ROP = 50 units Stockout cost = $40 per frame
Orders per year = 6 Carrying cost = $5 per frame per year

Safety Stock Example
ROP = 50 units Stockout cost = $40 per frame
Orders per year = 6 Carrying cost = $5 per frame per year
SAFETY
STOCK
ADDITIONAL
HOLDING COST STOCKOUT COST
TOTAL
COST
20 (20)($5) = $100 $0 $100
10 (10)($5) = $ 50 (10)(.1)($40)(6) = $240 $290
0 $ 0 (10)(.2)($40)(6) + (20)(.1)($40)(6) = $960 $960
A safety stock of 20 frames gives the lowest total cost
ROP = 50 + 20 = 70 frames

Safety stock 16.5 units
ROP 
Place
order
Probabilistic Demand
Inventory
level
Time
0
Minimum demand during lead time
Maximum demand during lead time
Mean demand during lead time
Normal distribution probability of
demand during lead time
Expected demand during lead time (350 kits)
ROP = 350 + safety stock of 16.5 = 366.5
Receive
order
Lead
time
Figure 12.8

Use prescribed service levels to set safety
stock when the cost of stockouts cannot be
determined
ROP = demand during lead time + ZsdLT
where Z = Number of standard deviations
sdLT = Standard deviation of demand during lead
time

Safety
stock
Probability of
no stockout
95% of the time
Mean
demand
350
ROP = ? kits Quantity
Number of
standard deviations
0 z
Risk of a stockout
(5% of area of
normal curve)

Probabilistic Example
m = Average demand = 350 kits
sdLT = Standard deviation of
demand during lead time = 10 kits
Z = 5% stockout policy (service level = 95%)
Using Appendix I, for an area under the curve of
95%, the Z = 1.65
Safety stock = ZsdLT = 1.65(10) = 16.5 kits
Reorder point = Expected demand during lead time +
Safety stock
= 350 kits + 16.5 kits of safety stock
= 366.5 or 367 kits

Other Probabilistic Models
▶ When data on demand during lead time is not available, there
are other models available
1. When demand is variable and lead time is constant
2. When lead time is variable and demand is constant
3. When both demand and lead time are variable

Demand is variable and lead time is constant
ROP = (Average daily demand
x Lead time in days) + ZsdLT
where sdLT = sd Lead time
sd = standard deviation of demand per day

Average daily demand (normally distributed) = 15
Lead time in days (constant) = 2
Standard deviation of daily demand = 5
Service level = 90%
Z for 90% = 1.28
From Appendix I
ROP = (15 units x 2 days) + ZsdLT
= 30 + 1.28(5)( 2)
= 30 + 9.02 = 39.02 ≈ 39
Safety stock is about 9 computers

Lead time is variable, and demand is constant
ROP = (Daily demand x Average lead
time in days) + Z x (Daily
demand) x sLT
where sLT = Standard deviation of lead time in days

Daily demand (constant) = 10
Average lead time = 6 days
Standard deviation of lead time = sLT = 1
Service level = 98%, so Z (from Appendix I) = 2.055
ROP = (10 units x 6 days) + 2.055(10 units)(1)
= 60 + 20.55 = 80.55
Reorder point is about 81 cameras

Both demand and lead time are variable
ROP = (Average daily demand
x Average lead time) + ZsdLT
where sd = Standard deviation of demand per day
sLT = Standard deviation of lead time in days
sdLT = (Average lead time x sd
2)
+ (Average daily demand)2s2
LT

Average daily demand (normally distributed) = 150
Standard deviation = sd = 16
Average lead time 5 days (normally distributed)
Standard deviation = sLT = 1 day
Service level = 95%, so Z = 1.65 (from Appendix I)
ROP = (150 packs´5 days)+1.65sdLT
sdLT
= 5 days´162
( )+ 1502
´12
( ) = 5´256
( )+ 22,500´1
( )
= 1,280
( )+ 22,500
( ) = 23,780 @154
ROP = (150´5)+1.65(154) @ 750+254 =1,004 packs

Single-Period Model
▶Only one order is placed for a product
▶Units have little or no value at the end of the
sales period
Cs = Cost of shortage = Sales price/unit – Cost/unit
Co = Cost of overage = Cost/unit – Salvage value
Service level =
Cs
Cs + Co

Single-Period Example
Average demand = m = 120 papers/day
Standard deviation = s = 15 papers
Cs = cost of shortage = $1.25 – $.70 = $.55
Co = cost of overage = $.70 – $.30 = $.40
Service level =
Cs
Cs + Co
=
= = .579
.55
.55 + .40
.55
.95
Service
level
57.9%
Optimal stocking level
m = 120

Single-Period Example
From Appendix I, for the area .579, Z  .20
The optimal stocking level
= 120 copies + (.20)(s)
= 120 + (.20)(15) = 120 + 3 = 123 papers
The stockout risk = 1 – Service level
= 1 – .579 = .422 = 42.2%

Fixed-Period (P) Systems
▶ Orders placed at the end of a fixed period
▶ Inventory counted only at end of period
▶ Order brings inventory up to target level
▶ Only relevant costs are ordering and holding
▶ Lead times are known and constant
▶ Items are independent of one another

Fixed-Period (P) Systems
On-hand
inventory
Time
Q1
Q2
Target quantity (T)
P
Q3
Q4
P
P
Figure 12.9

Fixed-Period Systems
▶ Inventory is only counted at each review period
▶ May be scheduled at convenient times
▶ Appropriate in routine situations
▶ May result in stockouts between periods
▶ May require increased safety stock

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