OPM 3000 Handout
Service Operations
Management: OPM 3000
Chapter 12: Inventory
Management with Steady
Demand
Ken Globerman
CUNY Baruch College
Narendra Paul Loomba Department of Management
Email: kenneth.globerman@baruch.cuny.edu
For Academic Use Only
Chapter 12:
Inventory Management with
Steady Demand
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OPM 3000 Handout
Learning Objectives
o
o
o
LO12-1. Evaluate optimal order quantities and performance
measures with the EOQ model.
LO12-2. Recognize the presence of economies of scale in
inventory management and understand the impact of
product variety on inventory costs.
LO12-3. Evaluate optimal order quantities when there are
quantity constraints or quantity discounts are offered.
12-2
Companies Need To Decide
How Much Product To Order,
At Any Given Time
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OPM 3000 Handout
The Economy Order Quantity
Introducing the EOQ Model
Economic order quantity (EOQ) model – a
model used to select an order quantity that
minimizes the sum of ordering and inventory
holding costs per unit of time
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The Economy Order Quantity
This model is built on the following assumptions:
o
Demand occurs at a constant rate R
o
There is a fixed order cost K per order
– This is independent of how much is ordered
o
There is a holding cost per unit of time h
– This includes all costs associated with keeping a unit of
inventory in stock for a period of time
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OPM 3000 Handout
The Economy Order Quantity
This model is built on the following assumptions:
o
All demand is satisfied from inventory
o
Inventory never spoils, degrades, or is lost
– Assumption that everything is eventually sold
o
Orders are delivered with a reliable lead time
o
There is a purchase price per unit that is
independent of the quantity purchased
– In other words, there is no quantity discount
not
always
true in
real life
discounts for
example happen
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in real life
The Economy Order Quantity
The textbook illustrates the EOQ model by going
through the exercise of Walmart purchasing of Tylenol
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OPM 3000 Handout
The Economy Order Quantity
The goal of EOQ is to minimize the sum of all
inventory costs in a period of time
o
Ordering cost per unit of time – is the sum of all
fixed ordering costs in a period of time
– If Walmart places 12 orders per year, then its ordering
costs is $72 (12 orders per year x $6 per order)
o
Holding cost per unit of time – the total cost to
hold inventory for a period of time
– If Walmart holds 100 bottles on average in inventory
throughout the year, its holding costs for the year is
$75
12-6
The Economy Order Quantity
o
EOQ cost per unit of time – the sum of ordering
and holding costs per unit of time
o
Purchasing cost – the cost to purchase inventory
in a period of time
– For Tylenol, $1872 per year ($3 per bottle [Walmart’s
purchase price] x 624 bottles per year)
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OPM 3000 Handout
Inventory Patterns & Tradeoffs
higher
holding costs
higher
holding cost
12-10
Deriving The EOQ Cost Function
We can now evaluate the average inventory for a
given period of time:
Once we know the average inventory, we can
calculate the holding cost per unit time:
Q is order quantity
Now let’s look at ordering costs…
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OPM 3000 Handout
Deriving The EOQ Cost Function
If Walmart sells R bottles per year and orders Q
bottles with each order it must make R/Q orders
per year (on average)
R is demand rate
Therefore, Walmart incurs the following ordering cost
per unit time (eg: per year)
ordering cost
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Deriving The EOQ Cost Function
Total inventory costs are the sum of ordering plus
holding costs
We have the following equation:
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OPM 3000 Handout
Graphing The EOQ Model
As our order quantity size goes up, we order less
times through the year and annual order costs go
down
But inversely, we have more inventory on hand, so
our annual holding costs go up!
12-10
Graphing The EOQ Model
EOQ Model Objective: Minimize Total Inventory Costs
12-10
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OPM 3000 Handout
The EOQ Model
In Class Exercise
Q = 12 and average inventory is
12-10
EOQ Optimal Order Quantity
The Optimal Order Quantity Q* minimizes total
inventory costs
o We can use calculus to minimize the function,
or simply refer to this formula solving for Q*,
the “Economic Order Quantity”:
Q* =
o
2× K × R
h
where K = the ordering cost, R = the demand and
h = the holding cost
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OPM 3000 Handout
EOQ Optimal Order Quantity
In Class Exercise
EOQ Cost
Once we calculate Q*, we can use this quantity to
determine the minimum EOQ inventory cost
In the previous Tylenol example, with Q* = 100
bottles, EOQ cost is:
As a % of cost per unit of time, the Tylenol ordering +
holding cost is $74.94/$1,872 = 4% of the purchasing
cost.
Is this a lot? For a low margin business, it sure is!
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OPM 3000 Handout
EOQ Cost
In Class Exercise
Intermission
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OPM 3000 Handout
Economies of Scale
When a process has certain fixed costs (such as
setup costs), we can get more “bang for the buck” by
producing in larger lots
Economies of scale – describes a relationship
between operational efficiency and demand in which
greater demand leads to a more efficient process
o
Our EOQ Tylenol model had fixed ordering costs
– Ordering costs were the same for 1 or 1,000 bottles
12-11
– But demand surely plays a role in our decision making
Economies of Scale
Application of the EOQ model on Tylenol with different
demand rates
Our original scenario
Insight 1: As order size increases, overall EOQ cost go up but EOQ
12-11
cost as a % of purchase cost goes down
Insight 2: As demand doubles, annual EOQ cost C(Q*) increases
at a much slower rate (41%)
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OPM 3000 Handout
The Impact Of Product Variety
How much product variety should your business
offer?
o
Offer too little – and you may not satisfy the variety
of customers’ tastes
o
But offer too much – and your demand for each
variety is effected, potentially reducing efficiency
and economies of scale
Product substitution – this occurs when people
may be willing to purchase a less-preferred version if
their most preferred version is not available
12-11
Back To The EOQ Model
Adding A Bit More Complexity
The Tylenol example was a bit simplistic in nature
o
Rarely can we order exactly the optimal lot size
(recall Q* was 100 bottles per order)
– Shipping companies often impose practical restrictions or
limitations on order size
o
And in the real world, we’re often incentivized by
price discounts for ordering in larger batches
– Recall the EOQ model ignored product purchasing costs12-11
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OPM 3000 Handout
Volume Discounting
More Definitions
o
Pallet – either a platform which is used to
stack inventory or the quantity of inventory
that is stacked on the platform
o
Tier – the quantity of product in one layer of
a pallet
o
Distribution center (DC) – a facility
designed to receive product from suppliers,
store inventory, and ship products to retail
stores (we’ve seen this one)
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Quantity Constraints
o
o
o
What would happen if Walmart could only order
Tylenol by the whole case (72 bottles in a case)
If the ideal order quantity is 100 bottles, what would
we do?
We would analyze the closest possible ordering
sizes: 72 bottles or 144 bottles
12-17
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OPM 3000 Handout
Quantity Constraints
In Class Exercise
12-17
Quantity Discounts
o
A quantity discount can be used as a
motivator to order larger quantities
Volume discount
o
Larger quantities increases the sum of
ordering and holding costs (above the
minimum)…
…BUT may make the overall cost (including
purchasing costs) more economical!
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OPM 3000 Handout
Quantity Discounts
o
Let’s go back to our Tylenol example and make the
following assumptions:
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EOQ Steps With
Quantity Discounts
o
Step 1: Evaluate the EOQ given the regular price
(account for any order size restrictions) and call this
Q*
Q* =
o
2× K × R
h
Note we have a tier restriction, which is 1,440
bottles. So technically we must order in multiples of
1,440. 1,317 if very close to one tier, so we’ll go
with 1,440 as our order quantity.
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OPM 3000 Handout
EOQ Steps With
Quantity Discounts
o
o
o
o
Step 2: If the EOQ is above the threshold for the
volume discounted price, Qd, re-calculate EOQ
given the discounted price
Call this quantity Q** and order at this level
In our example, this discount only applies when we
order at least one pallet
Since we are ordering less (one tier of a pallet),
step 2 does not apply
EOQ Steps With
Quantity Discounts
o
Step 3: If the EOQ is below the threshold for the volume
discounted price, Qd, then:
o
Step 3a: the sum of ordering + holding costs using EOQ
quantity and regular pricing is:
o
Add the purchasing costs of $195,000 (65,000 x $3/bottle)
and the total is $195,793. Call this C*.
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OPM 3000 Handout
EOQ Steps With
Quantity Discounts
o
Step 3: If the EOQ is below the threshold for the volume
discounted price, Qd, then:
o
Step 3b: The sum of ordering + holding costs using the min
quantity to get the discount and the discounted pricing is:
o
Add the purchasing costs of $187,200 (65,000 x $2.88/
bottle) and the total is $190,155 and call this Cd
EOQ Steps With
Quantity Discounts
o
Step 3: If the EOQ is below the threshold for the volume
discounted price, Qd, then:
o
Step 3c: We compare the two results: $190,155 < $195,783
and go with the minimum order quantity to receive the
volume discount
o
Why? The ordering + inventory costs may be higher, but the
savings from the volume discount outweigh it!
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OPM 3000 Handout
Summary EOQ Analysis With
Quantity Discounts
Graphical Illustration of the EOQ
Model With Quantity Discounts
o
The following graphic illustrates cost curves for a two tier
discounting situation. Note the two feasible order quantities.
Note: these
cost values
do not
correspond to
the previous
exercise
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OPM 3000 Handout
Quantity Discounts
In Class Exercise
12-17
The Effect Of Purchase Discounts
Takeaways
o
Bottom line: Volume discounts reduce overall
purchasing costs
o
Larger purchase quantities may be optimal even if
the discount appears to be small
o
Firms are more price sensitive than consumers
(even a 1% price discount can make a big
difference!)
12-18
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OPM 3000 Handout
Homework
1.
Do the ‘Chapter 12 Assessment’ (Quiz) on Connect
(required) by Sunday
2.
Do the Chapter 12 Problem Set to get more practice
3.
Read and complete the next chapter, ‘Chapter 15 Smart
Book’, on Connect (required) by Tuesday
4.
Check exact deadline times on Connect!
Service Operations
Management: OPM 3000
See You Next Week!
Ken Globerman
CUNY Baruch College
Narendra Paul Loomba Department of Management
Email: kenneth.globerman@baruch.cuny.edu
For Academic Use Only
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