Holding Cost - Management By The Numbers

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Inventory Management III:
Decision Making
This module discusses ordering costs, time between orders,
inventory holding costs, economic order quantity (EOQ),
quantity discounts, and production order quantity.
Authors: Stu James and Robert Robicheaux
© 2013 Stu James and Management by the Numbers, Inc.
This MBTN Module is designed to help managers answer
the question – how much of an inventoried item should be
ordered or manufactured? The following topics will be
covered:
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TOPICS COVERED
Topics Covered
Inventory Flow Over Time
Ordering Costs
Time Between Orders
Holding Costs
Economic Order Quantity (EOQ)
Total Annual Cost
Quantity Discounts
Production Order Quantity
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If demand for an item is constant over time, we can visualize inventory
flow as in the graph below. In this “perfect world”, the inventory level
would drop to zero just as the Order Quantity (Q) arrives to replenish
it; thus, inventory would never exceed value Q. The average inventory
level in the system would be represented by Q / 2. The distance from
P1 to P2 would be the Time Between Orders (P).
INVENTORY FLOW OVER TIME
Inventory Flow Over Time
Q
Inventory Level
Q/2
P1
P2
Time
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Given this idyllic world of constant flows, there are two basic types of
costs to consider to determine the appropriate order quantity.
Ordering Costs are the costs associated with placing an order or
starting a production process. In the situation of an item that was
ordered from a supplier these costs would include placing, delivering,
receiving and stocking the order, etc. Do not include costs that vary
directly with the quantity of the order.
Holding Costs are costs of maintaining inventory, such as capital
costs (interest on money tied up in inventory), storage space (rent and
utilities), inventory service costs (insurance on inventory, inventory
maint.), and inventory risk costs (obsolescence, spoilage, shrinkage).
Normally holding costs are described as a % of the value of inventory.
COSTS THAT IMPACT ORDER QUANTITY
Costs that Impact Order Quantity
Insight
You may realize that if you order smaller quantities more frequently,
annual ordering costs will be higher, but holding costs will be lower.
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Question 1: Janice is running low on inventory of brake pads at her
tank repair shop. Her materials manager is paid $50K / year including
all benefits, and it takes him about 2 hours to call the various potential
suppliers, place the order and stock it when it comes in. He currently
orders 100 pads/order. The suppliers charge a $50 flat rate for
delivery of the brake pads plus $1.00 / brake pad. What is the order
cost for a single order presuming a 40 hour week with 2 weeks of
vacation?
CALCULATING ORDERING COSTS
Calculating Ordering Costs
Answer:
Hourly Rate
= Annual Salary / Hours worked per year
= 50,000 / (40 * 50)
= 50,000 / (2000)
= $25 / hour
Cost of Order
= 2 hours * hourly rate + fixed delivery charge (only)
= 2 * $25 + $50 = $100
Note that the $1/brake pad is not included as it is a variable cost
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Definitions
Orders Per Year = Annual Demand (D) / Quantity Purchased (Q)
Time Between Orders (P) = 365 / Orders per Year (calendar days) or
Time Between Orders (P) = Business Days / Orders per Yr (bus. days)
TIME BETWEEN ORDERS
Time Between Orders
Question 2: If annual demand for tank brake pads is 1000 / year and
the quantity purchased is 100, how many orders are placed each year
and what is the time between orders in calendar days?
Answer:
Number of Orders per Year = 1,000 / 100 = 10 orders
Time Between Orders = 365 / 10 = 36.5 days
This intrigued Janice. She had never really thought about how often
she ordered the pads. Further, she now wondered what her
approximate cost was on an annual basis for placing all these orders.
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Definitions
Annual Ordering Costs = # Orders Per Year * Cost Per Order
-- or –
Annual Ordering Costs = (D / Q) * S
Where:
D = Annual Demand
Q = Quantity Ordered
S = Order or Set-up Cost
Question 3: What are Janice’s annual ordering costs if demand is
1000 units / year, they order 100 at a time and order costs are $100?
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CALCULATING ANNUAL ORDERING COSTS
Calculating Annual Ordering Costs
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Answer:
Annual Ordering Costs
= (D / Q) * S
= (1000 / 100) * 100
= (10) * 100 = $1000
That was more than Janice expected and started her wondering if it would
make sense to place fewer orders each year to lower the cost.
Insight
Janice was on to something. Annual ordering costs would go down if
she ordered less often, but she had a feeling that some other cost
would go up if she did that. That cost would be the “hidden” cost of
holding more inventory.
CALCULATING ANNUAL ORDERING COSTS
Calculating Annual Ordering Costs
As an example, Janice could order 1000 brake pads at the beginning
of the year and her order costs would only be $100 instead of $1000.
But where would she put all those brake pads?
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The holding costs of inventory increase with the size of the order
because the average inventory level (Q/2) is higher throughout the
year. Here is the formula for calculating holding costs:
Definition
Annual Holding Costs = K * C * (Q / 2)
Where :
K = Carrying or Holding Cost Rate (%)
C = Unit Cost
Q = Order Quantity
CALCULATING ANNUAL HOLDING COSTS
Calculating Annual Holding Costs
Question 4: Janice wonders what her annual holding costs are on the
brake pads based on historical quantities ordered and unit cost. The
brake pads cost $5 each (includes $1/pad delivery). She currently
orders 100 at a time because of a quantity discount, and she estimates
her holding costs at 25%. Calculate the annual holding costs.
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Answer:
Annual Holding Costs
= K * C * (Q / 2)
= 25% * $5 * (100 / 2) = $62.50 / year
Insight
Note that the annual ordering costs calculated previously is $1000 - far
more than the annual holding costs of $62.50. Perhaps Janice should
order less often (to lower the ordering costs) in exchange for a higher
average inventory level and higher holding costs.
CALCULATING ANNUAL HOLDING COSTS
Calculating Annual Holding Costs
The following slide shows some different combinations of holding costs
and ordering cost at different order quantities. What we’re really
aiming for is to lower the combined cost. Sometimes, however, there
are physical limitations (or cash limitations) on the amount that can be
ordered.
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Janice’s holding and ordering costs for various order quantities:
Quantity
(Q)
100
200
300
400
500
600
700
800
900
1000
Holding
Cost (HC)
$
62.50
$
125.00
$
187.50
$
250.00
$
312.50
$
375.00
$
437.50
$
500.00
$
562.50
$
625.00
Ordering
Cost (OC)
$ 1,000.00
$
500.00
$
333.33
$
250.00
$
200.00
$
166.67
$
142.86
$
125.00
$
111.11
$
100.00
Total Cost
$ 1,062.50
$ 625.00
$ 520.83
$ 500.00
$ 512.50
$ 541.67
$ 580.36
$ 625.00
$ 673.61
$ 725.00
Calculated costs for
various order quantities
where:
Demand (D) = 1000
Cost/Order (S) = $100
Carrying Cost (K) = 25%
Unit Cost (C) = $5
TOTAL ANNUAL HOLDING AND ORDERING COSTS
Total Annual Holding and Ordering Costs
Insight
Notice that the lowest total cost is at an order quantity of 400 units!
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Rather than create massive tables of various cost combination, we can
instead use the Economic Order Quantity (EOQ) formula where the
combined total of Annual Ordering Costs (OC) and Annual Holding
Costs (HC) is minimized. By definition, this is where OC = HC
Definition
2 * D * S or ((2 * D * S) / (K * C))^.5
K*C
D = Annual Demand (Historical or Forecasted)
S = Cost per Order (Set-up Cost)
K = Carrying or Holding Cost Rate (%)
C = Unit Cost
Economic Order Quantity =
Where :
ECONOMIC ORDER QUANTITY (EOQ)
Economic Order Quantity (EOQ)
Insight
Note that the EOQ model is based on certain assumptions. If reality
differs significantly from these assumptions, EOQ is less accurate.
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The classical EOQ model is helpful to guide managers who purchase
products needed in their companies or to plan production schedules.
Certain assumptions generally apply for EOQ to be used effectively.
• There should be a continuous and known rate of demand. This can
be derived from historical records analysis as well as sales and
marketing forecasts.
EOQ ASSUMPTIONS
EOQ Assumptions
• Lead times for delivery should be known. Constant is not really
necessary as long as changes or variations can be anticipated and
inventory managed to handle anticipated lead time variability.
• Price is independent of order quantity. We show here how quantity
discounts might affect purchase quantities.
• Transport costs are independent of quantity or timing of orders.
• All market demand can be satisfied. Safety stocks (extra inventory)
can be used to accommodate unusually high demand.
Now let’s see how EOQ would look graphically in Janice’s example…
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Graphical representation
of annual costs where:
Demand (D) = 1000
Cost/Order (S) = $100
Carrying Cost (K) = 25%
Unit Cost (C) = $5
ECONOMIC ORDER QUANTITY (EOQ)
Economic Order Quantity (EOQ)
Insight
By definition, the minimum total
cost (the EOQ) is where:
holding cost = ordering cost
Note that the graph corresponds
with the values from the table.
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Question 5: Janice is interested in using
EOQ to help her order the appropriate
amounts of brake pads. Recall that the
annual historical demand has been 1,000
units/year, cost per order is $100, and the
unit cost is $5. Her carrying cost rate is
25%. What is the EOQ for brake pads?
Calculated costs for
various order quantities
where:
Demand (D) = 1,000
Cost/Order (S) = $100
Carrying Cost (K) = 25%
Unit Cost (C) = $5
ECONOMIC ORDER QUANTITY (EOQ)
Economic Order Quantity (EOQ)
Answer:
EOQ
= ((2 * D * S) / (K * C))^.5
= ((2 * 1000 * 100) / (.25 * 5))^.5
= (20,000 / 1.25) ^.5
= 400 brake pads per order (same as the table!!)
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Definition
Total Annual Cost
= Holding Costs + Ordering Costs at EOQ (Q)
= K * C * (Q / 2) + (D / Q) * S
TOTAL ANNUAL COST
Total Annual Cost
Question 6: Janice now wants to know what her total annual costs
would be for brake pads if she orders the EOQ of 400.
Answer:
Total Annual Cost= (Q / 2) * K * C + (D / Q) * S
= (400/2)*25%*5 + (1000/400)*100
= $250 + $250
= $500
Demand (D) = 1000
Cost/Order (S) = $100
Carrying Cost (K) = 25%
Unit Cost (C) = $5
Note: At EOQ, the HC = OC, but remember that the actual order amount must
be rounded to the nearest whole number if the calculation results in a partial
unit (e.g., if EOQ is 399.5 round that to 400).
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The goal of an inventory management system is to minimize these
total costs while still providing excellent customer service. It is helpful
to review some directional concepts at this point.
Question 7: The President of the company
asks Janice how changes in the assumptions
impact the business. Take a moment to think
about how each variable in the EOQ formula
impacts the EOQ and total annual costs.
Demand (D) = 1000
Cost/Order (S) = $100
Carrying Cost (K) = 25%
Unit Cost (C) = $5
SOME HELPFUL CONCEPTS
Some Helpful Concepts
Answer:
INSIGHT
Consider how EOQ and
Total Costs change when
the key variables
DECREASE.
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Let’s throw a few wrinkles into this economic model. The first one is
Quantity Discounts. A quantity discount is when a supplier provides
a lower price (cost) if a higher quantity is purchased. Looking at an
example is probably the best way to see the impact on the purchase
quantity decision.
QUANTITY DISCOUNTS
Quantity Discounts
Question 8: When Janice calls up her supplier to place an order for
400 tank brake pads, the supplier informs her that there are discounts
for higher purchase quantities. Specifically, at 500 units the price is
reduced to $4.50 / unit and, if she orders 1,000 units, the price goes to
$4/unit. Saving money always seems like a good thing. Maybe she
should increase her order to receive the discount. How many should
Janice order?
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This is more difficult than you might expect. Again, our goal is to
minimize total annual costs. So the first step is to calculate the EOQs
for each price level.
Answer (Step 1):
EOQ ($5.00)
= 400 units (from previous example)
EOQ ($4.50)
= ((2 * D * S) / (K * C))^.5
= ((2 * 1000 * 100) / (25% * $4.50))^.5
= (200,000 / 1.125) ^.5
= 177,777 ^.5 = 421.637, or 422 brake pads per order
EOQ ($4.00)
= ((2 * D * S) / (K * C))^.5
= ((2 * 1000 * 100) / (25% * $4.00))^.5
= (20000 / 1.00) ^.5
= 200,000 ^.5 = 447.214, or 447 brake pads per order
QUANTITY DISCOUNTS
Quantity Discounts
As we’d expect, as the price decreases, the EOQ increases. But note how
little the EOQ rises with the quantity discounts. Both are below the quantity
needed to qualify for those discounts. What does that suggest?
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Step 2 is to calculate the total annual costs for each possible price /
quantity combination. Note that since the EOQs for $4.50 and for
$4.00 are below the quantity necessary to receive the discount, they
are not viable choices for Q and so we must calculate using the
minimum value Q that meets the quantity volume requirement.
QUANTITY DISCOUNTS
Quantity Discounts
Answer (Step 2):
Annual Cost ($5)
= $500 (calculated previously)
(Q=400)
Annual Cost ($4.50) = K*C*(Q/2) + (D/Q)*S
(Q=500)
= (500/2)*25%*$4.50 + (1000/500)*100
= $481.25
Annual Cost ($4.00) = (Q/2)*K*C + (R/Q)*S
(Q=1000)
= (1000/2)*.25*$4.00 + (1000/1000)*100
= $550.00
This would seem to indicate Q=500 (lowest), but are we forgetting something?
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Yes!! We’ve forgotten to add in the annual savings due to a lower unit
cost. So step 3 is to add in the additional savings with the discount
based on annual demand of 1000 units.
At $4.50, the savings would be $.50 x 1000 = $500
At $4.00, the savings would be $1.00 x 1000 = $1000
QUANTITY DISCOUNTS
Quantity Discounts
Answer (Step 3):
Annual Cost ($5)
= $500 (calculated previously)
Annual Cost ($4.50) = K*C*(Q/2) + (D/Q)*S – COGS Savings of $500
(Q=500)
= $481.25 - $500.00
= -$28.75
Annual Cost ($4.00) = (Q/2)*K*C + (R/Q)*S – COGS Savings of $1000
(Q=1000)
= $550.00 - $1000.00
= -$450.00
So, the lowest annual costs would be at an order quantity of 1000 units.
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Let’s consider the importance of the demand assumption. In Janice’s
example, we’ve used historical demand. Is that the best value to use?
Let’s consider two possible scenarios.
Scenario 1: Janice is about to call up her supplier again with the new
order quantity of 1000 units priced at $4.00. But, when Mark from the
marketing department stops by and sees that she’s about to place an
order for tank parts, he mentions that demand for tank parts is expected
to increase because of a promotion the marketing department is
planning. Mark checks with his manager and finds out the forecast for
this part is actually 2,000 units, double the historical demand. How will
this impact EOQ?
APPROPRIATE DEMAND ASSUMPTION
Appropriate Demand Assumption
Answer:
Janice would need to recalculate the EOQs based on annual demand of 2000
units. So, one managerial decision is whether to use historical demand or a
future forecast as the best estimate for demand (D).
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Janice picks up the phone again, now ready to place her order now
based on demand of 2000 units, but the production manager wanders
by muttering, “I can’t believe we have to change the pads in the tank
assembly from asbestos to ceramic, this is going to cause a delay in
our production lines”. Janice know that demand for brake pads is
generated from a combination of spare parts and in the production
process. So, another managerial consideration is the likelihood of
obsolesce. Here, Janet may need to recalculate only based on spare
parts demand.
APPROPRIATE DEMAND ASSUMPTION
Appropriate Demand Assumption
Insight
While EOQ is a very helpful tool in the inventory planning process,
remember that it is based on assumptions: that our estimate of future
demand is accurate, and demand is relatively constant, that the
carrying cost and order costs are accurate. Unit cost can also be
subject to different seasonal prices or production cost assumptions if
manufactured instead of purchased. So, don’t forget common sense!
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The Economic Lot Size (ELS) is a special case of EOQ for
manufacturing processes where instead of order costs it is typically
considered set-up costs for the manufacturing process.
Definition
ECONOMIC LOT SIZE (ELS)
Economic Lot Size (ELS)
2*D*S
or ((2 * D * S) / (K * C))^.5
K*C
D = Annual Demand (Historical or Forecasted)
S = Set-up Cost
K = Carrying or Holding Cost Rate (%)
C = Unit Cost
Economic Lot Size =
Where :
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Please see MBTN Inventory Management modules 1, 2
and 4 that cover other important concepts related to this
module.
MBTN | Management by the Numbers
INVENTORY MANAGEMENT– FURTHER REFERENCE
Inventory Management - Further Reference
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