### Calculations in a Periodic System

```Inventory Management IV:
Inventory Management Systems
This module discusses periodic vs. perpetual systems,
inventory position, quantity to order, time between orders,
target inventory, lead times, reorder point and safety stock.
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 – when should an inventoried item be ordered
or manufactured? The following topics will be covered:
TOPICS COVERED
Topics Covered
• Periodic Inventory Systems
• Inventory Position (I)
• Quantity to Order (Q)
• Time Between Orders (P)
• Target Inventory (T)
• Perpetual Inventory Systems
• Reorder Point (ROP)
• Safety Stock (SS)
MBTN | Management by the Numbers
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There are two general categories of inventory systems which differ
both from an operational and an accounting point of view.
Periodic Inventory Management is more likely to be used in smaller
businesses with a single location or where the stocking amount is
limited. In this approach, orders to replenish stock are set at predetermined intervals based on demand and order quantity. The order
amount is based on how many units are needed to reach a target level
of inventory.
TYPES OF INVENTORY SYSTEMS
Types of Inventory Systems
Perpetual Inventory Management is typically a computerized system
that continuously monitors usage/purchases and determines whether
stock needs to be replenished based on a reorder point. The reorder
point is based on demand, lead time, and the need for safety stock.
Let’s look at each of these systems in more detail and discuss
corresponding calculations that are part of each system.
MBTN | Management by the Numbers
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Let’s look at how inventory levels flow in a periodic system. In the
example below, stocks are replenished to target level (T) at some
constant interval (P) with quantity (Q) required to reach the target level.
Example, re-stocking retail shelf space daily or weekly.
T
Q3
Q1
Inventory
Level
= Order
P1
Q4
Q2
P2
P3
Time
INVENTORY OVER TIME IN A PERIODIC SYSTEM
Inventory Over Time in a Periodic System
P4
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At each review interval (P), the order amount (Q) is calculated based
on the target inventory (T) and the inventory position (I). Let’s start
with the easiest question - calculating the order amount (Q).
Definition
Quantity to Order (Q)
Where:
=T–I
I = Inventory Position
T = Target Inventory
CALCULATIONS IN A PERIODIC SYSTEM
Calculations in a Periodic System
Insight
This is sufficient (and simple) unless there are previous orders that are
not included in inventory (scheduled receipts) or demand that has not
been deducted from inventory (backorders).
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Let’s expand the definition of inventory position (I) to include
Scheduled Receipts (orders to replenish stock that have not yet been
added to inventory) and Backorders (demand that has not yet been
deducted from the inventory).
Definitions
Inventory Position (I) = OH + SR – BO
Where :
OH = Physical Quantity of Inventory On Hand
SR = Scheduled Receipts
BO = Backorders
CALCULATIONS IN A PERIODIC SYSTEM
Calculations in a Periodic System
Replacing this more complete definition of inventory position in our
quantity to order equation leads to:
Quantity to Order (Q)
or
=T–I
= T – (OH + SR – BO)
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Question 1: Fred’s Fine Foods uses a periodic system for inventory
control in his retail store. Each Wednesday, Fred checks the inventory
levels of his specialty items. His physical inventory count (how many
actual tins he has in stock) for his caramel toasted caraway seed tins
is currently 12 tins, but he has one customer who has a special order
of 30 tins, which he wasn’t able to fulfill from his on-hand stock. His
target inventory level is 25. He has no tins currently on order. What is
Fred’s Inventory Position (I) for the tins and how many tins should he
order to reach his target inventory?
CALCULATIONS IN A PERIOD SYSTEM
Calculations in a Periodic System
Inventory Position (I) = (OH + SR – BO)
= (12 + 0 – 30) = -18 Tins
Order Quantity (Q)
=T-I
= T - (-18)
= 25 – (-18)
= 43 Tins
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There are 2 approaches to determine the time between orders (P).
The first method (Periodic System) focuses on convenience. In our
example, Fred checks his stock weekly; however, it could also be done
on an annual or quarterly basis. The second approach (Perpetual
System) uses an order quantity (such as EOQ) and annual demand to
determine the time between orders.
Definition
Time Between Orders (P)
Where :
CALCULATIONS IN A PERIODIC SYSTEM
Calculations in a Periodic System
=Q/D
P = Time (in same period considered for demand)
Q = Order Quantity (often, Economic Order Quantity)
D = Demand (Annual, Monthly, Weekly, Daily)
e.g. If D is daily demand, time between orders would be in days.
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Question 2: Fred’s vendor for caraway seeds told Fred he could get a
discount if more than 100 tins were ordered at one time. Fred thought
to himself, “Great! That would mean that I wouldn’t have to check my
inventory as often and I might be able fulfill more special orders on the
spot.” Fred decided he’d like to review his inventory position every 3
months instead of weekly. Fred checked his records and found that
his annual demand for caraway seed tins was 800 each year. What
would Fred’s planned order quantity be and would he normally meet
the volume for the discount under this scenario?
CALCULATIONS IN A PERIOD SYSTEM
Calculations in a Periodic System
Time Between Orders (P) = Q / D (demand provided in years)
so, 3 months
= .25 year
and, .25 year = Q / 800
800 * .25
= Q = 200
Generally, Fred would meet the minimum if demand is fairly constant, BUT,
this is not guaranteed if he only orders the quantity necessary to meet T every
3 months. Take a moment to think why this is so.
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Now let’s move on to calculating the target inventory (T). It is fairly
straightforward if demand is constant and there is no delay from when
the quantity is determined to when the order is replenished. However,
if there is a lead time between when the order is placed and when the
stock is added to inventory, enough stock must be on hand to cover
the demand in the interim.
T
Q3
Inventory
Level
Q1
= Order
Placed
P1
Q2
P2 Time P3
Q4
INVENTORY OVER TIME IN A PERIODIC SYSTEM
Inventory Over Time in a Periodic System
P4
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To determine target inventory level (T), we’ll need to calculate
demand during the time between orders (P) and during lead time (L).
In our examples, we will presume demand and lead times are known
(and reliable). Safety stock (SS) is an extra buffer of stock to protect
against variations in demand or lead times. In a previous module,
we’ve discussed the statistical methods that can be used to calculate
safety stock. For this module, we’ll provide you with the value.
Definition
CALCULATIONS IN A PERIODIC SYSTEM
Calculations in a Periodic System
Target Inventory (T) = (D / working days per year) * (P + L) + SS
Where :
D = Annual Demand
L = Lead Time (in days)
P = Time Between Orders (in days)
SS = Safety Stock
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Question 3a: Jean-François wants to determine the appropriate
target inventory level and periodic review timetable for two parts he
stores in his custom bike shop. The first part is a specialty cassette
that costs \$200. The annual demand for this part is 60 units, he orders
5 cassettes at a time, and the safety stock is 2 units. On average, the
lead time for the cassette is 20 days. Assume 250 days.
For Bike Cassette:
Time Between Orders
CALCULATIONS IN A PERIODIC SYSTEM
Calculations in a Periodic System
P =Q/D
= 5 / 60
= 1 / 12 = Approx. 1x / month or
= 250 / 12 = 20.8 business days
Daily Demand
= D / 250 = 60 / 250 = .24 per business day
Target Inventory (T)
= .24 * (P + L) + SS
= .24 * (20.8 + 20) + 2 = 11.8 = 12 Cassettes
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Question 3b: The second part that Jean-François stocks is a
replacement tube that costs \$3. He sells 30 tubes per year and he
orders a case of 60 tubes per order. The tubes’ safety stock is 5 and
For Tube:
Time Between Orders
Daily Demand
Target Inventory (T)
=P=Q/D
= 60 / 30 = 2 years or 500 days
= D / 250 = 30 / 250 = .12
= .12 * (P + L) + SS
= .12 * (500 + 20) + 5 = 67.4 or 68 Tubes
CALCULATIONS IN A PERIODIC SYSTEM
Calculations in a Periodic System
Insights
Although Jean-François has calculated the time between orders at 2
years, he would still need to perform a physical inventory count at year
end for accounting and reporting purposes.
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Since the periodic system doesn’t, by design, optimize inventory
levels, what are the circumstances where it does make sense to
implement it?
• Since replenishments and potentially, physical inventory counts, are
made at fixed intervals, it may be more convenient and efficient to
use a periodic system.
WHEN TO USE A PERIODIC?
When to Use a Periodic System?
• If multiple items are ordered at the same time from the same vendor,
(\$) volume discounts may be available, and purchase and delivery
costs may be minimized by consolidating in a single purchase order.
• If inventoried items have low value and don’t take up much space
(e.g. order and review costs are much higher than carrying costs),
trying to carefully manage inventory may not be worth the extra cost
of computerized systems and specialized personnel.
MBTN | Management by the Numbers
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Now let’s look at how inventory levels flow in a perpetual system. Here,
inventory is constantly monitored and an order is placed when it
reaches a certain level called the reorder point (ROP). The quantity
ordered (Q) will be based on the EOQ and, unlike a periodic system,
will remain constant (unless the EOQ changes).
Inventory
Level
Q
Q
Q
Q
INVENTORY OVER TIME IN A PERPETUAL SYSTEM
Inventory Over Time in a Perpetual System
ROP
= Place an Order
Time
MBTN | Management by the Numbers
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Now consider the situation where there is lead time and the need for
safety stock in the system. In this graphic, demand continues after the
reorder point is reached and the order is placed. Notice the use of
safety stock (SS) below that lowers the probability of stock outs.
Without it, in the 2nd demand cycle, there would have been shortages.
Potential
Shortage!
Inventory
Level
Q
Q
Q
Q
INVENTORY OVER TIME IN A PERPETUAL SYSTEM
Inventory Over Time in a Perpetual System
R
SS
= Order
Placed
Time
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Definition
Reorder Point (ROP) = d * L + SS
Where :
d = daily Demand (or D / days in year)
L = Lead Time (in days)
SS = Safety Stock
Question 4: Jean-François wondered what the reorder point field is in
his inventory software. His friend, Marie Claire, who works as a
material manager, offers to help him use these features and provides
him with the above formula. If the safety stock is 2 cassettes, the lead
time is 20 days, and the annual demand is 60 units, what is the ROP?
CALCULATING THE REORDER POINT
Calculating Reorder Point
Reorder Point (ROP)
= d * L + SS
= (60 / 250) * 20 + 2 = 6.8 or 7 Units
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Please see MBTN Inventory Management modules 1-3
that cover other important concepts related to this module.
MBTN | Management by the Numbers
INVENTORY MANAGEMENT– FURTHER REFERENCE
Inventory Management - Further Reference
18
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