Independent demand inventory

MAN 3520 – Fall 2012
CP3 – Independent Demand Inventory: Page 1 of 30
FUNDAMENTALS OF INVENTORY
Within most organizations inventory exists in a variety of places, and in a variety of forms, and
for a variety of reasons. Although these inventories represent a substantial cost investment (in
some cases as much as 50% of total capital invested), they are necessary to provide a desired
level of service to customers. The objective of inventory management is to strike a balance
between inventory investment and customer service.

MAN 3520 – Fall 2012
FUNCTIONS OF INVENTORY
Inventory exists for a variety of reasons (i.e., serves several functions) within organizations.
1. Decoupling stages in the production process. Inventory between successive stages of a
transformation process make each stage less dependent upon the output of the prior stage.
If there is an interruption in output at one stage, succeeding stages may be able to
continue operation by feeding off the inventory held between stages. This applies both to
internal operations and to external linkages with suppliers. This inventory is called
buffering inventory.
2. Decoupling from demand fluctuations. This manifests itself in both seasonal inventory
and safety stock. When there is predictable variation in demand throughout the year, and
when an organization does not have the capacity to produce peak demand when it is
demanded, the organization may have to produce and store finished products in advance
of that demand. This inventory is called seasonal inventory. When there is unpredictable
(i.e. erratic and random) short term variation in demand, the organization may have to
maintain additional inventory to cover the unpredictable spikes in demand. This
inventory is called safety stock.
3. Volume purchasing. Purchases in large quantities may result in reduced purchase price
and/or reduced delivery cost. Such incentives often lead organizations to acquire more
inventory than is immediately needed. This inventory is called volume discount
inventory.
4. Hedge against possible future events. In many instances organizations perceive that
there may be a disruptive economic or environmental event in the not too distant future.
Inflation may suggest that there will soon be a price increase in some supply. Labor
negotiations may suggest that an impending trucker strike might affect delivery of
supplies. Weather conditions indicate that a brewing tropical storm might affect
shipments of supplies. In circumstances like these organizations may choose to order
more inventory than is immediately needed to provide protection in the event that any of
these situations actually occur. This inventory is called hedge inventory.

MAN 3520 – Fall 2012
TYPES OF INVENTORY
To better accommodate the functions of inventory, organizations maintain four types of
inventories.
1. Raw material inventory. Materials that are usually purchased and have not yet entered
the transformation process.
2. Work-in-process (WIP) inventory. Materials and components that have undergone some
change but have not yet advanced to the stage of completed product.
3. Finished-goods inventory. Completed products awaiting shipment.
4. Maintenance/repair/operating (MRO) inventory. Supplies necessary to keep machinery,
processes, facilities, and office operations running. These items do not get absorbed into
the products being made, but are crucial to the smooth operation of the organization.
They range from such things as lubricating oil for machines and janitorial cleaning
products, to printer toner cartridges and other office supplies.

MAN 3520 – Fall 2012
BASIC INVENTORY DECISIONS
There are two basic decisions that must be made for every item that is maintained in inventory.
These decisions have to do with the timing of orders for the item and the size of orders for the
item. We will be examining several models and philosophies related to these two decisions. As
noted on page 1, the objective of these inventory management models is to strike a balance
between inventory investment and customer service.
How Much?
Lot sizing decision
Determination of the
quantity to be ordered.
When?
Lot timing decision
Determination of the
timing for the orders
Basic Inventory Decisions

MAN 3520 – Fall 2012
INDEPENDENT VS. DEPENDENT DEMAND INVENTORY
Before examining specific inventory models, an important distinction must be made. Some
inventory items can be classified as independent demand items, and some can be classified as
dependent demand items. We need to make the timing and sizing decisions for all inventory
items, but we will find that the manner in which we make these decisions will differ depending
upon whether the item has independent demand or dependent demand.
Independent demand inventory item: Inventory item whose demand is not related to (or
dependent upon) some higher level item. Demand for such items is usually thought of as
forecasted demand. Independent demand inventory items are usually thought of as finished
products.
Dependent demand inventory item: Inventory item whose demand is related to (or dependent
upon) some higher level item. Demand for such items is usually thought of as derived demand.
Dependent demand inventory items are usually thought of as the materials, parts, components,
and assemblies that make up the finished product.

MAN 3520 – Fall 2012
RELEVANT INVENTORY COSTS
Relevant Inventory Costs
Item
Costs
Holding
Costs
Ordering/Setup
Costs
Shortage
Costs
Direct cost for
getting an item.
Purchase cost for
outside orders,
manufacturing cost
for internal orders.
Costs associated
with carrying items
in inventory. Storage
and other related
costs.
Fixed costs
associated with
placing an order
(either an ordering
cost for outside
orders, or a setup
cost for internal
orders).
Costs associated
with not having
enough inventory to
meet demand.

MAN 3520 – Fall 2012
BEHAVIOR OF COSTS FOR DIFFERENT INVENTORY DECISIONS
When assessing the cost effectiveness of an inventory policy, it is helpful to measure the total
inventory costs that will be incurred during some reference period of time. Most frequently, that
time interval used for comparing costs is one year. Over that span of time, there will be a certain
need, or demand, or requirement for each inventory item. In that context, the following describes
how the annual costs in each of the four categories will vary with changes in the inventory lot
sizing decision.
Item costs: How the per unit item cost is measured depends upon whether the item is one that is
obtained from an external source of supply, or is one that is manufactured internally. For items
that are ordered from external sources, the per unit item cost is predominantly the purchase price
paid for the item. On some occasions this cost may also include some additional charges, like
inbound transportation cost, duties, or insurance. For items that are obtained from internal
sources, the per unit item cost is composed of the labor and material costs that went into its
production, and any factory overhead that might be allocated to the item. In many instances the
item cost is a constant, and is not affected by the lot sizing decision. In those cases, the total
annual item cost will be unaffected by the order size. Regardless of the order size (which impacts
how many times we choose to order that item over the course of the year), our total annual
acquisitions will equal the total annual need. Acquiring that total number of units at the constant
cost per unit will yield the same total annual cost. (This situation would be somewhat different if
we introduced the possibility of quantity discounts. We will consider that later.)
Cost
Lot Size (how much decision)
Total Annual Item Cost (assumes
no quantity discounts)

MAN 3520 – Fall 2012
INVENTORY COST BEHAVIOR (CONTINUED)
Holding costs (also called carrying costs): Any items that are held in inventory will incur a
cost for their storage. This cost will be comprised of a variety of components. One obvious cost
would be the cost of the storage facility (warehouse space charges and utility charges, cost of
material handlers and material handling equipment in the warehouse). In addition to that, there
are some other, more subtle expenses that add to the holding cost. These include such things as
insurance on the held inventory; taxes on the held inventory; damage to, theft of, deterioration of,
or obsolescence of the held items, and opportunity costs associated with having money tied up in
inventory. The order size decision impacts the average level of inventory that must be carried. If
smaller quantities are ordered, on average there will be fewer units being held in inventory,
resulting in lower annual inventory holding costs. If larger quantities are ordered, on average
there will be more units being held in inventory, resulting in higher annual inventory holding
costs.
Total Annual Holding Cost
Cost

MAN 3520 – Fall 2012
Ordering (or setup) costs: Any time inventory items are ordered, there is a fixed cost
associated with placing that order. When items are ordered from an outside source of supply, that
cost reflects the cost of the clerical work to prepare, release, monitor, and receive the order. This
cost is considered to be constant regardless of the size of the order. When items are to be
manufactured internally, the order cost reflects the setup costs necessary to prepare the
equipment for the manufacture of that order. Once again, this cost is constant regardless of how
many items are eventually manufactured in the batch. If one increases the size of the orders for a
particular inventory item, fewer of those orders will have to be placed during the course of the
year, hence the total annual cost of placing orders will decline.
Cost
Total Annual Ordering Cost

MAN 3520 – Fall 2012
Shortage costs: Companies incur shortage costs whenever demand for an item exceeds the
available inventory. These shortage costs can manifest themselves in the form of lost sales, loss
of good will, customer irritation, backorder and expediting charges, etc. Companies are less
likely to experience shortages if they have high levels of inventory, and are more likely to
experience shortages if they have low levels of inventory. The order size decision directly
impacts the average level of inventory. Larger orders mean more items are being acquired than
are immediately needed, so the excess will go into inventory. Hence, smaller order quantities
lead to lower levels of inventory, and correspondingly a higher likelihood of shortages and their
associated shortage costs. Larger order quantities lead to higher levels of inventory, and
correspondingly a lower likelihood of shortages and their associated costs. The bottom line is
this: larger order sizes will lead to lower annual shortage costs.
Cost
Total Annual Shortage Cost

MAN 3520 – Fall 2012
All Four Cost Categories Combined: When all four inventory cost categories are
superimposed on the same graph, we obtain the following (somewhat cluttered) picture which
suggests that there is one best answer to the “how much decision.” The quantity that should be
ordered is the lot size that corresponds to the lowest point on the total annual cost curve. This
quantity is referred to as the “economic order quantity,” or EOQ.
Annual
Shortage Cost
Annual Item Cost
Annual
Holding Cost
Total Annual Cost
Annual
Ordering Cost
Cost

MAN 3520 – Fall 2012
BASIC ECONOMIC ORDER QUANTITY (EOQ) MODEL
The EOQ model is a technique for determining the best answers to the how much and when
questions. It is based on the premise that there is an optimal order size that will yield the lowest
possible value of the total inventory cost. There are several assumptions regarding the behavior
of the inventory item that are central to the development of the model
EOQ assumptions:
1. Demand for the item is known and constant.
2. Lead time is known and constant. (Lead time is the amount of time that elapses between
when the order is placed and when it is received.)
3. When an order is received, all the items ordered arrive at once (instantaneous
replenishment).
4. The cost of all units ordered is the same, regardless of the quantity ordered (no quantity
discounts).
5. Ordering costs are known and constant (the cost to place an order is always the same,
regardless of the quantity ordered).
6. Since there is certainty with respect to the demand rate and the lead time, orders can be
timed to arrive just when we would have run out. Consequently the model assumes that
there will be no shortages.
Based on the above assumptions, there are only two costs that will vary with changes in the order
quantity, (1) the total annual ordering cost and (2) the total annual holding cost. Shortage cost
can be ignored because of assumption 6. Furthermore, since the cost per unit of all items ordered
is the same, the total annual item cost will be a constant and will not be affected by the order
quantity. Inventory levels will fluctuate over time as in the following graph:
EOQ symbols:
D = annual demand (units per year)
S = cost per order (dollars per order)
H = holding cost per unit per year (dollars to carry one unit in inventory for one year)
Q = order quantity
Q = Order SizeQ QQ
Time
Q/2
Inventory
Level

MAN 3520 – Fall 2012
CLASSIC ECONOMIC ORDER QUANTITY (EOQ) MODEL
We saw on the previous page that the only costs that need to be considered for the EOQ model
are the total annual ordering costs and the total annual holding costs. These can be quantified as
follows:
Annual Ordering Cost
The annual cost of ordering is simply the number of orders placed per year times the cost of
placing an order. The number of orders placed per year is a function of the order size. Bigger
orders means fewer orders per year, while smaller orders means more orders per year. In general,
the number of orders placed per year will be the total annual demand divided by the size of the
orders. In short,
Total Annual Ordering Cost = (D/Q)S
Annual Holding Cost
The annual cost of holding inventory is a bit trickier. If there was a constant level of inventory in
the warehouse throughout the year, we could simply multiply that constant inventory level by the
cost to carry a unit in inventory for a year. Unfortunately the inventory level is not constant
throughout the year, but is instead constantly changing. It is at its maximum value (which is the
order quantity, Q) when a new batch arrives, then steadily declines to zero. Just when that
inventory is depleted, a new order is received, thereby immediately sending the inventory level
back to its maximum value (Q). This pattern continues throughout, with the inventory level
fluctuating between Q and zero. To get a handle on the holding cost we are incurring, we can use
the average inventory level throughout the year (which is Q/2). The cost of carrying those
fluctuating inventory levels is equivalent to the cost that would be incurred if we had maintained
that average inventory level continuously and steadily throughout the year. That cost would have
been equal to the average inventory level times the cost to carry a unit in inventory for a year. In
short,
Total Annual Holding Cost = (Q/2)H
Total Annual Cost
The total annual relevant inventory cost would be the sum of the annual ordering cost and annual
holding cost, or
TC = (D/Q)S + (Q/2)H
This is the annual inventory cost associated with any order size, Q.

MAN 3520 – Fall 2012
CLASSIC ECONOMIC ORDER QUANTITY (EOQ) MODEL
At this point we are not interested in any old Q value. We want to find the optimal Q (the EOQ,
which is the order size that results in the lowest annual cost). This can be found using a little
calculus (take a derivative of the total cost equation with respect to Q, set this equal to zero, then
solve for Q). For those whose calculus is a little rusty, there is another option. The unique
characteristics of the ordering cost line and the holding cost line on a graph are such that the
optimal order size will occur where the annual ordering cost is equal to the annual holding cost.
EOQ occurs when:
(D/Q)S = (Q/2)H
a little algebra clean-up on this equation yields the following:
Q2
= (2DS)/H
and finally
______
Q* = √2DS/H
(Q* represents the optimal value for Q; this is what we call the EOQ)
Economic Order Quantity (EOQ)
Annual
Holding Cost
Total Annual Cost
Annual
Ordering Cost
Cost

MAN 3520 – Fall 2012
EOQ ILLUSTRATION
Given the following data for an inventory scenario whose characteristics fit the assumptions of
the basic EOQ model:
D = 15,000 units per year
S = $3 per order
H = $1 per unit per year
LT = Replenishment lead time = 2 days
Assume we have 300 operating days per year
Find the following:
1. Average daily demand
2. EOQ
3. Number of orders placed per year
4. Total annual ordering cost
5. Total annual holding cost
6. Time between orders
7. Reorder point (in units)
8. Average inventory level
Answers:
1. Average daily demand
15,000 units/yr ÷ 300 days/yr = 50 units per day
______ ______________
2. EOQ = √2DS/H = √(2)(15,000)(3)/(1) = 300 units/order
3. Number of orders placed per year
D/Q = (15,000 units/yr)/(300 units/order) = 50 orders/yr
4. Total annual ordering cost
(D/Q)(S) = [(15,000units/yr)/(300 units/order)]($3/order) = $150/yr
5. Total annual holding cost
(Q/2)H = [(300 units/order/2)]($1/unit/yr) = $150/yr
6. Time between orders
(Q/d) = (300 units/order)/(50 units/day) = 6 days/order
[or, 300days/yr÷50 orders/yr = 6 days/order]
7. Reorder point (in units)
ROP = (daily demand)(Lead time) = (50 units/day)(2 days) = 100 units
8. Average inventory level
Q/2 = 300 units/2 = 150 units

MAN 3520 – Fall 2012
OBSERVATIONS ABOUT OUR EOQ ILLUSTRATION
Results of computations
EOQ = 300 units
Number of orders placed per year = 50
Average inventory level = 150 units
Annual ordering cost = $150
Annual holding cost = $150
Time between the placement of orders = 6 days
Observation #1: Watch the inventory level instead of the calendar for “when” decision
We discovered that our order quantity of 300 units would lead to a replenishment every 6 days.
We projected that we would run out on days 6, 12, 18, 24, 30, 36, etc. With a 2 day lead time,
we were smart enough to order 2 days in advance of when we would run out, which had us
placing orders on days 4, 10, 16, 22, 28, 34, etc. We only have to watch the calendar to keep
track of when those order instants arise so that we can place the orders.
An alternative to watching the calendar would be to watch the inventory levels. Recall that the
average daily demand for this item is 50 units per day. This means that at the moment we place
an order, we have just enough inventory to cover the demand that will occur during the 2 day
lead time. The demand during the 2 day lead time is 2 days x 50 units per day = 100 units. So, all
we have to do is keep our eyes on our inventory level, and when it reaches 100 units, that is the
signal that it is time to reorder. This level of inventory that triggers a reorder is called the reorder
point (R).
EOQ = 300
100ROP
Inventory Level
Time

MAN 3520 – Fall 2012
OBSERVATIONS ABOUT OUR EOQ ILLUSTRATION
Observation #2: Model is robust (insensitive to errors in estimates for input data)
We estimated our holding cost to be $1/unit/yr when we made our EOQ calculation. Suppose this
estimate was in error, and the actual holding cost that will be incurred is $2/unit/yr (an error of
100%!). If we had been aware of this true holding cost, and had used $2/unit/yr in our EQQ
calculation, we would have determined the EOQ to be 212 units, and the ordering cost and
holding cost would have each been $212, for a total annual cost of $424 (you can practice the
application of the model to confirm these numbers on your own).
But, unfortunately we were not aware that the holding cost would be $2/unit/yr, so we made our
EOQ calculation using the incorrect $1/unit/yr. That calculation had us ordering 300 units each
time we placed an order. With this order size, the true cost we will incur is as follows:
Ordering cost: (D/Q)S = (15,000 units/yr/300 units/order)($3/order) = $150
Holding cost: (Q/2)H = (300 units/order/2)($2/unit/yr) = $300
Total annual cost = $150 + $300 = $450
In summary, we could have been incurring an annual cost of $424 if we had better information
about the holding cost, and were ordering the correct EOQ of 212 units. But, we used the wrong
holding cost in our model (we were off by 100%), ended up ordering 300 units every time we
ordered, and incurred an annual cost of $450.
Notice that the cost we are incurring ($450) is a little more than 6% higher than the absolute
minimum cost ($424) that we might have incurred. Not bad. We made a 100% error on the input
side, but our results are only about 6% worse than they could have been. That is because the total
cost line on our cost graph is relatively flat in the vicinity of the EOQ. You can drift to the right
or left of the optimal order size and find that the resulting cost doesn’t rise substantially. This is
what is meant by the model being robust (or insensitive to errors).

MAN 3520 – Fall 2012
IMPACT OF CHANGING ASSUMPTIONS ON MODEL DEVELOPMENT
Our focus has been on the basic EOQ model. That is just one of dozens of inventory models for
independent demand items. The basic EOQ model was derived from a set of underlying
assumptions. If any of those assumptions do not fit a particular situation, then one must turn to a
different model. Each of those available models is predicated upon a different set of underlying
assumptions. Some of the more popular ones (and ones described in the textbook) are
summarized below. We will not be expected to be knowledgeable about or work with any of
these model extensions.
Economic Production Quantity (EPQ) Model: When replenishment items come from inside
sources, the entire batch is usually not received all at once (instantaneous replenishment), but
instead is gradually received as a production batch is run (continuous replenishment). The pattern
of inventory level fluctuations over time changes, resulting in a slightly different quantitative
model for the optimal lot size.
Quantity Discount Model: When the supplier is willing to offer a lower price if large quantities
of an item are ordered, the total annual purchase cost line will no longer be horizontal, but will
instead have step decreases in it. This will lead to a total cost curve that has breaks in its
continuity (step changes) resulting in a slightly different model for determining the optimal order
size.
Controlled Backorder Model (not mentioned in the book): In some instances it might be
beneficial to have shortages. If the backorder cost of a shortage is not very high, but the cost of
carrying inventory is relative high, it may be more cost effective to incur some back orders on
each order cycle (the saw tooth graph dips below the horizontal axis on each order cycle). This
means that there will be less inventory being carried on average (resulting in lower holding
costs) and some shortages that will incur some cost. How low below the horizontal axis this
graph dips is a function of the relative values of the cost of holding inventory and the cost of
incurring a shortage.
Single-Period Inventory Model: Sometimes a unique situation that arises is one in which there
will be demand for an item in only one period, so the challenge is to determine the order size
(stock size) that will best accommodate the anticipated (and uncertain) demand. Any items
stocked in excess of demand will be scrapped. Any demand in excess of what has been stocked
will represent a missed opportunity for more profit. (This problem is sometimes referred to as the
newsboy problem, or the Christmas tree problem.)
These are but a few of the many variations to the basic EOQ model that are in existence. They all
are designed to provide optimal answers to the how much and when questions. Choice of a
model should be dictated by the characteristics of the inventory situation that you are facing.

MAN 3520 – Fall 2012
DEMAND VARIABILITY AND UNCERTAINTY
The basic EOQ model assumes that demand rate is constant and predictable. As a result we
always knew when we were going to run out of inventory, so we could always reorder in a
timely fashion so that the new replenishment order would be received just when we ran out of
inventory.
In reality demand rates are rarely constant and rarely completely predictable. It is more likely
that demand rates will vary from day to day, and there will be uncertainty about what those
demand rates will be at any one time. Consequently, there is a possibility that we may run out of
inventory before a replenishment order arrives. To prevent a shortage situation organizations
must rely on safety stock.

MAN 3520 – Fall 2012
ILLUSTRATION OF SAFETY STOCK DETERMINATION
Data:
Average daily demand = 50 units per day
Operating year contains 300 days of operation (D = 15,000 units per year)
Ordering cost S = $3 per order
Holding cost H = $1 per unit per year
Lead time = 1 day
Computations:
EOQ (from EOQ formula) = 300 units per order
Resulting number of orders per year = 50 orders per year
Reorder point = 50 units (the average number of units demanded during the 1 day lead time)
Additional Data:
Demand is not always a constant 50 units per day. There is variability in daily demand according
to the following table of demands and probabilities:
Daily Demand 10 20 30 40 50 60 70 80 90
Probability .01 .04 .05 .2 .4 .2 .05 .04 .01
Cumulative Probability .01 .05 .10 .30 .70 .90 .95 .99 1.00
LTLT
Time
Reorder
Point, 50
Inventory Level
300 300

MAN 3520 – Fall 2012
The graph above suggests that if you waited until you had 50 units left in inventory before
placing an order for 300 more units, you would be O.K. if the demand during the 1 day lead time
was 10, 20, 30, 40, or 50. However, if the demand during the 1 day lead time was 60, 70, 80, or
90 you would have had a shortage. The size of the shortage would depend upon how many units
were demanded during the lead time, but the maximum possible shortage would have been 40
units (if demand was the largest possible value of 90).
You can prevent shortages by providing safety stock when there is uncertainty in demand.
(Safety stock can be viewed as a cushion placed at the bottom of the saw tooth graph of
inventory fluctuations over time.) If you wanted to guarantee that you would never have a
shortage in this situation, you would need 40 units of safety stock at the bottom of the graph to
"dip into" if demand spiked to higher than average values. But, adding 40 units of safety stock
really means that you have elevated your reorder point. You are not waiting until there are only
50 units in inventory to place your order. You are ordering when there are 90 units in inventory.
And, of course, 90 units are sufficient to cover the worst case scenario for this problem. The
graph below illustrates the impact of 40 units of safety stock maintained in the system.
Safety
Stock, 40 LTLT
Time
Original
Reorder
Point, 50
Inventory Level
300 300

MAN 3520 – Fall 2012
HOW MUCH SAFETY STOCK IS APPROPRIATE?
Service level: The probability that demand during lead time will not exceed the inventory on
hand when the order is placed.
In the previous illustration, it was suggested that you might provide 40 units of safety stock. If
you had done so, you would never experience a shortage. You would have achieved a service
level of 100%. This might not be a desirable solution for this problem. We are carrying a
relatively high amount of safety stock, and there is a very low probability that lead time demand
will actually go as high as 90 units (only a 1% chance).
If you had chosen to carry only 30 units of safety stock (order when inventory drops to 80 units),
you will be fine if lead time demand is anything up to and including 80 units. If lead time
demand turns out to be 90 (there is a 1% chance of that), you will come up 10 units short. But,
since you had enough inventory to cover 99% of the demands that might have occurred, you
achieved a 99% service level. Many people might opt for this policy, for it will reduce the
average annual level of inventory carried (i.e., reduce holding costs) and run only a slight risk of
incurring a shortage cost.
Others might be even more aggressive, and opt for an even lower service level. We could have
achieved a 95% service level with a reorder point of 70 (only 20 units of safety stock). We've
lowered our inventory holding costs even further, but exposed ourselves to even more shortage
cost risk.

MAN 3520 – Fall 2012
INVENTORY MONITORING APPROACHES
Fixed Quantity, or Q System: This approach maintains a constant order size, but allows the
time between the placement of orders to vary. This method of monitoring inventory is sometimes
referred to as a perpetual review method, a continuous review system, a reorder point system,
and a two-bin system. The inventory level is continuously (perpetually) monitored, and when the
inventory drops to the reorder point level, a replenishment order is placed. The size of the order
is constant (fixed quantity, typically the calculated economic order quantity for the item).
Because demand continues to occur while we are waiting for the replenishment order to arrive
(i.e., demand continues to occur during the lead time), the inventory level will generally be
below the reorder point level when the replenishment arrives. This type of system provides
closer control over inventory items since the inventory levels are under perpetual scrutiny.
How much decision: Order size is constant (fixed).
When decision: Time between the placement of orders can vary.
Time
Reorder
Point
LT
Q
Order
#2
LT
Order
#1 Q
LT
Q
Order
#3
Inventory Level

MAN 3520 – Fall 2012
Periodic Review Systems: There are two, Fixed Period System (described in the textbook),
and a hybrid system (described below but not in the textbook)
Fixed Period System: This approach maintains a constant time between the placement of
orders, but allows the order size to vary. This method of monitoring inventory is sometimes
referred to as a fixed interval system. It only requires that inventory levels be checked at fixed
periods of time. The amount that is ordered at a particular time point is the difference between
the current inventory level and a predetermined maximum inventory level (also called an order
up to level, or a target level). If demand has been low during the prior time interval, inventory
levels will be relatively high when the review time occurs, and the amount to be ordered will be
relatively low. If demand has been high during the prior time interval, inventory levels will have
been depleted to low levels when the review time occurs, and the amount to be ordered will be
higher. Since demand continues to occur during the lead time, inventory levels will increase
when the replenishment order arrives, but not all the way up to the maximum (i.e., target) level.
How much decision: Order size can vary.
When decision: Time between the placement of orders is constant (fixed).
LT
Q3
Order
#3
Q2
LT
Q1
T1
Maximum (or “order up to” or “target”) inventory level
Time
LT
Order
#2
Order
#1
Inventory Level
T2
T3
Review time, T1
Review time, T2
Review time, T3

MAN 3520 – Fall 2012
Hybrid System: This approach allows both the order size and the time between the placement
of orders to vary. This method of monitoring inventory is sometimes referred to as an optional
replenishment system, or a min-max system. It is a hybrid system because it combines elements
of both the fixed quantity system and the fixed period system. It is similar to the periodic review
system in that it only checks inventory levels at fixed intervals of time, and it has a maximum
inventory level (or “order up to” or “target” level). However, when one of those review periods
arises the system does not automatically place an order. An order is only placed if the size of the
order would be sufficient to warrant placing the order. This determination is made by
incorporating the reorder point concept from the continuous review system. At the review period
the inventory level on hand is compared to a minimum level for the item. If inventory has not
fallen below this minimum level, no order is placed. However, if the inventory level has dropped
below this minimum level, an order is placed. The size of the order is the difference between the
inventory on hand and the maximum inventory level. Since demand continues to occur during
the lead time, inventory levels will increase when the replenishment order arrives, but not all the
way up to the maximum (i.e., target) level.
How much decision: Order size can vary.
When decision: Time between the placement of orders can vary.
Second order is placed
at T3
since the
inventory has fallen
blow the minimum LT
Q2
Order
#2
LT
Q1
T1
Maximum (or “order up to” or “target”) inventory level
Time
Minimum
Level
Order
#1
Inventory Level
T2
T3
First order is placed
at T1
since the
inventory has fallen
blow the minimum
No order at T2
since inventory is
not below the
minimum

MAN 3520 – Fall 2012
POSITIVES AND NEGATIVES OF
INVENTORY MONITORING APPROACHES
Approach
Advantages
(Positive aspects)
Disadvantages
(Negative aspects)
Fixed Quantity
- provides tighter control over
inventory items
- less safety stock needed
- requires constant monitoring
(constant scrutiny)
- problems with multiple items
from same source (many items
arrive in separate shipments)
Fixed Period
- joint shipping advantage with
multiple items from same source
- does not require constant
monitoring
- requires more safety stock
- occasional small “nuisance”
orders may result
- provides looser control over
inventory items
Hybrid
- joint shipping advantage with
multiple items from same source
- does not require constant
monitoring
- no small “nuisance” orders
- requires more safety stock
- provides looser control over
inventory items
COMPARISON OF INVENTORY MANAGEMENT SYSTEMS
System Order Size Time Between Orders
Fixed Quantity Constant (fixed) Varies
Fixed Period Varies Constant (fixed)
Hybrid Varies Varies

MAN 3520 – Fall 2012
ABC CLASSIFICATION OF ITEMS
It is not unusual for organizations to maintain many items in inventory (hundreds or even
thousands). Each of these items needs to be controlled. An important question is “How much
scrutiny does each item deserve?” Some of these items may have a high annual investment, and
logic would suggest that these items deserve very close scrutiny. On the other hand, some items
may have a low annual investment (these are often referred to as “nuts and bolts items”), and
they probably do not need as much attention. ABC analysis provides a mechanism to separate the
"important few" from the "trivial many" so that the appropriate level of control can be assigned
to each item. ABC analysis assigns all inventory items to one of these three classifications: A
items need the tightest degree of control, while C items do not need very close scrutiny. The
general graphical display for an ABC classification appears as follows:
This type of diagram is referred to as a Pareto graph, and is relevant to a variety of situations.
Cumulative % of Items 100%
A Items B Items C Items
Cumulative % of Value
100%

MAN 3520 – Fall 2012
ILLUSTRATION OF ABC ANALYSIS
The following table displays an organizations inventory items, their value per unit, and their
annual usage. (Note: To keep things manageable on the page, this illustration is greatly scaled
down from reality. Most organizations would be dealing with considerably more than the ten
inventory items displayed below.)
Inventory
Item Number
Annual
Usage
Value
Per Unit
Annual
Dollar Usage
1 10,000 $13 130,000
2 14,000 $5 70,000
3 2,000 $6 12,000
4 10,000 $3 30,000
5 5,000 $5 25,000
6 50,000 $8 400,000
7 30,000 $10 300,000
8 5,000 $1 5,000
9 4,000 $5 20,000
10 2,000 $4 8,000
Total $1,000,000
Rearrange items in decreasing order of annual dollar usage:
Item
Number
Annual
$ Usage
% of
Line Items
Cumulative
% of Items
% of
Value
Cumulative
% of Value
ABC
Class*
6 $400,000 10% 10% 40 40 A
7 $300,000 10% 20% 30 70 A
1 $130,000 10% 30% 13 83 B
2 $70,000 10% 40% 7 90 B
4 $30,000 10% 50% 3 93 C
5 $25,000 10% 60% 2.5 95.5 C
9 $20,000 10% 70% 2 97.5 C
3 $12,000 10% 80% 1.2 98.7 C
10 $8,000 10% 90% .8 99.5 C
8 $5,000 10% 100% .5 100 C
Total $1,000,000
*Note: When classifying the items as A, B, or C items, it can be somewhat subjective as to
where the lines are drawn. With the unrealistically small demonstration above, the first 20% of
the inventory items constitute 70% of the inventory value, so these items (Items 6 and 7) will be
designated as A items. On the other extreme, 60% of the items constitute only 10% of the
inventory value, so these items (Items 4, 5, 9, 3, 10, and 8) will be designated as C items. In the
middle, 20% of the items constitute 20 % of the inventory value, so these items (Items 1 and 2)
will be designated as a B item.

MAN 3520 – Fall 2012
DEVELOPMENT OF THE ABC INVENTORY PARETO GRAPH
Cumulative percentages extracted from previous table (and rotated 90 degrees)
Items (rearranged order)
1st
1
1st
2
1st
3
1st
4
1st
5
1st
6
1st
7
1st
8
1st
9
All
10
Cumulative % of items 10 20 30 40 50 60 70 80 90 100
Cumulative % of value 40 70 82 90 93 95.5 97.5 98.7 99.5 100

MAN 3520 – Fall 2012
ALTERNATE REPRESENTATION OF OUR ABC ANALYSIS
The data reflected in the Pareto graph could also be displayed in a bar chart, as illustrated in the
textbook. The following is such a representation for our simple ABC illustration.
10 20 30 40 50 60 70 80 90 100
A items
B items
C items

Independent demand inventory

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