Inventory Management
MNG221- Management Science –
Lecture Outline
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Types of inventory
Reasons for holding inventory
Stock costs
Objective of inventory management
Pareto analysis
Deterministic and stochastic models
Inventory Management
• Stock may be classified into:
–Raw materials
–Work-in-progress
–Finished goods
–Resources, Labor, Cash
The classification depends on the
nature of the firm.
Inventory Management
• The main purpose of inventory is simply
to meet customer demand.
• It often represents a significant cost to
a business firm, (including insurance,
obsolescence, depreciation, interest,
opportunity costs, storage costs, etc.)
• Therefore inventory related costs can be
controlled, through the management of
inventory levels.
Inventory Management
Elements of Inventory Management
Elements of Inventory Management
• Inventory is defined as a stock of items
kept on hand by an organization to use
to meet customer demand.
The Role of Inventory
The main reasons for holding inventory
are:
• To satisfy demand immediately
• To meet seasonal or cyclical demand
Elements of Inventory Management
The Role of Inventory
• To allow for unimpeded production and
provide
independence
between
operations.
• To take advantage of bulk purchasing
price discounts.
• To absorb seasonal fluctuations.
• A necessary part of the production
process.
Elements of Inventory Management
The Role of Inventory (continued)
• Inventory may also accumulate because
of poor control methods, obsolesce and
suboptimal decisions.
Elements of Inventory Management
Demand
• A crucial component and the basic
starting point for the management of
inventory is customer demand, because
it exists for the purpose of meeting the
demand of customers.
• Customers can be Internal (machine
operator) or External (Individual
purchasing goods from stores)
Elements of Inventory Management
Demand (Continued)
• An essential determinant of effective
inventory management is an accurate forecast
of demand.
• The demand for items in inventory is classified
as dependent or independent
– Dependent Demand items are used internally
to produce a final product
– Independent Demand items are final products
demanded by an external customer.
Elements of Inventory Management
Inventory Costs
• There are three basic costs associated
with inventory:
–Carrying Costs - are the costs of
holding items in storage.
–Ordering
Costs - are the costs
associated with replenishing the stock
of inventory being held.
Elements of Inventory Management
Inventory Costs
–Shortage costs - also referred to as
stockout costs, occur when customer
demand cannot be met because of
insufficient inventory on hand.
Elements of Inventory Management
Inventory Costs
• The
objective
of
inventory
management is to employ an inventory
control system that will indicate how
much should be ordered and when
orders should take place to minimize
the sum of the above three inventory
costs
Inventory Management
Inventory Control Systems
Inventory Control Systems
• An Inventory System is a structure for
controlling the level of inventory by
determining how much to order (the
level of replenishment) and when to
order.
• There are two basic types of inventory
systems: a continuous (or fixed order
quantity) system and a periodic (or fixed
time period) system.
Inventory Control Systems
• The primary difference in the two
systems is that in a:
–Continuous system - an order for the
same amount is placed whenever the
inventory decreases to a certain level.
–Periodic system - order is placed for a
variable after an established passage
of time.
Inventory Control Systems
Continuous Inventory System
• In a continuous inventory system,
(alternatively referred to as a perpetual
system or a fixed order quantity system)
a constant amount is ordered when
inventory declines to a predetermined
level, referred to as the reorder point.
• This fixed order quantity is called the
economic order quantity
Inventory Control Systems
Continuous Inventory System
• The inventory level is closely and
continuously
monitored
so
that
management always knows the inventory
status.
• However, the cost of maintaining a
continual record of the amount of
inventory on hand can also be a
disadvantage of this type of system.
Inventory Control Systems
Periodic Inventory System
• In a periodic inventory system, (also
referred to as a fixed time period
system or periodic review system) an
order is placed for a variable amount
after a fixed passage of time.
Inventory Control Systems
Periodic Inventory System
• The inventory level is not monitored
at all during the time interval
between orders.
• It has the advantage of requiring little
or no record keeping
• It has the disadvantage of less direct
control
Inventory Management
Economic Order Quantity Models
Basic Model
Economic Order Quantity Models
• The most widely used and traditional
means for determining how much to
order in a continuous system is the
Economic Order Quantity (EOQ) model,
also referred to as the Economic Lot
Size Model.
• The function of the EOQ model is to
determine the optimal order size that
minimizes total inventory costs.
Economic Order Quantity Models
The Basic EOQ Model
• It is essentially a single formula for
determining the optimal order size that
minimizes the sum of carrying costs and
ordering costs.
Economic Order Quantity Models
The Basic EOQ Model
Assumptions
• Demand is known with certainty and is
relatively constant over time.
• No shortages are allowed.
• Lead time for the receipt of orders is
constant.
• The order quantity is received all at once.
Economic Order Quantity Models
The Basic EOQ Model
The Inventory Order Cycle
Economic Order Quantity Models
The Basic EOQ Model
• Q is the point at which ordering and
carrying costs react inversely to each
other in response to an increase in the
order size.
• R is the point at which a new order is
placed with enough lead time for the
reordering of stock.
Economic Order Quantity Models
The Basic EOQ Model – Carrying Costs
• Carrying cost is usually expressed on a
per-unit basis for some period of time on
an annual basis (i.e., per year), and
sometimes as a percentage of average
inventory.
Average Inventory = Q or ∑Q points over period, t
2
number of points
Economic Order Quantity Models
The Basic EOQ Model – Carrying Costs
Economic Order Quantity Models
The Basic EOQ Model – Carrying Costs
Thus,
Carrying cost is
Ordering Costs is
Total Inventory Cost is
The EOQ cost model
Economic Order Quantity Models
The Basic EOQ Model
• The Optimal Value Of Q corresponds to
the lowest point on the total cost curve
or the point where the ordering cost
curve intersects with the carrying cost
curve.
Economic Order Quantity Models
The Basic EOQ Model
• Thus The Optimal Value Of Q by
equating the two cost functions and
solving for Q, as follows:
Economic Order Quantity Models
The Basic EOQ Model
• Alternatively, the optimal value of Q can be
determined by differentiating the total cost
curve with respect to Q
Economic Order Quantity Models
The Basic EOQ Model
• The total minimum cost
Economic Order Quantity Models
The Basic EOQ Model - Example
• The I-75 Carpet Discount Store wants to
determine the optimal order size and total
inventory cost given an estimated annual
demand of 10,000 yards of carpet, an annual
carrying cost of $0.75 per yard, and an
ordering cost of $150.
• The store would also like to know the number
of orders that will be made annually and the
time between orders (i.e., the order cycle).
Economic Order Quantity Models
The Basic EOQ Model – Example
• The model parameters as follows:
Economic Order Quantity Models
The Basic EOQ Model – Example
• The optimal order size is computed as
follows:
Economic Order Quantity Models
The Basic EOQ Model – Example
• The total annual inventory cost is determined by substituting Qopt
into the total cost formula, as follows:
Economic Order Quantity Models
The Basic EOQ Model – Example
• The number of orders per year is
computed as follows:
Economic Order Quantity Models
The Basic EOQ Model – Example
• Given that the store is open 311 days annually
(365 days minus 52 Sundays, plus Thanksgiving
and Christmas), the order cycle is determined as
follows:
Economic Order Quantity Models
The Basic EOQ Model
• The optimal order quantity determined in general, is an
approximate value, because it is based on estimates of
carrying and ordering costs as well as uncertain demand.
• This in practice it is acceptable to round off the Q values
to the nearest whole number.
• However, the EOQ model is robust; because Q is a square
root, errors in the estimation of D, Cc, and Co are
dampened.
Inventory Management
Economic Order Quantity Models
Non-instantaneous Model
Economic Order Quantity Models
Non-instantaneous Receipt Model
• A variation of the basic EOQ model is achieved
when the assumption that orders are received
all at once is relaxed.
• It is also referred to as the Gradual Usage, or
Production Lot Size, model.
• In this EOQ variation, the order quantity is
received gradually over time and the
inventory level is depleted at the same time it
is being replenished.
Economic Order Quantity Models
Non-instantaneous Receipt Model
• This is a situation most commonly found
when the
–Inventory user is also the producer
–When orders are delivered gradually
over time
–When retailer and producer of a
product are one and the same.
Economic Order Quantity Models
Non-instantaneous Receipt Model
The EOQ model with Non-instantaneous Order Receipt
Economic Order Quantity Models
Non-instantaneous Receipt Model
• The ordering cost component of the basic
EOQ model does not change.
• However, the carrying cost component is not
the same for this model variation because
average inventory is different.
• The maximum inventory level is not simply Q;
it is an amount somewhat lower than Q,
Economic Order Quantity Models
Non-instantaneous Receipt Model
• Unique parameters of this model:
–p = daily rate at which the order is
received over time, also known as the
production rate
–d = the daily rate at which inventory is
demanded
Economic Order Quantity Models
Non-instantaneous Receipt Model
• As such, the maximum amount of
inventory that is on hand is computed
as follows:
Economic Order Quantity Models
Non-instantaneous Receipt Model
• Given the maximum inventory level, the
average inventory level is determined
by dividing this amount by 2, as follows:
Economic Order Quantity Models
Non-instantaneous Receipt Model
• The total carrying cost, using this
function for average inventory, is:
Economic Order Quantity Models
Non-instantaneous Receipt Model
• Thus, the total annual inventory cost is
determined according to the following
formula:
Economic Order Quantity Models
Non-instantaneous Receipt Model
• Therefore, to find optimal Qopt, we equate
total carrying cost with total ordering cost:
Economic Order Quantity Models
Non-instantaneous Receipt Model Example
• Assume that the I-75 Carpet Discount Store
has its own manufacturing facility
• further assume that the ordering cost, Co, is
the cost of setting up the production process
• Recall that Cc = $0.75 per yard and D = 10,000
yards per year.
• The manufacturing facility operates 311 days
and produces 150 yards of the carpet per day.
Economic Order Quantity Models
Non-instantaneous Receipt Model Example
• Thus the parameters are:
Economic Order Quantity Models
Non-instantaneous Receipt Model Example
• The optimal order size is determined as
follows:
Economic Order Quantity Models
Non-instantaneous Receipt Model Example
• This value is substituted into the following
formula to determine total minimum annual
inventory cost:
Economic Order Quantity Models
Non-instantaneous Receipt Model Example
• The length of time to receive an order
or production run is computed as
follows:
Economic Order Quantity Models
Non-instantaneous Receipt Model Example
• The number of orders per year is actually the
number of production runs that will be made,
computed as follows:
Economic Order Quantity Models
Non-instantaneous Receipt Model Example
• Finally, the maximum inventory level is
computed as follows:
Inventory Management
Economic Order Quantity Models
Shortages Model
Economic Order Quantity Models
Shortages Model
• The assumptions of our basic EOQ model is
that shortages and back ordering are not
allowed
• The EOQ model with shortages relaxes the
assumption that shortages cannot exist.
• However, it will be assumed that all demand
not met because of inventory shortage can be
back ordered and delivered to the customer
later.
Economic Order Quantity Models
Shortages Model
The EOQ model with Shortages
Economic Order Quantity Models
Shortages Model
• Because back-ordered demand, or shortages,
(S), are filled when inventory is replenished,
the maximum inventory level does not reach
Q, but instead a level equal to Q - S.
• Therefore, the cost associated with shortages
has an inverse relationship to carrying costs.
• As the order size, Q, increases, the carrying
cost increases and the shortage cost declines.
Economic Order Quantity Models
Shortages Model
Cost model with shortages
Economic Order Quantity Models
Shortages Model
• The individual cost functions are provided as
follows, where S equals the shortage level and
Cs equals the annual per-unit cost of shortages:
Economic Order Quantity Models
Shortages Model
• Combining these individual cost components
results in the total inventory cost formula:
Economic Order Quantity Models
Shortages Model
• The three cost component curves do not
intersect at a common point, as was the
case in the basic EOQ model.
• As such, the only way to determine the
optimal order size and the optimal shortage
level, S, is to differentiate the total cost
function with respect to Q and S.
Economic Order Quantity Models
Shortages Model
• Set the two resulting equations equal to zero,
and solve them simultaneously.
• Doing so results in the following formulas for the
optimal order quantity and shortage level:
Economic Order Quantity Models
Shortages Model Example
• Assume that the I-75 Carpet Discount Store
allows shortages and the shortage cost, Cs, is
$2 per yard per year.
• All other costs and demand remain the same
Economic Order Quantity Models
Shortages Model
• Several additional parameters of the EOQ model with
shortages can be computed for this example, as follows:
• The time between orders, identified as t in is computed
as follows:
Economic Order Quantity Models
Shortages Model
• The time during which inventory is on hand, t1, and the
time during which there is a shortage, t2, during each
order cycle can be computed using the following
formulas: