Inventories are materials stored, waiting for processing,
or experiencing processing. They are ubiquitous in modern business.
Observation of almost any company balance sheet reveals that
a very significant part of its assets comprise inventories
of raw materials, products within the production process, or
Because of their practical and economic importance, the subject
of inventory control is a major consideration in many situations.
Questions must be constantly answered as to when and how much
raw material should be ordered, when a production order should
be released to the plant, what level of safety stock should
be maintained at a retail outlet, or how in-process inventory
is to be maintained in a production process. These questions
are amenable to quantitative analysis through the subject of
inventory theory. The Inventory Add-in add-in embodies some
of the mathematical results of inventory theory. The Inventory
Add-in is part of the OM/IE collection of the Jensen add-ins.
It is described at the website www.ormm.net.
This game simulates some of the stochastic systems considered
by the add-in and the subject of inventory theory.
We consider here an inventory
holding a single product as illustrated in the figure below.
The figure might represent a raw material inventory. The flow
out of inventory is a relatively continuous activity where
individual items are placed into the production system for
processing. To replenish the inventory, an order is placed
to a supplier. After some delay time, called the lead-time,
the raw material is delivered in a lot of a specified amount.
At the moment of delivery, the rate of input is infinite and
at other times it is zero. Whenever the instantaneous rates
of input and output to a component are not the same, the inventory
level changes. When the input rate is higher, inventory grows;
when output rate is higher, inventory declines.
Usually the inventory level remains positive. This corresponds
to the presence of on hand inventory. In cases where demand
exceeds the available inventory customers must either wait
or sales may be lost. When the customer is willing to wait,
we show the shortage as a negative inventory value. We call
this a backorder or shortage condition. A backorder is a stored
output requirement that is delivered when the inventory finally
becomes positive. Backorders are possible for some systems,
while they are not for others. A finished product inventory,
for example, may promise later delivery if a customer arrives
to find no product available. The will generally be extra costs
when inventory is backordered.
a customer with alternative suppliers may go elsewhere if he
or she finds the inventory empty. This is called a lost sale.
The inventory may go to zero, but will never be negative. The
demands on the inventory that occur while the inventory level
is zero are called lost sales. For most businesses, lost sales
are bad. There is generally a cost of goodwill suffered by
the disappointed customer. The cost is at least the value of
the profit foregone from a lost sale.