Inventory Control Guide Page 5
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402.2 Parameters
Before trying to build any model for controlling the inventories, let us first review and formalize
all the actors of the play.
Demand
D
( item / time )
The first data is the demand. The choice of the time unit is arbitrary, but it must be clear. We
will consider different kinds of demand.
constant / variable
A demand equal to 100 items per month, for each month, is said to be constant.
A known demand of 100 items for January, 200 items for February and 150 for March is said
to be variable. When computing the aggregated plan, a variable demand was considered.
random (σ≠0) / deterministic (σ= 0)
The demand is said to be deterministic if it does not admit any variation. If the monthly
demand is 100 items, then it will be 100 each month if it is deterministic. Otherwise, the
demand is random and the value 100 gives only the average demand.
In this section, we will consider constant demand only, with deterministic or random
distribution. Variable demand is considered when considering other lot sizing techniques.
We will always use σ to denote the standard deviation of the demand.
Lead time
Lt
( time )
The lead time is defined as the time between the moment an order is placed (at a supplier or
at a shop) and the moment the items are delivered. It could also be random.
time between order and reception
If you order from a supplier, the lead time comprises at least the order processing time, the
picking and packing time, the transport time and the reception time. Must also be added all the
waiting times: for the picking and packing and for the transport. If your supplier is short of the
items you ordered, you must also add the time for replenishing the inventory of the supplier.
If you launch a production order, the lead time comprises at least the picking of all the raw
materials, the waiting time in front of the first shop, the processing time of the complete lot in
the shop, the waiting for transportation facilities and the transportation to the stores. Note that
the cycle ( waiting time in front of a shop, processing time in the shop, waiting for transport
and transport ) must be accounted for each visited shop.
Review time :
Rt
( time )
time between two checking points
With permanent review, the inventory is checked permanently, that is an order decision can
be placed at any time. This could be too expensive. A cheaper solution consists in checking
the inventory periodically only. The review time is the time between two successive checks. If
you check only every Friday, then Rt = 1 week.
unsatisfied demand
What happens to the orders which cannot be satisfied must be clearly specified. If there is no
more inventory when an order is placed, the customer can just go to another shop. This is the
lost sales model. He could also wait patiently for the items to arrive. This is the backorder
model. Intermediate models exist where the customers loose patience with time. In each
model, an unsatisfied demand generates a cost.
lost / customer impatience / backorder
Prod 2100-2110
Inventory Control
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