1. 13. Deterministic Inventory Control Models
Introduction:
Inventory, in wider sense, defined as any idle resource of an enterprise. The word
inventory refers to any kind of resource having economic value and is maintained to fulfil
the present and future needs of an organization. Such resources may be classified into
three categories: (i) Physical resources such as raw materials, semi-finished goods,
finished goods, etc. (ii) human resource such as unused labour and (iii) financial resource
such as working capital, etc.
Types of Inventories:
1. Lot-size (or cycle) Inventories:
Lot-size (or cycle) Inventories exist whenever one produces (or buys) in larger
quantities than are needed to satisfy the immediate requirements.
2. Pipeline (or transit) Inventories:
These arise due to the fact that transportation time is involved in transferring
substantial amount of resources. For example, when coal is transported from the
coalfields to an industrial town by train, then the coal, while in the transit, cannot
provide any service to the customers for power generation or for burning in furnaces.
3. Buffer Inventories:
These are maintained to meet uncertainties of demand and supply. Such “buffer”
inventories which are in excess of those necessary to just meet the average demand
during the lead time (the time elapsing between placing the order and having the
goods in stock ready for use), held for protecting against the fluctuation in demand
and lead time are also termed as safety stocks
4. Seasonal (or Anticipating) Inventories:
Anticipation inventories are held for the reason that a future demand for the product
is anticipated. Production of specialized items like crackers well before Diwali,
umbrellas and raincoats before rains set in, fans while summers are approaching,
are all examples of anticipating inventories. Thus seasonal inventories are built up
in advance or procured during the period of low demand to be used in peak demand
period.
5. Decoupling Inventories:
If various production stages operate successively then in the event of breakdown of
one or any disturbance at some stage can affect the entire system. This kind of inter-
dependence is not only costly but also disruptive for the entire system. The
inventories used to reduce the interdependence of various stages of production
system are known as decoupling inventories.
Inventories Decision:
In any inventories controls situation there are three basic questions to be answered.
They are:
a. How much to order? That is to say, what is the optimal quantity of an item that
should be ordered whenever an order is placed?
b. When should the order be placed?
c. How much safety stock should be kept? Thus, what quantity of an item in excess of
the expected requirements should be held as buffer stock in anticipation of the
variations in demand and/or the time involved in acquiring fresh supplies?

2. Inventories Costs
Various costs associated with inventory control are often classified as follows:
a. Set-up cost:
This is the cost associated with the setting up of machinery before starting
production. Set-up cost is generally assumed to be independent of quantity ordered
for or produced.
b. Ordering cost:
This is a cost associated with ordering or raw material for production purposes.
Advertisements, consumption of stationery and postage, telephone charges, rent for
space used by purchasing department, traveling expenditures incurred, etc.
constitute the ordering cost.
c. Purchase (or production) cost:
The cost of purchasing (or producing) a unit of an item is known as purchasing (or
producing) cost. The purchase price will become important when quantity discounts
are allowed for purchases above a certain quantity or when economics of scale
suggest that the per unit production cost can be reduced by a larger production run.
d. Carrying (or holding) cost:
The carrying cost is associated with carrying inventories. This cost generally
includes the costs such as rent for space used for storage, interest on the money
locked-up, insurance of stored equipment, production, taxes, depreciation of
equipment and furniture used, etc.
e. Shortage (or stock out) cost:
The penalty cost for running out of stock (i. e. when an item cannot be supplied on
the customer’s demand) is known as shortage cost. This cost includes the loss of
potential profit through sales of items and loss of goodwill, in terms of permanent
losses of customers and its associated lost profit in future sales.
Other factors involved in inventories analysis:
Besides the costs that determine the profitability, other factor play an important role
in the study of inventory problems are the following:
a. Order Cycle
An ordering cycle is the time period between two successive placement of orders.
The ordering cycle may be determined in one of the two ways:
(1) Continuous review: In this case the level of inventory is updated
continuously as current level is reached at which point is reached (also
called reorder point) a new order is placed.
(2) Period review: In this case the orders are placed at equal interval of time,
but the size of the order may vary with the variations in demand.
b. Lead time or delivery tag
When an order is placed, it may require some time before delivery is reached. The
time between the placement of an order and its receipt is called delivery lag or lead
time.
c. Stock Replenishment
When the stock is purchased from outside sources, instantaneous replenishment
occurs; while uniform replenishment may occur when the product is manufactured
locally within the firm.

3. d. Planning Horizon (or period)
The time period over which the inventory level will be controlled is called the
period horizon. This horizon may be finite or infinite depending upon the nature of
the demand for the commodity.
ECONOMIC ORDER QUANTITY
The inventory problems in which demand is assumed to be fixed and completely
pre-determined are usually referred to as the Economic Order Quantity (EOQ) or Lot-size
problems. By the order quantity we mean the quantity produced or procured during one
production cycle. This is also termed as re-order quantity. When the size of order increases,
the ordering costs (cost of purchasing, inspection, etc.) will decrease whereas the inventory
carrying costs (cost of storage, insurance, etc.) will increase. Thus in the production process
there are two opposite costs, one encourages the increase in the order seize and the other
discourages. Economic Order Quantity (EOQ) is that size of order which minimizes total
annual costs of carrying inventory and cost of ordering.