INVENTORY THEORY

The word inventory refers to any kind of resource that has economic value and is maintained to fulfil
the present and future needs of an organization.

Resources may be classified into three broad categories:

(i) physical resources such as raw materials, semi-finished goods, finished goods, spare parts,
lubricants, etc.,

(ii) human resources such as unused labour (manpower)

(iii) financial resources such as working capital, etc

REASONS FOR CARRYING INVENTORY

Improve customer service An inventory policy is designed to respond to individual customers and/
or organizations request for products or services in an instantaneous manner.

Reduce costs Inventory holding (or carrying) costs are the expenses that are incurred for storage of
items. However, holding inventory items in the warehouse can indirectly reduce operating costs such
as loss of goodwill and/or loss of potential sale due to shortage of items. It may also encourage
economies of production by allowing larger, longer and more production runs.

Maintenance of operational capability The inventory of raw material and work-in-progress items
act as buffer between successive production stages so that downtime in one stage does not affect
the entire production process.

Irregular supply and demand Any unexpected change in production and delivery schedule of a
product or a service adversely affect operating costs and customer service level. Hence, an optimum
level of inventory and efficient delivery schedules improves customer service level by meeting
customer’s demand.

Quantity discounts Large size replenishment orders help to take advantage of price-quantity
discount. However, such an advantage must keep a balance between the storage cost and costs due
to obsolescence, damage, theft, insurance, etc. Investment on large stock of inventory due to bulk
purchase, reduces cash that can be used for other purposes.

Avoiding stockouts (shortages) Under situations like, labour strikes, natural disasters, variations in
demand, and delays in supplies, etc., inventories act as buffer and provide protection against
reputation of constantly being out of stock as well as loss of goodwill.
Purchase cost
This cost is the actual price per unit (in Rs) paid for the procurement of items. The price per
unit, C of an item is independent of the size of the quantity ordered or purchased (or manufactured).

The purchase cost is given by:

Purchase cost = (Price per unit) × (Demand per unit time) = C.D

Further,
Purchase cost = Price per unit when order size is Q × Demand per unit time
= C(Q) . D

Carrying (or holding) cost

The inventory cost incurred for carrying (or holding) inventory items in the warehouse is referred as
carrying cost.

Carrying cost can be determined by two different ways:

(a) Carrying cost = (Cost of carrying one unit of an item in the inventory for a given length of time,
usually one year) × (Average number of units of an item carried in the inventory for a given length of
time)

(b) Carrying cost = (Cost of carrying one rupee’s worth of inventory for one year) × (Rupee value of
units carried)

Ordering (or set-up) cost

The inventory cost incurred each time an order is placed for procuring items from the vendors is
referred
as ordering cost

Ordering cost = (Cost per order/per set-up) × (Number of orders/set-ups placed in the given period)

Shortage (or stock out) and customer-service cost

The shortage occurs when inventory items cannot be supplied due to delay in delivery or demand
becomes more than the expected demand. The shortage can be viewed in two different ways:

(i) Customers are ready to wait for supply of items, (back ordered): In this case there is no loss of
sale but the nature and magnitude of back ordering cost, extra paper work and expenses incurred
in processing the order is not exactly known.

(ii) Customers are not ready to wait for supply of items: In this case, an organization may suffer with
a loss of customer goodwill and therefore causes loss of sale. The loss of goodwill is expected to
increase in proportion to the length of the delay, and causes decline in the growth of business due
to loss of potential revenue.

Shortage cost in a given period may be calculated as follows:

Shortage cost = (Cost of being short one unit of an item) × (Average number of units short)

The average number of units short in a given period is determined as follows:

Average number of units short =([{Minimum shortage}+{Maximum shortage}]/2)x(Period of shortage)

Total inventory cost
If price discounts are offered, the purchase cost per unit becomes variable,and
depends on the quantity purchased. In such a case, the total inventory cost is calculated as follows:

Total variable inventory cost (TVC) = Purchase cost + Ordering cost + Carrying cost + Shortage cost

But, if price discounts are not offered, the purchase cost per unit of an item remains constant and is
independent of the quantity purchased, then the total inventory cost is calculated as follows:

Total inventory cost (TC) = Ordering cost + Carrying cost + Shortage cost

Demand
The size of demand refers to the number of units of the item required in each period (cycle or
season)
The pattern of demand is the manner in which inventory items are required by the customers

Order cycle
The order cycle is the time period between two successive replenishments
it may be determined in one of the following two ways:

1. Continuous Review: In this case, the number of units of an item on hand are known and an order
of fixed size is placed every time the inventory level reaches at a pre-specified level, called order
point or reorder level. This decision rule is also referred to as the two-bin system, fixed order size
system or Q-system.

2. Periodic Review: In this case the orders are placed at equal intervals of time, but the size of the
order may vary depending on the inventory on hand as well as on order at the time of the review.
This decision rule is also referred to as the fixed order interval system or P-system.

Stock replenishment
The replenishment of stock may occur instantaneously or gradually. Instantaneous
replenishment is possible when the stock is purchased from outside sources, while gradual
replenishment is possible due to a finite production rate within the firm.

Lead time or (delivery lag)

The delivery of the items ordered may not reach instantaneously (immediately). The time delay
between placing an order and receipt of delivery is called delivery lag or lead time. In general, the
lead time may be deterministic or probabilistic.

Economic Order Quantity

The, EOQ is the optimal replenishment order size (or lot size) of inventory item (or items) that
achieves the optimum total (or variable) inventory cost during the given period of time.
List of symbols used We shall use the following symbols for the development of various inventory
models discussed in this chapter. The brackets indicate the unit of measurement of each of them.

C = purchase (or manufacturing) cost of an item (Rs per unit)

C0 = ordering (or set-up) cost per order (Rs per order)
r = cost of carrying one rupee’s worth of inventory expressed in terms of per cent of rupee value
of inventory (per cent per unit time)
Ch = C ⋅ r = cost of carrying one unit of an item in the inventory for a given length of time (Rs per
item per unit time)
Cs = shortage cost per unit per time (Rs per unit time)
D = annual requirement (demand) of an item
Q = order quantity (units) per order
ROL = reorder level (or point) at which an order is placed
LT = replenishment lead time (delivery time or period)
n = number of orders per time period
t = reorder cycle time (time period), i.e. time interval between successive orders to replenish
inventory stock.
tp = production period (time)
rp= production rate (quantity per unit time) at which quantity Q is added to inventory
TC = total inventory cost (in Rs)
TVC = total variable inventory cost (in Rs)