Inventory Systems For Independent Demand
Inventory Systems For Independent Demand
Inventory Systems For Independent Demand
Chapter 15
Inventory Systems for Independent Demand
Definition of Inventory
“Inventory” is the stock of any item, or resource used in an organization. Inventory or
stock refers to the materials or components that an organization needs mainly for
production purpose. However, after production, finished goods may also be kept as
inventory up to a certain period before sending those to distribution centers.
On the other hand, an “Inventory System” is the set of policies and controls that monitors
the levels of inventory and determines –
Inventory management is primarily about specifying the size and placement of stocked
goods in warehouses at different locations within a facility. Inventories are maintained as
buffers to meet uncertainties in demand, supply and movements of goods. While
manufacturers stock is kept in warehouse, retailer‟s inventory is kept in the shop.
Generally, retailers stock-keeping ability is very low. Inventory links –
1) Raw materials – Purchased raw materials from suppliers which are used to
produce products.
2) Finished good – The final products which are sold to the customers
3) Component parts – Inputs mainly required in assembly industries
4) Office Supplies – To run the administrative and support activities
5) Work-in-Process (WIP) – semi-finished or partially processed materials, which
are neither raw material, nor finished good.
6) Maintenance stock – Often quite good amount/numbers of spare parts are stocked
for maintenance
7) Pipeline inventory – It is the inventory which is on the way for shipment to
manufacturer from supplier. It is no more considered as part of the total stock of
supplier, rather a stock for the manufacturer (or, recipient). Pipeline inventory is
also known as in-transit stock.
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Dr. M. Ahsan Akhtar Hasin, IPE, BUET.
Demand Types
In inventory management, it is important to understand the difference between two types
of demand:
1. Independent demand
2. Dependent demand
Independent demand – If demand of an item does not depend on demand of other items,
then it is independent demand. Generally, finished good items (the first level of
BOM) have this kind of demand. E.g. Computer, Television, Bicycle, etc. Demands
of these products are forecasted. This chapter deals with independent demand.
Inventory Costs
A major objective of inventory management is to keep its total inventory cost minimum.
Appropriate lot size of procurement depends on these cost elements. These are:
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Dr. M. Ahsan Akhtar Hasin, IPE, BUET.
Inventory Models
There are two general types of inventory systems or models.
1) Fixed Order quantity model – In each order, a fixed quantity is bought, time interval
between two successive orders may be different. It is “event triggered”. That is,
this model initiates an order when the event of reaching a specified reorder level
occurs. It requires regular monitoring or checking of inventory levels. Once it
goes down to a certain minimum level (called Re-order Point – ROP), it is
ordered again. That‟s why this is also called Perpetual system, which requires
that every time a withdrawal from inventory is made, immediately its remaining
stock needs to be counted to see if it has reached RoP level. This requires that
inventory records be updated on a regular basis. A common such model is
Economic Order Quantity (EOQ) model, which literally means “an order
quantity which is most economical”, as far as Total Inventory cost per year is
concerned.
2) Fixed Time Period model – This model is limited to placing orders at the end of a
predetermined time period. Materials are ordered at a regular time interval;
quantity in an order may vary depending on amount of on-hand stock. Here,
regular counting is not that important. This is known as Periodic system.
As regular and close monitoring takes place in a fixed order quantity model, this ensures
timely submission of order to reduce stockout probability, unless there is uncertain
fluctuation of demand. It is also appropriate for important items such as critical repair
parts, because there is regular and closer monitoring which ensures quicker response to
potential stockout. This chapter discusses Economic Order Quantity (EOQ) model, which
is a Fixed Order Quantity model, in detail.
Fixed Order Quantity models, specifically EOQ, attempt to determine the specific point
RoP (or, R), at which the next order will be placed and the size of the order will be EOQ
(or, Q). This RoP is equivalent to Lead Time (of procurement, or purchasing lead time),
when expressed in terms of “time L” (e.g. days). It means that the process of next order
(Re-order) should be started L days in advance, before the stock goes to zero.
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Dr. M. Ahsan Akhtar Hasin, IPE, BUET.
1. If an organization buys in large lots (i.e. order size Q becomes large), then
number of orders per year will be low, and thus ordering cost per year will be low.
However, because of large-lot procurement, average on-hand inventory will be
higher for longer-time consumption. This will increase holding cost. In
conclusion, while ordering cost goes down, holding cost goes up. Thus, these two
costs are conflicting.
2. If an organization buys in smaller lots ((i.e. order size Q becomes small), then
number of orders per year will be high, and thus ordering cost per year will
increase. However, because of small-lot procurement, average on-hand inventory
will be lower for shorter-time consumption. This will decrease holding cost. In
conclusion, while ordering cost goes up, holding cost goes down. Thus, again it is
found that these two costs are conflicting.
Total cost
Costs
Holding cost
Ordering cost
Purchase price or
material cost
EOQ Quantity/order
The consumption rate being uniform, the usage of materials and build-up of stock will
follow a “sawtooth” curve as follows:
Inventory
ROP (R)
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Dr. M. Ahsan Akhtar Hasin, IPE, BUET.
The „sawtooth‟ curve shows that when the inventory position drops to RoP level, the next
order (re-order) is placed. The materials will arrive after L days from then.
Total Inventory cost per year = Annual Purchase price + Annual Ordering cost + Annual
Holding cost
D Q
or, TC = DC S H ; where,
Q 2
D = Annual demand/requirement, C = Purchase price/unit,
Q = EOQ = Order quantity, S = Ordering cost/order ($/order),
H = Holding cost/unit/year (Sometimes expressed as percentage i of unit purchasing
price) = iC,
L = Purchasing Lead Time, R = Re-Order Point/level = d L (where, d is average
daily demand);
The second step in developing an inventory model is to find that order quantity for which
total cost is a minimum. Mathematically this can be obtained by differentiation of TC
(total cot) with respect to lot size Q. This will yield the following result:
2 DS
Total cost TC will be minimum, when EOQ Q
H
However, if lead time is uncertain, then extra stock is kept which is known as “Safety
Stock”. Safety stock must be maintained to provide some level of protection against the
risk of stockouts. The computation of safety stock is based on probability of statistics.
A 90% CSL value means that in 90% cases, customer orders or demands are met with on-
hand inventory. For the rest 10% chances of stockout, additional stock is built-up, which
is known as Safety stock. However, remember that additional stock means additional
holding cost, what the companies do not want.
In calculating the amount of safety stock, a company needs to take into account standard
deviation of demand, which requires Normal distribution of statistics.
As a simple alternative, several industries determine the approximate extra stock from
past experience, in terms of a percentage. Let‟s say, a company may decide to keep 10%
extra stock as a cushion to fluctuation of demand during lead time. If RoP without safety
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Dr. M. Ahsan Akhtar Hasin, IPE, BUET.
stock is 100 units, then safety stock would be (100×0.1 =) 10 units. This means that
revised RoP would be 110 units. That means that when the company has 110 units of
material on-hand, they have to re-order.
2 DS 2(1000 )(5)
EOQ Q = = 89.4 ≈ 89 units.
H 1.25
1000
ROP = d L = 5 = 13.7 ≈ 14 units;
365
D Q 1000 89
Total cost TC = DC S H = 1000(12.50) (5) (1.25) = 12,611 $ /year
Q 2 89 2
Notes:
1. If discount is given when buying large quantity (large lot size), then this method
is not applicable.
2. In case of determining production lot size (Economic Production Quantity –
EPQ), this method is not applicable.
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Dr. M. Ahsan Akhtar Hasin, IPE, BUET.
ABC Classification
In the 19th century, Villefredo Pareto (an Italian Economist), in a study of the distribution
of wealth in Milan (Italy) found that “About 80% of country‟s wealth is occupied by
about 20% of the people” and vice versa. This is known as Pareto Principle, and also as
80-20 rule.
Later on, it was found that this is true in our everyday lives, and certainly true in
inventory systems. Based on this, ABC classification of inventory is suggested. The ABC
classification scheme divides inventory items into three monetary groups: high dollar
value volume (A), moderate dollar volume (B), low dollar volume (C). A class items
would mean those items which are very low in quantity but very high in dollar value. On
the other extreme side, C class items are those which are very high in quantity, but have
very low dollar value.
% value 90%
70%
A B C
35%
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