Operation Research, Inventory control, EOQ, ABC analysis

1. Operation research
Inventory Control
Introduction
Holding cost or Carrying cost
Derive : Economic order quantity (EOQ)
Example
ABC Analysis

2. Introduction
Inventory control
The term is generally used to indicate raw material, work-in-
progress (intermediate good), finished goods, packaging material
and other stock
Inventory Decisions
The following are the decisions made for every item of inventory.
i) How much amount of an item should be ordered when the
inventory of that item is to be restored.
ii) When to restore the inventory of that item

3. Holding cost or Carrying cost
Costs associated with carrying or holding goods in stock is known as
carrying or holding cost which is denoted by Ch per unit of goods for
a unit of time, respectively. However cost is assumed to be varying
directly the size of inventory as well as the time for which the item
is in stock.

4. The following components constitute the holding cost.
i) Invested capital costs (Interest charged on capital investment)
ii) Record keeping and administrative costs
iii) Handling cost:- It includes all costs associated with movement of stock
such as cost of labour, overhead and other machinery required for this
purpose.
iv) Storage cost: - This involves the rent of storage space or depreciation
in interest even if own space is used.
v) Depreciation, deterioration or obsolescence cost: - Such cost is due to
the item in stock being out of fashion or the item undergoes chemical
changes during storage (e.g. rusting of iron), breakage and spoilage.
vi) Insurance cost
Carrying cost= (Cost of carrying one unit of item) x (Average number of units
carried)

5. Economic order quantity (EOQ)
Definition and explanation
Economic order quantity (EOQ) is the order size that minimizes the sum
of ordering and holding costs related to raw materials or merchandise
inventories.
In other words, it is the optimal inventory size that should be ordered
with the supplier to minimize the total annual inventory cost of the
business.
Other names used for economic order quantity are optimal order size
and optimal order quantity.

6. The ordering and holding costs
The two significant factors that are considered while determining
the economic order quantity (EOQ) for any business are
the ordering costs and the holding costs.

7. A brief explanation of both the costs is given below:
Ordering costs
The ordering costs are the costs that are incurred every time an order
for inventory is placed with the supplier. Examples of these costs include
telephone charges, delivery charges, invoice verification expenses and
payment processing expenses etc.
The total ordering cost usually varies according to the frequency of
placing orders.
Mostly, it is directly proportional to the number of orders placed during
the year which means If the number of orders placed during the year
increases, the annual ordering cost will also increase.

8. Holding costs
The holding costs (also known as carrying costs) are the costs that are
incurred to hold the inventory in a store or warehouse.
Examples of costs associated with holding of inventory include occupancy
of storage space, rent, shrinkage, deterioration, obsolescence, insurance
and property tax etc.
The total holding cost usually depends upon the size of the order placed
for inventory. Mostly, the larger the order size, the higher the annual
holding cost and vice versa. The total holding cost is some time expressed
as a percentage of total investment in inventory.

9. Question : Derive Equation Of EOQ
The economic order quantity is the level of quantity at which the
combined ordering and holding cost is at the minimum level.
Relation between the ordering and holding cost:
There is an inverse relationship between ordering cost and holding
cost. Keeping the annual demand constant if for example the
number of orders decreases, the ordering cost will also decrease
but the holding cost will rise and vice versa.

12. At EOQ POINT Both cost are equal
( D/Q ) Co = ( Q/2 ) Ch
Q2 = (2DCo ) / Ch
Where,
D = Demand per year
Co = Cost per order
Ch = Cost of holding per unit
of inventory

13. Total annual Carrying cost = (Average Inventory) * (Carrying cost/unit/year)
= (Q/2) * Co
Total annual Ordering Cost = (Optimal number of orders in a year) * (Ordering
cost/order) = (D/Q) * Ch
Minimum Total annual Variable Cost = TVC =
= Total annual Ordering Cost + Total annual carrying cost
= (Q/2) * Co + (D/Q) * Ch
Cost of Material Per year = Annual Demand * Price of Material = D*C

14. Total Cost TC = DC + TVC

16. Example: 1
The material is used uniformly throughout the year. The data
about annual requirement, ordering cost and holding cost of this
material is given below:
Annual requirement: 2,400 units
Ordering cost: $10 per order
Holding cost: $0.30 per unit
Determine
1) The economic order quantity (EOQ) of material,
2) Number of orders per year,
3) Reorder cycle time,
4) Combined ordering and holding cost,

17. Solution
EOQ =

18. N=D/EOQ
Where N=Number of orders per year
N= Annual demand/EOQ
N= 2,400 units/400 units
N= 6 orders per year
Reorder cycle time t = EOQ/D =400/ 2400= (1/6) year
= 12months/6
= 2 Months
Ordering cost Co
= Number or orders per year × Cost per order
= 6 orders × $10
= $60

19. Holding cost
= Average units × Holding cost per unit
= (400/2) × 0.3
= $60
Combined ordering and holding cost at economic order quantity
(EOQ):
= Ordering cost + Holding cost
= $60 + $60
= $120
Notice that both ordering cost and holding cost are $60 at economic
order quantity. The holding cost and ordering cost at EOQ tend to be
the same.

20. Example: 2
A company uses 3000 units of a product, its carrying cost is
30%of average inventory. Ordering cost is Rs. 100 per order.
Unit cost is Rs. 20.
Calculate
EOQ and the total cost.
Solution
D = Total Demand=3000 units
Ch = carrying cost =30% of Rs. 20=Rs.6
Co = Ordering cost =Rs.100

21. Optimum lot size is
EOQ =
The total cost is equal to
Total cost = Material cost + Total variable cost
=DC + TVC
= Rs. 61897 .36

22. The production department for a company requires 3600kg.of row
material for manufacturing a particular item per year. It has been
estimated that the cost of placing an order is Rs.36& the cost of carrying
inventory is 25 percentage of the investment in the inventories. The price
is Rs.10 per kg. The purchase manager wishes to determine an ordering
policy for raw material.
Calculate
a. The optimal lot size, EOQ
b. The optimal order cycle time
c. The minimum yearly variable inventory cost
d. The minimum yearly total inventory cost
Example: 3

26. Question : Discuss ABC Analysis

27. Classification of Inventory in ABC analysis