Inventory Management – Economic Order Quantity

The primary objective of a good inventory management system is to keep the inventory costs to the minimum. The three major elements of inventory cost are as below:

a) Ordering Cost

b) Storage Cost (cost of carrying inventory)

c) Stock-out Cost (cost of lost sales due to inventory shortages)

Several inventory models have been built based on the above. Below are the most commonly used inventory models

  1. Replenishment System
  2. Fixed Order Quantity System

Replenishment System

Under this system the quantity to be ordered is not fixed. Instead ordering time and maximum stock level for each material are fixed. There are frequent reviews of the stock. The quantity ordered is decided based on the lead time of the material, maximum stock level and the stock held on the date of review.

Fixed Order Quantity System

The quantity to be ordered is fixed under this method. Re-orders are made once the stock reaches a certain pre-determined level called ‘Re-order level’. This is typically fixed based on the average consumption during the lead time plus some buffer stock.

The best way to determine the fixed quantity to be ordered would be using the concept of Economic Order Quantity. This concept is designed in a manner to ensure that the overall inventory costs are lowest. In other words Economic Order Quantity (EOQ) is that quantity level to be ordered each time so as to keep the inventory costs to the minimum.

There are three alternate methods to determine the Economic Order Quantity namely

i) Algebraic method

ii) Tabular method

iii) Graphical method

Algebraic Method:

Two components of Inventory costs that are considered in computing the EOQ are ‘ordering cost’ and ‘storage cost’. With increase in lot size of purchases, the ordering cost decreases and storage cost increases. On the other hand with decrease in lot size of purchases, the ordering cost increases and storage cost decreases. EOQ deals with striking a balance between these two factors. The following algebraic formula is used to compute EOQ. 

EOQ = 2CO/S

Where C = Annual consumption of the material

           O = Ordering cost per order

           S = Annual storage cost per unit

The above formula has been derived as below

At EOQ, Total Ordering Cost = Total Storage Cost

i.e. (# of orders X Ordering cost per order) = (Avg units stored X Annual storage cost per unit)

(C / EOQ X O ) = (EOQ /2 X S)

Cross multiplying we would have (EOQ)2 = 2CO / S

Therefore, EOQ = 2CO/S

Example: From the following information determine the Economic Order Quantity of Material ‘X’

Consumption of Material ‘X’ per month – 500 units
Cost of placing an order – $ 40
Purchase price per unit of ‘X’ – $ 200
Storage cost – 1.5% per annum

Solution:

EOQ = 2CO / S

= 2 x (500×12) x 40 / 3 = 400 units

Note: S = $200 X 1.5% = $ 3

Tabular Method:

When there are quantity discounts offered by the supplier at different lot sizes purchased i.e. purchase price of material varies at different quantity levels, the tabular method is used to determine Economic Order Quantity. It is illustrated in the below example

Example: The supplier of Material ‘ABC’ has given the below quantity discount offer

Price per unit ($)                Units

120                                      Less than 250 units

118                                      250 and less than 800 units

116                                      800 and less than 2,000 units

114                                      2000 and less than 4,000 units

112                                     4000 units and above

Inventory carrying costs are 10% p.a. Order placing cost per order is $ 600. Annual consumption of the material is 4,000 units.

Compute the Economic Order Quantity

Solution:

Follow the below steps to find out EOQ under Tabular method

1) Pick up one lot size from each of the tiers. It is recommended to pick up a lot size that is an exact fraction of Annual Consumption

2) Compute the total inventory cost for each lot size picked

3) The lot size where the total cost is lowest would be the EOQ

Lot

 Size
(U)

Price

per unit

 (P)

Purchase

Cost
(X = C x P)

# of orders
(N = C / U)

Ordering

Cost
(Y = N x O)

Storage

 cost p.u

(S = P x 10%)

Storage Cost
(Z = U / 2 x S)

Total Cost
(X + Y + Z)

200

 $ 120

 $   480,000

20

 $  12,000

 $   12.00

 $         1,200

 $ 493,200

250

 $ 118

 $   472,000

16

 $    9,600

 $   11.80

 $         1,475

 $ 483,075

800

 $ 116

 $   464,000

5

 $    3,000

 $   11.60

 $         4,640

 $ 471,640

2000

 $ 114

 $   456,000

2

 $    1,200

 $   11.40

 $       11,400

 $ 468,600

4000

 $ 112

 $   448,000

1

 $       600

 $   11.20

 $       22,400

 $ 471,000

C = Annual Consumption of Material = 4,000 units

O = Ordering cost per order = $ 60

Sine the total cost at 2,000 units lot size is lowest, it is the optimal quantity to buy.

Comments

  1. Mr Aditya says:

    This has reference to point 1 … “It is recommended to pick up a lot size that is an exact fraction of Annual Consumption”

    my view is that one SHALL take a lot size that is an exact fraction of Annual Consumption …. otherwise No. of orders will be in fraction… where on can theoritically calculate EOQ but in practice one can not place orders in fraction.

    • Hi Aditya,

      Here are my thoughts / views

      For deciding on EOQ, I recommend picking up a lot size that would result in exact fraction of Annual Consumption (which would of course avoid fraction # of orders), we both have same view here.

      However, if we decide to continue keeping orders that are fraction in number and if the most economical lot size falls in that category (say 2.3 orders)….recompute the total cost by rounding the no. of orders upwards (i.e, 3 orders). Now, if the revised total cost is still the lowest of other options, the EOQ remains the same, else it would be the second best alternative as computed initially.

      Cheers!!

  2. Hi,

    For the computation of the storage cost, why do you divide the lot size per 2 ?

    Z = U / 2 x S

    Thanks !

    • @Thibaud…typically it is assumed that the rate of consumption of inventory is even throughout the period and the closing stock moving towards zero. Therefore, average inventory is considered equal to 50% of the goods purchased.

      Hence, average inventory in the given case is considered at half the lot size.

      Thanks

  3. AKPE SMART says:

    clssify the interlocking system of costing

  4. it is not giving in proper manner

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