Financial Management & Cost Accounting

Module 7. Inventory management

Lesson 39
TECHNIQUES OF INVENTORY MANAGEMENT

39.1 Techniques of Inventory Management

In order to achieve the goal of maintaining optimum level of inventories in a firm and ensuring that inventories are managed efficiently and effectively. Several inventory management techniques have been suggested. The main techniques are

1) EOQ model

2) ABC analysis

3) HML classification

4) SDE classification

5) VED classification

6) FSN Analysis

7) JIT (Just-in-Time)

8) Inventory turnover ratio

39.2 Economic Order Quantity (EOQ MODEL)

Before learning the EOQ model, it is necessary to understand the different types of costs in context of inventory.

EOQ Model

Main Assumptions are as follow

1) The annual demand (or annual usage) of the material is certain and known in advance.

2) The rate of usage of material is constant throughout the year (e.g. the usage rate does not fluctuate).

3) There are only two costs Ordering Cost and Holding Cost.

4) There is no Shortage Cost.

5) The price per unit of the material is constant.

6) The Ordering cost per order is constant.

7) The holding cost per unit per annum is constant.

Let,

Q = Order Size or Order Quantity

D = Annual demand or annual usage

S= Ordering Cost per Order or Cost of one Order

H= Holding cost per unit per annum (e.g. the cost incurred behind storage of one

Unit of an item for one year)

Holding Cost is expressed in two ways

a) Rs. 20 per unit per annum.[p.u.p.a]

b) As a percentage of price (or inventory value)

i = Percentage cost of inventory (%)

p = Price per unit of item

H= i p

(For example, if percentage carrying cost of an item is 24% p.a and its price per unit is Rs 100 then holding cost H= 0.24 x 100= Rs 24 )

1) Ordering Cost

Annual Ordering Cost = {Cost of one order}x{No of order during the year}

Annual O.C= S x (D/Q) (We can see that the relationship between ordering cost and order size is Inverse, E.g. if the order size Q increases, ordering cost decreases and vice Versa) Consider the following,

D=1200 units

S= Rs 50 per order

Order Size	No of Orders	Ordering Cost
100 units	12 Order	50x12=600
200 units	6 Order	50x6=300
600 units	2 Order	50x2=100

As order size Q increases, the ordering cost decreases.

2) Holding Cost

Annual Holding = {Cost of holding one unit for one year}x{Average Inventory}

H.C = H x (Q/2)

(Note: Average Inventory has been taken as Q/2)

Clearly, as order quantity Q increase the holding cost also increases.

Considering that there are only two (Variable) costs w.r.t inventory,

Total Inventory cost= Annual Ordering Cost+ Annual Holding Cost

The goal of a inventory manager is to try to minimize this total inventory cost.

Graphical Presentation of inventory costs and order quantity:

Fig. 39.1 EOQ model

From the Figure 39.1, it can be seen that,

Total inventory cost is Lowest, at the point where D.C and H.C Intersect. At the point of intersection total inventory cost is minimum, also.

O.C = H.C

(D/Q) x S= (Q/2) x H

Q² = (2DS)/H

(This order quantity which minimize the total inventory cost is called Economic Order Quantity)

(Note: The equation for EOQ can also be dived in the following manner).

Total annual cost of Inventory= Annual purchase cost+ Annual ordering cost+ Annual holding cost

T.C= {Annual demand x Price per unit} + {Cost of one order x No of orders during the year}+{ Cost of holding one unit for one year Average inventory}

T.c = (D x P) + ((D/Q) x S) + (H x (Q/2))

In order to minimize this equation, we have to differentiate it w.r.t

(DTC/dQ)= O+ {-DS/Q²} + {H/2}

OO= ({-DS/Q²) + (H/2)

The annual demand of electric switches in ABC LTD is 50,000 switches. If the ordering cost per order is Rs. 100 and carrying cost per unit per annum is Rs. 25, then find

a) EOQ

b) Annual ordering cost

c) Annual holding cost

d) Average Inventory

e) Number of order during the year

Solution:

D= 50,000 units

H= Rs 25 per unit per annum

S= Rs 100

a) EOQ= 632.455 units

b) Average Inventory = 632.455/2 = 316 units

c) No of orders = D/Q = 50,000/633 = 79 orders

Ordering Cost and Holding Cost

d) O.C = (D/Q) x S = (50,000/632.455) x100 = Rs 7905

Hence, at EOQ we find O.C=H.C

For Komfort ltd, the annual demand of an item is 75,000 units. The cost of placing one order for the company comes to Rs 35 per order. The price per unit of the item is Rs.5000 and the inventory carrying cost is 2% per months.

a) Find EOQ, O.C, H.C, Average inventory, Number of Orders

b) If the supplier is willing to give 10% discount in price, if orders are placed in the size of 100 units. Should the company accept the discount or should it stick to its EOQ?

Solution:

Annual Demand D= 75,000 unit

Ordering cost = Rs 35 per order

Percentage carrying cost = 2% per month

Percentage carrying cost = 2% x 12 = 24% per annum

Note: All costs, ordering and Holding cost are to be expressed on annual basis.

P= Rs 5000 per unit

EOQ= 66.14 units

Average Inventory= Q/2 = 66.14/2 = 33.07

Number of order during the year = D/Q = 75,000/66.14= 1133.89 order= 1134 orders

O.C= (D/Q) x S = (75,000/66.14) x 35 = Rs. 39,688

H.C = (Q/2) x H = (Q/2) x i x P = (66.14/2) x 0.24xx 5000 = 39,688

The company is faced with two choices 1) Either to place orders at economic order size Q=66.14 units or 2) place orders in size of 100 units and get 10% discount in price.(Discount condition)

Answer

One thing to be kept in mind is that the goal of inventory manager is to minimize the total cost of inventory T.C. Hence the solution is clear, that orders should be placed at order quantity which gives the lowest cost of inventory. We have to find the total inventory cost T.C. for order size Q=66.14 unit and T.C at discount condition

P=5000 x 0.9= Rs. 4500 per unit

1) Total inventory Cost T.C at EOQ

T.C _EOQ= Annual Purchase Cost + Annual ordering Cost+ annual holding cost

T.C _EOQ = (D x P) + ((D/Q) x S) + ((Q/2) x H)

= (D x P) + ((D/Q) x S) + ((Q/2) x iP)

= (75000 x 5000) + ((75000 x 35)/66.14) + ((66.14/2) x 0.24 x 5000)

= 37, 50, 00,000+39,687+39,687

=Rs. 37, 50, 79,372.44

2) T.C Discount

Discount Conditions are

When Q= 5000 units

P=Price=4500 per unit

T.C _Discount = DP + ((D/Q) x S) + ((Q/2) x i x p)

= (75000x4500) + ((75000x35)/100)+((100/2)x0.24x4500)

= 33, 75, 00,000+26,250+54,000

= Rs. 33, 75, 80,250

T.C _Discount Rs. 33, 75, 80,250 < T.C _EOQ 37, 50, 79,372

As T.C _Discount is less than T.C _EOQ the company should accept the discount and the optimum order size is 100 units