A manufacturing company has determined from an analysis of its accounting and production data for a certain part that :
a. Its demand is 9000 units per annum and is uniformly distributed over the year,
b. Its ordering cost is RS. 40 per order,
c. The inventory carrying charge is 0 percent of the inventory value.

Further it is known that the lead time is uniform and equals 8 working days and that total working days in a year are300.

Determine :

1. The economic order quantity EOQ :

2. The optimum number of orders per annum:

3. The total ordering and holding cost associated with the policy of ordering and amount equal to EOQ.

4. The re order level.

5. The number of days stock at re orders level.

6. The length of the inventory cycle.

7. The amount to savings that would b possible by sitching to the policy of ordering EOQ determined in ( i) from the present policy of ordering the requirements of this part thrice a year and .

8. The increase in the total cost associated with ordering ( a) 20 percent more ( b) 40 percent less than the EOQ.

Solution:

We are given that s = 9000 units / year Rs. 40order , I = 0.09 c, = Rs 2 unit
H = i x c = 0.09 x 2 = 0.18
Also lead time 8 working days and total working days in the year = 300 .

1. EOQ Q * = 2AD / 2 = 2x 40 xx 9000x/x0.18 = 2000 units

2. Optimum number of orders per year , N = D / Q * = 9000/2000= 4.5

3. Total variable cost T ( Q * ) = 2ADh = 2x 40x 9000x 0.18x= Rs. 360

4. Te order level = lead time in days x demand per day
= 8 x 9000/ 300 = 240 units.

5. Number of days stock at the re order level = 8 ( equal to lead time )

6. Length of inventory cycle T *= Q * / D = 2000/ 9000= 0.222year or 0.222 x 3000= 66.7days

Alternatively T * ( in days ) Q * demand per day = 2000/ 30 = 66.7 days

7. For the present policy of an order quantity = 3000 units.

Ordering cost = 40x 3 = Rs. 120

Holing cost = 3000/ 2 x 0.18 = Rs. 270

T 3000= 120+270= Rs 390

Thus saving in cost = Rs 390 - Rs 360 = Rs. 30 per year.

8. Ordering 20% higher than EOQ:

Ordering quantity = 120/ 100= 2400 units

With Q * = 2000 and Q = 2400 k = 2400/ 2000= 1.2

We have T (Q)/ T (Q*) = 1 / 2 ( 1/ K + k ) ( 1/ 1.2+ 1.2 ) = 61/ 60

Thus the cost would increase by 1/ 60 the or 360 x 1/ 60 = Rs. 6

Ordering 40 % lower than EOQ :

In such a situation k = 0.60 and T (Q) / T (Q*) = 1/ 2 ( 1/0.60+ 0.60) = 17/15

Thus the increase in cost would be 2 / 15 over the cost for EOQ and would equal 360 x 2 / 15 = RS 48 .