Question

Following information in an inventory problem is available:
Annual demand 8,400 units
Unit price (`) 2.4
Ordering cost (`) 4.0
Storage cost (`) 2%
Interest rate 10% p.a.
Lead time 1/2 month
Calculate EOQ, Reorder level and total annual inventory cost. How much does the total inventory
cost vary if the unit price is changed to `5 ?

Answer 1

Economic Order Quantity should be 1183.216 units.

Re-Order Level should be 8158.392 units.

Total Inventory Cost should be Rs. 20,216.84.

Variation in Total Inventory cost if price per unit is changed to 5 should be 21865.16

Explanation:

In the given question,the following information has been provided,

Annual demand of item(A) = 8400 units

Price per unit = Rs. 2.4

Ordering cost per order (O)= Rs.4

Carrying/Storage Cost (C) = 2% of Price per unit

Interest Rate = 10% p.a

Lead Period/Lead time = 0.5 months

1) Calculation of Economic Order Quantity (EOQ):

EOQ = $\sqrt{} 2 \times A \times O / \sqrt{} C$

        = $\sqrt{} 2 \times 8400 \times 4 / \sqrt{} 2.4 \times 0.02$

           = 1183.216 units

2) Calculation of Re-Order Level(ROL):

        ROL= Buffer stock level + [ Normal/Average Usage + Normal Lead time]

Now,In order to calculate ROL we will have to calculate Buffer stock level first.

Since there is no information about the Maximum or Minimum Stock level therefore we will take Average Stock level as 8400 units.

Now,

Average Stock level = Buffer stock level + $\dfrac{1}{2} \times Re order quantity$

                                        $8400 = \dfrac{1}{2} \times 1183.216$ + Buffer stock level

                                     

                                        $8400 \times 2 = 1183.216 + 2\times$Buffer stock level

                        Buffer stock level = 7808.392

Now,

ROL = $7808.392 + [ 8400 \times \dfrac{1}{12} \times \dfrac{1}{2} ]$

       = 8158.392 units          

3) Calculation of Total Inventory Cost :

      Total Inventory Cost = Total Purchase cost + Total Relevant cost

                                           = Total Purchase cost + $\sqrt{} 2\times A\times O \times C$

                                           = $[ 8400 \times 2.4 ] + [ \sqrt{} 2 \times 8400 \times 4 \times 0.048 ]$            

           

                                           = 20160 + 56.794

                                            = 20216.794

Part 2:       Calculation of Variation in Total Inventory cost if Price per unit       changes to Rs.5        

EOQ = $\sqrt{} 2 \times 8400 \times 4 / \sqrt{}5 \times \dfrac{2}{100}$

         =820.3469

$2 \times$Buffer stock level = Average stock level - EOQ

                                  = $8400 \times \dfrac{1}{2} - 820.3496$

    Buffer stock level     = 3379.65

ROL = $3379.65 + [ 8400 \times \dfrac{1}{24} ]$

         =  3729.65

Total Inventory cost = $8400 \times 5 + \sqrt{} 2\times 8400 \times 4 \times 0.1$

                                   = 42082

Therefore,Variation in Total Inventory Cost = $42082 - 20216.84$

                                                                         = 21865.16