Question

The manager of a company is facing an inventory problem with regard to an item whose demand is known to be evenly distributed with an annual value of
8,000 units. The cost of placing an order is Rs 50 while the annual carrying cost of one unit in inventory is Rs 5. Further it is known that the lead time is uniform and equals 8 working days and that the total working days in a year is 320 days.
Using the present information, determine:
When stock-outs are not permitted
(i) The economic order quantity, EOQ;
(ii) The optimum number of orders per annum;
(iii) The total ordering and holding cost associated with the policy of ordering an amount equal to the EOQ;
(iv) The reorder level;
(v) The number of days’ stock at reorder level;
(vi) The length of the inventory cycle;
(vii) The amount of savings that would be possible by switching to the policy of ordering the EOQ determined in (i) from the policy of ordering the
requirements of this part four(4) a year; and
(viii) The increase in the total cost associated with the ordering (1) 20% more and (2) 40 % less than the EOQ.
When stock-outs are permitted
(ix) Because of high carrying cost, the manager is planning to have stock-outs but does not want to lose customer goodwill. He has determined that the unit shortage cost is Rs 10. Using the present information,determine,
(1) The optimal order quantity;
(2) The maximum level of inventory;
(3) The optimum number of shortage units;
(4) The total inventory cost involved with this policy, and
(5) Represent graphically the inventory profile for the first three cycles.

Answer 1

(i) Ans:- Economic order quantity = square root of [(2 x demand x ordering costs) ÷ carrying costs]

= square root of (2*8000*50)/5 = 400

(ii) Ans:- Optimum number of orders per annum = Annual demand / EOQ = 8000/400 = 20

(iii) Ans:- Total ordering cost = Optimum number of orders per annum*cost of placing an order

= 20*50 = Rs. 1000

Total holding cost = Optimum number of orders per annum*Annual carrying cost

= 20*5 = Rs. 100

(iv) Ans:- Reorder Level = Lead Time in Days × Daily Average Usage = 8*(8000/320) = 200