Explanation
Optimal Order Size (EOQ):
- D = Annual demand (100,000 units)
- S = Ordering cost per order (Rs. 160)
- H = Holding (carrying) cost per unit per year (Rs. 2)
the optimal order size (EOQ) is 4,000 units.
(ii) Total Inventory Cost:
To find the total inventory cost, we can use the EOQ model’s total cost formula:
[Total Cost = {D}{EOQ} S + {EOQ}{2} H + D P]
Where:
- D = Annual demand (100,000 units)
- EOQ = Optimal order quantity (4,000 units)
- S = Ordering cost per order (Rs. 160)
- H = Holding (carrying) cost per unit per year (Rs. 2)
- P = Cost per unit (Rs. 20)
[Total Cost = 4,000 + 2,000 + 2,000,000]
[Total Cost = Rs. 2,006,000]
So, the total inventory cost is Rs. 2,006,000.
(iii) Number of Orders Placed in a Year:
To find the number of orders placed in a year, divide the annual demand by the EOQ:
Number of Orders = {D}{EOQ} {{100,000}{4,000} = 25
So, 25 orders will be placed in a year.
(iv) Time Gap Between Two Orders:
To find the time gap between two orders, you need to calculate the time between orders. Since there are 365 days in a year, you can divide this by the number of orders per yearRounded up, the time gap between two orders is approximately 15 days.
(v) Supplier Discount Decision:
The supplier offers a discount of 5% on orders of 10,000 units or more. In this case, your optimal order size (EOQ) is 4,000 units, which is below the 10,000-unit threshold for the discount. Therefore, you should not accept the supplier’s offer of a 5% discount, as your optimal order size (EOQ) is lower than the quantity required to qualify for the discount.
