- 7 Marks
FM – L2 – Q109 – Inventory Management
Question
Entity G uses 105 units of an item of inventory every week. These cost GH₵150 per unit. They are stored in special storage units and the variable costs of holding the item is GH₵4 per unit each year plus 2% of the inventory’s cost.
Required
(a) If placing an order for this item of material costs GH₵390 for each order, what is the optimum order quantity to minimise annual costs? Assume that there are 52 weeks in each year.
(b) Suppose that the supplier offers a discount of 1% on the purchase price for order sizes of 2,000 units or more. What will be the order size to minimise total annual costs?
Answer
(a) The annual holding cost per unit of inventory = GH₵4 + (2% × GH₵150) = GH₵7.
Annual demand = 52 weeks × 105 units = 5,460 units.
EOQ = √((2 × 390 × 5,460) / 7) = 780 units.
(b) A discount on the price is available for order sizes of 2,000 units or more, which is above the EOQ.
The order size that minimises cost is therefore either the EOQ or the minimum order size to obtain the discount, which is 2,000 units.
Annual costs
| EOQ (780 units) | Discount (2,000 units) | |
|---|---|---|
| Purchases | (5,460 × GH₵150): 819,000 | ((5,460 × GH₵150 × 99%): 811,215 |
| Holding costs | (GH₵7 × 780/2): 2,730 | (GH₵7 × 2,000/2): 7,000 |
| Ordering costs | (GH₵390 × 5,460/780): 2,730 | (GH₵390 × 5,460/2,000): 1,064 |
| Total costs | 824,460 | 819,279 |
Conclusion
The order size that will minimise total annual costs is 2,000 units.
- Topic: Inventory Management
- Uploader: Samuel Duah