Brothers Company asks you to look at the company’s inventory position. They thin
ID: 2577029 • Letter: B
Question
Brothers Company asks you to look at the company’s inventory position. They think that inventories might be too high as result of the Manager’s tendency to order large quantities. Brothers has decided to examine the situation for one key product – fly rods that cost $320 each to purchase and prepare for sale. Annual sales for the product are 2,500 units (rods), and the annual carrying cost is 10 percent of inventory value. The company has been buying 500 rods per order and placing another order when the stock on hand falls to 100 rods. Each time SSP (SSP is a company that orders rods from Brothers) orders, it incurs a cost equal to $64. Sales are uniform throughout the year.
1. Brothers believes that the Economic Ordering Quantity (EOQ) model should be used to help determine the optimal inventory situation for this product. State the EOQ model.
2. What is the formula for calculating the total inventory cost?
3. What is the EOQ for the fly rods? What will the total inventory cost be for this product if SSP orders the EOQ amount?
4. What is SSP’s added cost if it orders 500 fly rods rather than the EOQ amount? What if it orders 250 rods each time?
5. Suppose it takes three days for SSP to receive its orders and package the rods before they are ready for sale. Assuming certainty in production time and usage, at what inventory level should SSP order more fly rods? (assume 360-day year, that SSP is open every day and that SSP orders the EOQ amount).
6. There is uncertainty in SSP’s usage rate as well as in order delays, so the company must carry a safety stock to avoid running out of the fly roads and facing a loss sale. If SSP carries a safety stock of 50 rods, what effect would this policy have on total inventory cost?
Explanation / Answer
1. EOQ model (Economic Order Quantity Model)
It is the order quantity that minimizes total holding costs and ordering costs for the year due to ordering at optimum level of quantity. Even if all the assumptions don't hld exactly, the EOQ gives us a good indication of whether or not current order quantities are reasonable.
2. Formula for calculating Total Inventory cost = Total purchase costs + Total holding costs + Ordering costs
Total purchase costs = Annual demand for item * Cost per unit
Total holding costs = (Average inventory) * annual per unit holding costs
Ordering costs = (Orders placed per year) * cost to place each order
3. EOQ for fly rods = square root of [(2 * demand * ordering costs per order) / carrying costs per unit]
= square root of [(2 * 2500 * 64) / 320*10%]
= square root of 10000 = 100 units (rods)
Total inventory costs at EOQ = Total purchase costs + total ordering costs + total carrying costs
= 2500*320 + (2500/100)*64 + 10% * (100*320)/2
= 800000 + 1600 + 1600
= 803200
4. Inventory cost at 500 ordering quantity = 2500*320 + (2500/500)*64 + 10% * (500*320)/2
= 800000 + 320 + 8000 = 808320
Added cost / incremental cost = 808320 - 803200 = 5120
Inventory costs at 250 ordering quantity = 2500*320 + (2500/250)*64 + 10% * (250*320)/2
= 800000 + 640 + 4000 = 804640
Added cost / incremental cost = 804640 - 803200 = 1440
5. If the supply delay is of 3 days, it must place the order when 3 days sales quantity is left.
= (2500 * 3)/360 = 21 units
6. In case company carries safety stock, it will increase our inventory holding costs.
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