A retailer has collected the following information about an item of inventory: W
ID: 450366 • Letter: A
Question
A retailer has collected the following information about an item of inventory:
Weekly demand (assume 50 weeks in a year) =
410 units
Ordering costs
$10 per order
Holding cost per unit per year
27% of unit cost
Standard deviation of demand
62 units
Lead time
2 weeks
The retailer currently purchases this item from Supplier A at the price of $5.90 a unit, regardless of the lot size. The retailer currently uses EOQ model. Recently another supplier, Supplier B, has offered a different deal: If the item is ordered in lot size of smaller than 1,000 units, the price would be $6.10 apiece. However, if the order size is 1,000 or more, the price per unit drops to $5.75. Given this information determine the following:
1The safety stock for this item, assuming the company has a policy of no more than 3% stock out.
2The ROP for this item.
3Whether, the retailer should accept this new offer from Supplier B. Why or why not?
4What would be the net savings or net loss to the retailer’s if it decides to accept the offer from Supplier B?
Weekly demand (assume 50 weeks in a year) =
410 units
Ordering costs
$10 per order
Holding cost per unit per year
27% of unit cost
Standard deviation of demand
62 units
Lead time
2 weeks
Explanation / Answer
1.
Z @ 97 % = 1.88
Safety stock = z * Standard deviation of demand * Sqrt(lead Time) = 1.88 * 62 * sqrt(2) = 164.841 = 165 units
2.
ROP = Demand during lead time + safety stock
ROP = (410 * 2) + 165 = 985 units
3.
EOQ = Sqrt((2 * Annual Demand * Ordering Cost) / (Holding cost * Price))
EOQ = Sqrt ((2 * 410 * 50 * 10) / (0.27 * 5.90)) = 507.32 = 507
Annual Cost = (Annual Demand * price) + ((annual demand / EOQ) * ordering cost) + ((EOQ / 2) * Price * Holding Cost)
Annual Cost at EOQ = (20500 * 5.90) + ((20500 / 507) * 10) + ((507 / 2) * 0.27 * 5.9) = 121758.2
Supplier B:
Annual Cost at (Q = 1000) = (20500 * 5.75) + ((20500 / 1000) * 10) + ((1000 / 2) * 0.27 * 5.75) = 118856.3
Retailer should accept offer from supplier B because the annual cost is low for the order size greater than 1000.
4.
Net Saving = $(121758.2 – 118856.3) = $2901.9 = $2902
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