1) A jewelry firm buys semiprecious stones to make bracelets and rings. The supplier quotes a price of $8 per stone for quantities of 600 stones or more, $9 per stone for orders of 400 to 599 stones, and $10 per stone for lesser quantities. The jewelry firm operates 200 days per year. Usage rate is 25 stones per day, and ordering costs are $48. If annual carrying costs are 30 percent of unit cost, what is the optimal order size?
2) A chemical firm produces sodium bisulfate in 100-pound bags. Demand for this product is 20 tons per day. The capacity for producing the product is 50 tons per day. Set up costs $100, and storage and handling costs are $5 per ton a year. The firm operates 200 days a year. (Note: 1 ton = 2,000 pounds).
a) How many bags per run are optimal?
b) What would the average inventory be for this lot size?
c) Determine the approximate length of a production run, in days.
d) About how many runs per year would there be?
e) How much could the company save annually if the setup cost could be reduced to $25 per run?
3) Classify the following list of items as A, B, or C item.
Item Estimated Annual Demand UnitPrice
H4-010 20,000 2.50
H5–201 60,200 4.00
P6-400 9,800 28.50
P6-401 14,500 12.00
P7-100 6,250 9.00
P9-103 7,500 22.00
TS-300 21,000 45.00
TS-400 45,000 40.00
TS-041 800 20.00
V1-001 33,100 4.00
4) A small grocery store sells fresh produce, which it obtains from a local farmer. During the strawberry season, demand for fresh strawberries can be reasonably approximated using normal distribution with a mean of 40 quarts per day and a standard deviation of 6 quarts per day. Excess costs run 35 cents per quart. The grocery orders 49 quarts per day.
a) What is the implied cost of shortage per quart?
b) Why might this be reasonable figure?
5) A manager must set up an inventory ordering system for newly developed production item, P34, which can be ordered at a cost of $15 per unit and at any time with a lead time of two weeks and acceptable stock-out risk of 2.5 percent. The company operates 50 weeks a year, and the weekly usage rate is normally distributed with an average of 60 units, and a standard deviation of 4 units per week. If the annual holding cost is 30 percent of the cost, and the cost of placing an order is $70,
a) What is the order quantity?
b) When should the manager reorder?