Question:

Suppose you distribute pints of Ben and Jerry’s frozen yogurt in the Delaware valley. The demand, which we suppose to be constant, for this product is 80,000 pints annually. The annual holding cost for each pint in your freezer is 30% of the price you pay for it, and the cost to process each order is $40. You buy these pints in lots that are delivered immediately, but the price you pay for each pint depends on the quantity you order at a time. There are 250 working days in the year. The price schedule offered to you is the following:

P1 = $1.75 ea. if you buy less than 20,000 pints at once

P2 = $1.72 ea. if you buy at least 20,000 pints at once.

(a.) What is the optimal policy? What is the total annual inventory cost associated with this policy? (Use POM-QM.)

(b.) How many orders do you process per year? What period of time will each order last?

(c.) If your freezers could only hold 3,000 pints of Ben and Jerry’s frozen yogurt at a time, would this affect your policy? Why or why not? In other words, describe what, if anything, will change from your answer in part (a.).