College of Engineering
Industrial Engineering and Engineering Management
Production and Inventory Systems (0405-431)
Homework # 2
• Each student should solve the homework by himself, no groups are allowed.
• No late homework will be accepted.
• Organize your solutions in a neat way.
• Try to use sketches, graphs, diagrams whenever suitable.
• A printed cover page showing your name, ID, hw#, Name of the instructor, Course title and the Course number are a must.
• In addition to correct solution, neatness will be taken into consideration in the grading.
Question 1 (50 points):
Davids Delicatessen flies in Hebrew National salamis regularly to satisfy a growing demand for the salamis in Silicon Valley. The owner, David Gold, estimates that the demand for the salamis is pretty steady at 175 per month. The salamis cost Gold $1.85 each. The fixed cost of calling his brother in New York and having the salamis flown in is $200. It takes three weeks to receive an order. Golds accountant, Irving Wu, recommends an annual cost of capital of 22 percent, a cost of shelf space of 3 percent of the value of the item, and a cost of 2 percent of the value for taxes and insurance.
a. How many salamis should Gold have flown in and how often should he order them?
b. How many salamis should Gold have on hand when he phones his brother to send another shipment?
c. Suppose that the salamis sell for $3 each. Are these salamis a profitable item for Gold? If so, what annual profit can he expect to realize from this item? (Assume that he operates the system optimally.)
d. If the salamis have a shelf life of only 4 weeks, what is the trouble with the policy that you derived in part (a)? What policy would he have to use in that case? Is the item still profitable?
Question 2 (50 points):
A large automobile repair shop installs about 1,250 mufflers per year, 18 percent of which are for imported cars. All of the imported-car mufflers are purchased from a single local supplier at a cost of $18.50 each. The shop uses a holding cost based on a 25 percent annual interest rate. The setup cost for placing an order is estimated to be $28.
a. Determine the optimal number of imported-car mufflers the shop should purchase each time an order is placed, and the time between placement of orders.
b. If the replenishment lead time is six weeks, what is the reorder point based on the level of on-hand inventory?
c. The current reorder policy is to buy imported-car mufflers only once a year. What are the additional holding and setup cost incurred by this policy?