1. A company can produce the substrate for a semiconductor chip in-house (in its factory) or it can purchase the substrate from a contractor. If the substrate is produced in-house, there is a cost of $20 each time the machine is set up, and each set up takes 2.75 days. The production rate is 100 units per day. The cost of materials is $2 for each substrate produced. If the substrate is purchased from a contractor, it will cost $2 for each substrate purchased and an additional $15 for each order placed. The cost of holding the item in stock, whether purchased or produced in-house, is $0.02 per substrate per day. The company estimates that it will need 26,000 substrates each year.

(a) Under the assumptions of EPQ, determine the optimal production quantity and the minimum total cost per day of production of the substrate in the company.

(b) Under the EOQ assumptions, determine the optimal order quantity and minimum total cost per day to order substrate from a contractor.

(c) Lime plans to introduce a continuous improvement (CI) program. Assuming that this program is successful and can reduce some of the company's “fat”, determine the maximum cost per order that the company would be willing to pay to order the substrate rather than produce it in-house. (Note that this may be higher or lower than the current cost per order.)

2. Each year, Sherwin-Williams resells 20,000 cans of primer, which it buys from a supplier for $1 per can. Each time Sherwin-Williams places an order, it incurs a fixed cost of $100 for processing. Assume that the EOQ conditions are met and that Nivek's believes that unfilled orders can be backordered (and filled at a later date) at a cost of $2 per can per month. Also assume that the annual carrying cost of excess inventory is $4.80 per unit. Suppose that when a new shipment arrives from your supplier, Sherwin-Williams can fill the back orders immediately.

(a) Determine the optimal order quantity.

(b) Using the optimal order quantity, determine the maximum shortage that will occur.

(c) Using the optimal order quantity, determine the fraction of time that there will be a shortage (ie, no positive inventory).

3. Consider the EOQ model with delayed demand. If the optimal policy is used, determine the following in terms of K,c,λ,h,l and Q∗ only:
(a) The average time a demand waits to be satisfied. [Including the demands that are filled instantly.]

(b) The average time a part spends in available inventory. [Including parts that spend 0 time in available inventory.]

4. Using the parameter values from Problem #2, repeat Problem #3, that is, determine
(a) The average time a demand waits to be satisfied.

(b) The average time a part spends in available inventory.