1. A company can either produce the substrate for a semiconductor chip in-house (at its factory) or it can buy the substrate from a contractor. If the substrate is produced at the company, there is a $20 cost each time the machine is set up and each set-up requires 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, then it will cost $2 for each substrate purchased, and an additional $15 for each order that is placed. The cost of maintaining the item in stock, whether is 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 EPQ assumptions, determine the optimal production quantity and the minimum total cost per day of producing the substrate at the company.
(b) Under the EOQ assumptions, determine the optimal order quantity and the minimum total cost per day of ordering the substrate from a contractor.
(c) Lime plans to introduce a Continuous Improvement (CI) program. Assuming this program is successful and is able to trim some of the company’s “fat,” determine the maximum per order cost that the company would be willing to pay so that ordering the substrate would be preferred to producing it in-house. (Note this may be more or less than the current per order cost.)
2. Each year, Sherwin-Williams resells 20,000 cans of paint primer, which it purchases from a supplier for $1 per can. Each time Sherwin-Williams places an order, it incurs a ?xed cost of $100 for processing. Assume that the EOQ conditions hold, and that Nivek’s believes that un?lled orders can be backlogged (and ?lled at a later date) at a cost of $2 per can per month. Suppose also that the annual holding cost for surplus inventory is $4.80 per unit. Assume that, when a new shipment arrives from its supplier, Sherwin-Williams can ?ll backorders 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 stockout (i.e., no positive inventory).
3. Consider the EOQ with backlogged demand model. If the optimal policy is used, determine the following in terms of K,c,λ,h,l, and Q∗ only:
(a) The average time that a demand waits to be ?lled. [Including demands that are ?lled instantaneously.]
(b) The average time that a part spends in on-hand inventory. [Including parts that spend time 0 in on-hand inventory.]
4. Using the parameter values in Problem #2, repeat Problem #3, i.e., determine
(a) The average time that a demand waits to be ?lled.
(b) The average time that a part spends in on-hand inventory.