Inventory control subject to known demand (2)

A company produces different components for cars. One particular component is an air filter that is suppliedon an exclusive contract to one of their collaborating partners at a constant rate of 200 units monthly. The company produces the filters at a rate of 6000 per month. Setup time for changing the settings on the equipment for producing this filter is 1.5 hour and the company estimates a cost of $1550. per hour for wages and lost profit during setup. The filter costs the company $ 25 to produce, and they are sold for the price of $55. The company has established a 22% annual interest rate for determining the total holding costs.

1. How many filters should the company produce in each production run, to minimize the annual holding and setup costs?
2. What is the maximum level of inventory on stock, and what are the setup costs and the holding costs with this production strategy?
3. What is the cycle time and what proportion of each cycle is used for production (uptime) with this strategy?
4. Another producer has specialized on producing air filters and offers the first company to buy the same type of filters at a price of $30. each. The cost will be $1500. for each order if the company accepts this offer. Will you recommend the company to continue producing the filters, or buy from the other producer?

The other producer wants to deliver in larger batches and offers two types of discounts. Find the optimal order quantity and relevant costs for each of them.

5. All unit discounts: Price $29. when buying at least 1500, and price 28kr. when buying at least 2000.
6. Incremental quantity discount: Price $28. for the items in an order in excess of 1500 and price $26.for the items in excess of 2000.

this is operation management. inventory control subject to know demand (2)