OM423b Homework 1

1. Consider a manufacturer who orders a particular part to supply a production process. Assume that the cost and demand characteristics for the ordered part satisfy the assumptions of the EOQ. Specifically, suppose that demand occurs at a constant rate of 37 units per day during the 365 days in which the manufacturing plant operates annually. The unit cost of purchased parts is $20/unit, and the annual holding cost is estimated to be 33% of the unit cost. Assuming that it costs $35 to place an order, determine:
   1. EOQ for the part
   2. Annual holding cost, annual order cost and total relevant costs associated with this order quantity.

2. Consider the same situation as described in question 1 with the exception that the supplier of the ordered part uses a standard sized pallet for shipment. Specifically, assume that the supplier ships parts in pallets of 45 units. Moreover, suppose that the supplier requires a 14-day period to deliver an order. In this case:
   1. What would be the optimal order quantity?
   2. What are the total relevant costs associated with the optimal order quantity?
   3. Does the modified order quantity result in higher ordering costs, higher holding costs, or both and why?
   4. What would be the inventory level at which new orders should be placed (ROL)?
   5. What would be the optimal time between consecutive orders?

3. Reconsider question 1 and assume that the supplier can deliver orders of any size, i.e., the pallet size restriction of question 2 no longer applies. Suppose that the demand rate provided is just an estimate and that the daily demand rate may be as low as 33 units/day or as high as 41 units/day, i.e., roughly a ±11% range. If we chose to implement the EOQ based on the estimate of 37 units/day:
   1. What is the maximum increase in total relevant costs that we may incur over the upcoming year?
   2. Construct a chart to show how the TRC changes as the actual demand rate varies within the specified range.

4. You work for a company and are tasked with the decision of purchasing a product or making the product in house. Demand for the product is 10,000 units per week. The supplier charges $25.10 per unit, $200 per order, and sells in batches of 500 units. Your plant can produce 20,000 units per week and incurs costs of $19 per unit and $700 per setup. Holding cost in either situation is $1.30 per unit per week and both the supplier and your plant operate 45 weeks out of the year.
   1. What is the optimal production quantity (EPQ)
   2. What is the optimal order quantity (EOQ)?
   3. Do you make the product or purchase it and why?