Question

A fertilizer plant acquires phosphate from a single source. The plant's annual phosphate requirement has a normal distribution with a mean of 25,000 metric tons and the standard deviation of 1,500 metric tons. The lead time for phosphate supply is 10 days. To place an order, an administrative employee spends around one hour reviewing the inventory level, preparing the order, tracking the delivery, and updating records. When the delivery is received, it takes roughly two worker hours to unload, inspect, and store the material. The administrative staff member is paid $28 per hour and the warehouse employees are paid $18 per worker hour. Delivery charges are $1000 per shipment. The company purchases phosphate at $390 per metric ton. The annual cost of capital is 5%. Other annual costs of holding inventory are estimated to be 5% of the purchase cost. How much should the plant order at a time? What will be the Reorder Point if the desired service level during the lead time is 99%?

Answer 1

The plant should order approximately 423 metric tons of phosphate at a time. The reorder point, with a desired service level of 99%, is approximately 249,041 metric tons.

Step-by-step explanation:

To determine how much the plant should order at a time, we can use the Economic Order Quantity (EOQ) formula. The formula is:

EOQ = sqrt((2 × Annual Demand × Setup Cost) / Holding Cost per Unit)

In this case, the annual demand is the mean phosphate requirement (25,000 metric tons), the setup cost is the administrative employee's time (1 hour) multiplied by their hourly wage ($28), and the holding cost per unit is the annual cost of holding inventory (5% of the purchase cost, which is $390 per metric ton).

Using these values, we can calculate the EOQ as follows:

EOQ = sqrt((2 × 25000 × 28) / (390 × 0.05))

EOQ ≈ 423 metric tons (rounded to the nearest whole number).

The reorder point can be calculated using the formula:

Reorder Point = Lead Time Demand + Safety Stock

In this case, the lead time demand is the mean phosphate requirement during the lead time (25,000 metric tons × 10 days), and the safety stock is the z-score corresponding to the desired service level during the lead time (99%) multiplied by the standard deviation of the phosphate requirement (1,500 metric tons).

Using these values, we can calculate the reorder point as follows:

Reorder Point = (25000 × 10) + (2.326 × 1500)

Reorder Point ≈ 249,041 metric tons (rounded to the nearest whole number).