Question

A fertilizer plant acquires phosphate from a single source. the plants weekly phospahte requirement has a normal distribution with a mean of 680 metric tons and the standard deviation of 22 metric tons. the lead time for phosphate supply is 5days (app. 0.714 week). 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 inventory is received, it takes roughly two workers to unload, inspect and store the materials in a warehouse. the administrative stafff member is pid $26 per hour and the warehouse employees are paid $16 per worker hour. delivery charges are $800 per shipment. the company purchases phosphate at #400 per metric ton. The annual cost of capital is 5%. other annual cost of holding inventory are estimates to be 2% 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 98%?

Answer 1

To determine the optimal order quantity and reorder point, we need to consider the economic order quantity (EOQ) and the safety stock. The EOQ is the order quantity that minimizes total inventory costs, taking into account the holding costs and the ordering costs. The reorder point is the level at which a new order should be placed to avoid stockouts during the lead time.

Step-by-step explanation:

To determine the optimal order quantity and reorder point, we need to consider the economic order quantity (EOQ) and the safety stock. The EOQ is the order quantity that minimizes total inventory costs, taking into account the holding costs and the ordering costs. The reorder point is the level at which a new order should be placed to avoid stockouts during the lead time.

To calculate the EOQ, we can use the formula: EOQ = sqrt((2 * Annual Demand * Ordering Cost) / Holding Cost). Given that the annual demand is the mean phosphate requirement, the ordering cost is the administrative employee's hourly rate multiplied by the time spent on ordering processes, and the holding cost is the purchase cost multiplied by the annual cost of holding inventory, we can calculate the EOQ.

To calculate the reorder point, we need to consider the lead time demand, which is the mean phosphate requirement multiplied by the lead time. The safety stock is the inventory buffer needed to account for demand fluctuations during the lead time, and it can be calculated using the formula: Safety Stock = Z * sqrt(Lead Time Demand Variance), where Z is the z-score corresponding to the desired service level. By adding the safety stock to the lead time demand, we can determine the reorder point.