Question

A firm sells a product with monthly demand of 1000 units. The holding cost is $4 per unit per year, the ordering cost is $150 per order, and the backorder cost is $50 per unit. Demand exhibits some variability and management has estimated that monthly demand follows a normal distribution with a standard deviation of σ=120 units. Lead time is two months. a. Find the optimal ordering quantity.

Answer 1

The question concerns calculating the optimal ordering quantity for a product with variable demand, leading into inventory management concepts like EOQ, Reorder Point, and Safety Stock, crucial for minimizing costs and preventing stockouts.

Step-by-step explanation:

The student's question regards finding the optimal ordering quantity for a firm's product. This involves calculations related to inventory management, specifically the Economic Order Quantity (EOQ) model which seeks to minimize the total holding costs and ordering costs.

However, the provided information does not allow for the direct calculation of the EOQ because it requires variability and lead time considerations; hence, the advanced inventory management techniques such as the Reorder Point formula and Safety Stock calculations would be more appropriate. These take into account standard deviations of demand and lead time to safeguard against stockouts. The student is also asked about total revenue, total cost, and profit, which relate to a firm's profitability at different production levels. These concepts are critical in determining the pricing and production strategy of a firm, affecting its market performance.