Question

The Gator merchandise store next to the stadium uses a continuous review system to track the sales and inventory levels of their football jerseys. Suppose that, in an off- season, the daily demand for the jerseys sold is approximately normally distributed with a mean of 15 jerseys and a standard deviation of 2 jerseys. Suppose that the jerseys have a constant delivery lead time of 7 days, and the unit purchase cost is $96/jersey. Fixed cost of ordering is $75/order. Suppose that Gator fans have little patience, causing the sale to be lost in the case of a stockout. The unit loss-of-goodwill cost associated with the lost sale is $5/unit. Further, assume the store uses an inventory carrying charge based on a 25 percent annual interest rate and the off-season lasts 200 days.

Determine the optimal values of the order quantity and the reorder level for the off-season (for the purpose of this problem you can ignore the infinite planning horizon assumption for the (q,r)- policy and pretend the offseason is the only time in the year the store is open). If the algorithm has not converged after iteration 2, please report q2 and r2 as the optimal order quantity and reorder level. Further, ignore the fact that jerseys would normally be integers only.

Answer 1

The student needs to use economic order quantity (EOQ) and reorder point calculations to determine the optimal order quantity and reorder level for the Gator store's off-season football jersey inventory, taking into account demand distribution, lead time, costs, and carrying charge.

Step-by-step explanation:

The student's question pertains to a continuous review inventory system at the Gator merchandise store and requires determining the optimal order quantity and reorder level for football jerseys during the off-season. The demand for jerseys is normally distributed with a mean of 15 and a standard deviation of 2. The lead time for delivery is 7 days and the cost per unit is $96. The fixed ordering cost is $75, and there is a loss-of-goodwill cost of $5 per unit in the event of a stockout. An inventory carrying charge is based on a 25 percent annual interest rate with the off-season lasting 200 days. To calculate the optimal values, economic order quantity (EOQ) and reorder point formulas would be used. Due to the complexity and the need for iterative calculations, assistance with spreadsheet software or a specific inventory management algorithm might be necessary. If convergence is not achieved after two iterations, q2 and r2 are reported as the tentative optimal figures.