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.

a) 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.
b) What is the expected number of lost sales per inventory cycle and expected safety stock when a replenishment order is received based on the policy in part a) ?
c) Determine the average annual cost of inventory holding, setup and stock-out associated with the policy from part a)
d) What Type 1 service level is being achieved with the policy from part a)? e) What Type 2 service level is being achieved with the policy from part a)?
f) What would the reorder level and order quantity, if the company were to use a Type 1 service level of 97 percent?

Answer 1

The optimal values of the order quantity and reorder level for the off-season can be determined using the (q,r)- policy.

Step-by-step explanation:

To determine the optimal values of the order quantity and reorder level for the off-season, we need to use the (q,r)- policy. The order quantity (q) represents the number of jerseys to order each time, and the reorder level (r) is the inventory level at which a replenishment order should be placed. The optimal values can be found using the following formula:

q = sqrt((2 * D * S * K) / H)

r = D * L + Z * sqrt(D * S * L)

Where D is the demand per day, S is the standard deviation of the demand per day, K is the unit purchase cost, H is the holding cost rate, L is the lead time, and Z is the safety stock multiplier. Given the provided values, the optimal order quantity (q) is 19 jerseys and the reorder level (r) is 129 jerseys.

Keywords: order quantity, reorder level, (q,r)- policy, off-season, inventory level