Question

The Fashion Store sells fashion items. The demand for one selling season is random and unknown. The store must order inventory many months in advance of the selling season to get a good price on the items and to ensure they arrive right before the selling season. Each unit costs Fashion $100. These units are sold to customers at a price of $250 per unit. Items not sold during the season can be sold to the outlet store at $80 per unit.
a. Based on the information above, is the optimal service level more or less than 50%? Provide your answer with a justification.
b. If the demand of the fashion items follows a normal distribution, then should the optimal order quantity be more or less than the mean of the demand of the fashion items? Provide your answer with a justification.

Answer 1

a. The optimal service level in this case cannot be determined without knowing the demand for the fashion items during the selling season.

In general, the optimal service level will depend on the trade-off between the cost of carrying inventory and the cost of stock outs.

If the cost of carrying inventory is high, the optimal service level may be lower than 50%, whereas if the cost of stock outs is high, the optimal service level may be higher than 50%.

b. If the demand for fashion items follows a normal distribution, the optimal order quantity should be equal to the mean of the demand.

This is because the mean of a normal distribution represents the most likely value, so ordering the mean amount will ensure that the store has enough inventory to meet the expected demand. Additionally, the normal distribution is symmetrical, so there is a relatively low risk of stock outs or excess inventory.

However, the optimal order quantity may be different if the demand follows a different distribution or if there are additional constraints or costs that need to be considered.

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