Question

In a newsvendor problem, like the Zamatia example from class, which of the following (check all that apply) are situations where the optimal order quantity for a retailer will either decrease OR stay the same. The probability of demand being zero increases. The probability of higher demand values increases. The purchase cost for the retailer of the item decreases. The salvage value for the retailer of the item decreases.

Answer 1

The key equations used in newsvendor problem are

Critical ratio = Cu/(Cu+Co) where Cu is cost of understocking and Co is cost of overstocking.

Here,

Co = Cost of purchase – salvage price

Cu = Selling price – cost of purchase

Based on the critical ratio, we usually consider the z value. And based on z value we determine the optimal demand. This means if the z value is above 0.5 and increases upward, the optimal demand will be more. That is only possible is Cu is more than Co. Thus as the relationship between Co and Cu changes, the optimal order quantity changes too.

Using this logic, we can choose between last two options. If the purchase cost decreases while the salvage cost and the selling price remains the same, then the value of Cu will increase and Co will decrease. This will increase the optimal order quantity.

If the salvage value decreases and selling price and cost remains the same then the value of Co will increase. This means that the critical ratio will reduce. As a result the optimal order quantity will reduce.

The other two questions need to consider the probability distribution. Now, probability is a share of the value of 1. This means if the probability of demand being 0 increases that means that the probabilities of the other will likely reduce. This also means that the chance of overstocking increase. Thus the optimal order quantity should reduce.

If the probability of higher demand value increase, then we should stock up more. That is simple logic and as a result the optimal order quantity should increase.

Summarizing this, if the optimal order quantity has to decrease or remain the same then the following conditions need to happen

• The probability of demand being 0 increase
• The salvage value for the retailer decrease.