Question

Store A uses the newsvendor model to manage its inventory. Demand for its product is normally distributed with a mean of 500 and a standard deviation of 100. Store A purchases the product for $10 each unit and sells each for $30. Inventory is salvaged for $5.What is its expected profit if Store A’s order quantity is 400 units? Please provide clear answers, not misleading

Answer 1

We need to find the optimal order quantity:

• The underage cost is Cu=Price−Cost=$30 - $10 = $ 20
• The overage cost is Co=Cost−Salvage Value=$10−$5=$5
• The critical fractile is f=Cu/(Cu+Co) =$20/($20+$5) = 0.80

• The z-value of the critical fractile is z=NORM.S.INV(0.80) = 0.842

• The optimal order quantity is Q=Mean+z∗Standard Deviation=500+0.842∗100≈ 584

The maximum profit is achieved if the store sells 400 units:

Maximum Profit=(Price−Cost)∗ Sell Units - Overage Cost * (Optimal Quantity - Sell) = ($30−$10)∗400 - (184 * 5) = $ 7,080