Question

A store 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 300. Store A purchases the product for $10 each unit and sells each for $25. Inventory is salvaged for $5. What is the optimal quantity the store should order of its product

Answer 1

702.20

Step-by-step explanation:

Optimal order quantity Q = D+ z σ

Where D is the average demand = 500 units

And σ is the standard deviation of demand = 300

Cu = Cost of stock-out (underestimation) = Selling price – unit cost = $25 -$10 = $15

Co = Cost of excess inventory (overestimation) = Unit cost – Salvage Value = $10 – $5 = $5

Therefore Service level = Cu / (Cu + Co)

= $15/ ($15 + $5)

= 0.75 or 75%

For service level 75% the Z value = 0.674

Therefore, Q = 500+0.674*300 = 702.20