Newsvendor model

How do you find probability for in stock if you know the quantity to order, expected demand and standard deviation?

1. Find z = [ Q - mu ] / sigma. 2. Convert z to probability using the standard normal distribution table or the Excel function Normsinv. 3. In-stock probability = inverse of norm distribution of z, stockout probability = 1 - in-stock probability

How do you an order quantity that satisfies in-stock probability?

1. Find z such that cumulative distribution of z is equal to in-stock probability. 2. Convert z-statistic into the order quantiy Q = mu + z * sigma

What are the steps to find the order quantity that maximizes expected profit?

1. critical ratio Cu/[Co+Cu]. This is the probability on the cumulative distribution. 2. Find corresponding z. 3. convert z into order quantity Q = mu + z * sigma

How do you calculate expected lost sales?

1. find z for the order quantity 2. find L[z] either by looking it up in the table or by using the Excel function L[z] = Normdist(z,0,1,0)-z*(1-Normdist[z,0,1,1]) 3. expected lost sales = sigma * L[z]

How do you find z by in-stock probability?

Normsinv [ in-stock probability ]

What is a critical ratio?

Probability on the cumulative distribution function

What is the first step to calculate expected sales?

Expected lost sales

What does the probability less than 0.5 mean?

It is better to buy less than the expected demand because the costs of the inventory are greater than the missed opportunity costs

[formula] Expected leftover inventory

= Q - expected sales = Q - mu + expected lost sales

[formula] Expected profit

= [ [price - cost] * expected sales] - [[cost - salvage vlaue) *.expected leftover inventory]

[formula] Expected demand

= expected sales + expected lost sales

[formula ] Expected sales

= mu - expected lost sales

What does z represent in the newsvendor model?

Quantity