Newsvendor Model

In-stock Probability

has stock available for every customer. That occurs if demand is less than or equal to the order quantity, In-stock probability = F(Q)

Newsvendor Model Performance Measures

For any order quantity we would like to evaluate the following performance measures: In-stock probability -Probability all demand is satisfied Stockout probability -Probability some demand is lost -The expected number of units left over after demand (but before salvaging) Expected profit Expected lost sales -The expected number of units by which demand will exceed the order quantity Expected sales -The expected number of units sold. Expected left over inventory

Newsvendor model Implementation Steps

Generate a demand model: -Determine a distribution function that accurately reflects the possible demand outcomes, such as a normal distribution function. Gather economic inputs: -Selling price, production/procurement cost, salvage value of inventory Choose an objective: -e.g. maximize expected profit or satisfy an in-stock probability. Choose a quantity to order

Additional questions to consider... Suppose you are making an order quantity decision using the newsvendor model

If your forecast uncertainty increases, do you order more or do you order less? At the end of the season, a merchandiser notices that 80% of the items he manages have left over inventory. Another merchandiser notices that only 20% of her items have left over inventory. Who makes better decisions?

Stock out probability

1 minus the probability demand is Q or lower. Stock out probability = 1 - F(Q)

Newsvendor Models-Problem Characteristics

A fixed, relatively short selling period Product loses value rapidly or is perishable Demand is highly uncertain Limited supply opportunity -One initial purchase/ordering before the selling season starts Industry characteristics shared by most innovative/fashion products -Clothing/Apparel (fashion apparel, e.g. Zara) -Perishable products -Catalog sales, -Seasonal promotional items (e.g. Christmas, Valentine's Day, etc)

The Demand-Supply Mismatch Cost

Definition - the demand supply mismatch cost includes the cost of left over inventory (the "too much" cost) plus the opportunity cost of lost sales (the "too little" cost) The maximum profit is the expected profit without any mismatch costs, i.e., every unit is sold and there are no lost sales. Mismatch cost = maximum profit - expected profit

Newsvendor Model Summary

The model can be applied to settings in which ... -There is a single order/production/replenishment opportunity. -There is Demand is uncertain. -a "too much-too little" challenge: =If demand exceeds the order quantity, sales are lost. =If demand is less than the order quantity, there is left over inventory. Firm must have a demand model that includes an expected demand and uncertainty in that demand. -With the normal distribution, uncertainty in demand is captured with the standard deviation parameter. At the order quantity that maximizes expected profit, the probability that demand is less than the order quantity equals the critical ratio: -The expected profit maximizing order quantity balances the "too much-too little"costs.