ISEN 315 Spring 2011 Dr. Gary Gaukler

Newsvendor Model - Assumptions Assumptions: One short selling season No re-supply within selling season Single procurement at start of season Known costs, known demand distribution

Newsvendor Model – Continuous Demand Demand: pdf f(x) Cdf F(x) Cost parameters: overage co: cost per unit of inventory remaining at end of season underage cu: cost per unit of unsatisfied demand Total cost over season: G(Q, D)

Newsvendor Example Selling a magazine with a one-week selling season Weekly demand ~N(11.73; 4.74) Purchase cost $0.25 Salvage value $0.1 Selling price $0.75 Underage cost: Overage cost: Critical ratio:

Determination of the Optimal Order Quantity for Newsvendor Example

Check in tables: Which z-value corresponds to F(z)=0.77? Look up: Table A4 in the Nahmias book: z=0.74 This is the standard normal z-value, hence need to scale it to our demand distribution:

Different overage and underage costs Simple Buy & Sell A retailer buys a product from the manufacturer / wholesaler at unit price c and sells the product at unit price p. Inventory remaining at the end of the selling season has no value.

Different overage and underage costs Buy & Sell with Salvage Value A retailer buys a product from the manufacturer / wholesaler at unit price c and sells the product at unit price p. Inventory remaining at the end of the selling season can be salvaged at a unit salvage price of s. Note: instead of salvage value s, could have a buyback b from the manufacturer

Different overage and underage costs Buy & Sell with Holding and Shortage Costs A retailer buys a product from the manufacturer / wholesaler at unit price c and sells the product at unit price p. The inventory remaining at the end of the selling season has no value. The retailer incurs a holding cost of h for each unit remaining at the end of the selling season. Also, for every unit short, the retailer incurs a penalty cost of pi.

Extension – initial inventory Assume we have initial inventory of y units

Extension – initial inventory and setup cost Assume we have initial inventory of y units, and there is a setup cost K when we order

When to Use Newsvendor Models Short selling season, no replenishment Buying seasonal goods –Fashion products Making last-run decisions –Product end of life

A Behavioral Issue Consider you are a buyer for a store that sells DVDs. You can return unsold DVDs to the wholesaler for a small restocking fee, say 20% of the wholesale cost of $5. Your profit margin on each DVD is high: $10.