Transcript Lecture 10
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 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.