### 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
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.
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