The user needs to specify the selling price, the total unit cost, and the
salvage value of the product.

For example, Reebok sells the NFL jerseys at $21.60 per unit.

It costs Reebok $9.50 per unit to make the jersey.

Unsold jerseys are sold at a salvage (residual) value of $8.46 per
unit.

For the demand-loss model, a single jump drops the demand forecast to
zero.

Only the volatility term and the rate of jumps are needed to describe the
demand process for the demand-loss model.

In the early-sales model, a single jump occurs at a known time during the
forecast-evolution horizon.

This time indicates the moment when the early-sales information is
observed.

The impact of the early-sales information on the demand forecast is
represented by the log-normal distribution.

The user needs to specify the constant volatility, the time of observing
the
early sales, and log-normal distribution parameters.

In the jump-diffusion model, jumps occur according to a Poisson process
with
a jump rate.

The impact of jumps on the demand forecast is modeled by a log-normal
distribution.

The user needs to specify the constant volatility, the rate of jumps, and
the log-normal distribution parameters.

Estimation of constant volatility:

To estimate the constant volatility we need the initial forecasts of
mean demand and the standard deviation.

If the mean demand and the standard deviation are 1000 units and 500
units, respectively,

the coefficient of variation (CV, which is ratio of standard deviation to
mean demand) becomes 0.5.

Then, the constant volatility is estimated as volatility =
sqrt(ln(CV^2+1))
= 0.4723.

When the CV is equal to one, then the volatility becomes equal to 0.8325.

### Isik Bicer

### Verena Hagspiel

### Suzanne de Treville

Assistant Professor of Supply Chain Management

Associate Professor of Industrial Economics and Technology Management

Swiss Finance Institute Professor of Operations Management

(co-Editor-in-Chief of the Journal of Operations Management)

Rotterdam School of Management, Erasmus University

Norwegian University of Science and Technology

University of Lausanne

Note: This research was conducted when both Isik Bicer and Verena Hagspiel were working at the University of Lausanne under the supervision of Suzanne de Treville.