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

Isik Bicer

Verena Hagspiel

Verena Hagspiel

Suzanne de Treville

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.