# Single Period Model Calculator

Instructions: You can use this Single Period Model Calculator, by providing the average demand for the period $$(\mu)$$, the standard deviation of demand $$(\sigma)$$, the sales price, the cost per unit and the salvage value, using the form below:

Sales Price =
Cost Per unit =
Salvage Value =
Average Demand for the period $$(\mu)$$ =
St. Deviation of Demand $$(\sigma)$$ =

#### Single Period Model Calculator

More about the Single Period Model for you to have a better grasp of the way the results are obtained. The Single Period Model (or usually known as the newsboy problem) occurs when there is a need to make an order size decision for one period, for the specific case in which the units will have a degree of obsolescence at the end of the period, and they will have a certain salvage value at the end of the period (which is typically less than the cost per unit, and it is usually \$0). For this type of model, first we need to compute the costs of shortage and overage:

$\text{Cost of Shortage } = C_s = \text{Sales Price per unit} - \text{Cost per unit}$ $\text{Cost of Overage } = C_s = \text{Cost per unit} - \text{Salvage value per unit}$

Then, we compute the optimal service level:

$SL = \frac{C_s}{C_s + C_o}$

and we need to compute the z-value associated to that service level: $$z* = \Phi^{-1}(SL)$$. So then, now we compute the optimal order quantity, using the following:

$\text{Optimal Order Quantity} = \mu + z* \times \sigma$

Another model that falls beyond the most traditional models is the constant service time model, just to give one example.

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