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 and provided by this calculator.

What is the single period model? 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:

\[ \text{Optimal Order Quantity} = \mu + z* \times \sigma \]
Single Period model: The newsboy dilemma

Other waiting line models

The idea of waiting line model is the same across all types: There is process in which you find a server or several servers, and where you need to wait in line if a server is not available right away.

The difference among all the different waiting line models lies on how those servers distribute their work and how the waiting lines are organized.

One of the simplest model is the single server model, in which as the name suggests, there is only one server serving customers who wait in line for their turn.

Though these models are conceptually simple, the math involved to compute the waiting line metrics is not trivial, and some models do require sophisticated math tools to get average waiting in line and queue size.

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

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