# Newsboy: The newsboy model In SCperf: Functions for Planning and Managing Inventories in a Supply Chain

## Description

Implements the newsboy (or newsvendor) model with normal demand.

## Usage

 `1` ```Newsboy(m, sd, p, c, s = 0) ```

## Arguments

 `m` Mean demand during the period `sd` Standard deviation of demand during the period `p` The selling price, where p > c `c` Uhe unit cost `s` The salvage value (default:0), where s < c

## Details

When the demand is a random variable with normal distribution, the optimal stocking quantity that minimize the expected cost is: Q=m+z*sd, where z is known as the safety factor and Q - m=z*sd is known as the safety stock. 'Note that the newsboy problem is not formulated in terms of per unit holding cost h=c-s and penalty cost b=p-c.

## Value

A list containing:

 `Q` Optimal order-up-to quantity `SS` Safety stock `ExpC` Expected cost `ExpP` Expected profit `CV` Coefficient of variation of the demand `FR` Fill rate, the fraction of demand served from stock `z` Safety factor

## References

- Porteus E. L. (2002) Foundations of Stochastic Inventory Theory, Stanford University Press, Stanford, CA.

- Gallego G. (1995) Newsvendor Problem. IEOR 4000 Production Management.

- Ayhan, Hayriye, Dai, Jim, Foley, R. D., Wu, Joe, (2004): Newsvendor Notes, ISyE 3232 Stochastic Manufacturing & Service Systems.

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ``` ## Not run: # Example Porteus # # Suppose demand is normally distributed with mean 100 and standard # deviation 30. If p = 4 and c = 1, then CR = 0.75 and Q=120.23. # Note that the order is for 20.23 units (safety stock) more than the # mean. Note also that ExpC(120.23) = 38.13 and ExpP(120.23)=261.87, # with FR=0.96. ## End(Not run) Newsboy(100,30,4,1) ## Not run: # Example Gallego # # Suppose demand is normal with mean 100 and standard deviation 20. The # unit cost is 5, the holding and penalty cost are 1 and 3 # respectively. From the definition of the holding and penalty # cost we find that p=4, then CR = 0.75 and Q = 113.49. Notice that the # order is for 13.49 units (safety stock) more than the mean, # ExpC(113.49) = 25.42 and ExpP(113.49) = 274.58, with fill rate of # 97 percent. ## End(Not run) Newsboy(100,20,4,1) ```