SCperf (version 1.1.1)

Newsboy: The newsboy model

Description

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

Usage

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

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

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 \(b=p-c\).

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.

See Also

EOQ, EPQ, WW, SS

Examples

# NOT RUN {
 
# }
# 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.
# }
# 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.
# }
# NOT RUN {
Newsboy(100,20,4,1)

# }