Newsboy {SCperf} | R Documentation |
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 |
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.
See Also
EOQ, EPQ, WW, SS
Examples
## 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)