PD {RM2} | R Documentation |
PD
unconstrains demand data in quantity-based revenue management.
PD(demand = demand, tau = 0.5, eps = 0.005)
demand |
demand vector with constrained and unconstrained entries. A 0 in the name of an entry means that the corresponding demand is unconstrained. Conversely, a 1 in the name of an entry suggests that the corresponding demand is constrained. |
tau |
fixed constant that reflects how aggresive the unconstrainig is. The default value is 0.5. |
eps |
small number used as the stopping criterion. The default value is 0.005. |
PD
unconstrains demand data in quantity-based revenue management. The observed demand entries, some of which are constrained because the product class was closed, are assumed to be realizations from an underlying normal distribution with mean \mu and standard deviation \sigma. The objective is to find the parameters \mu and \sigma of this underlying demand distribution.
param |
parameters of demand distribution |
niter |
number of iterations |
demand |
unconstrained demand vector |
history |
parameter convergence history |
Tudor Bodea tudor.bodea@ihg.com
Dev Koushik dev.koushik@ihg.com
Mark Ferguson mark.ferguson@mgt.gatech.edu
Talluri, K. T. and Van Ryzin, G. (2004) The Theory and Practice of Revenue Management. New York, NY: Springer Science + Business Media, Inc. (Pages 485–486).
# SPECIFY THE SEED set.seed(333) # SPECIFY REAL PARAMETERS OF THE DEMAND DISTRIBUTION rmean <- 20 rsd <- 4 nrn <- 20 # GENERATE REAL DEMAND rdemand <- round(rnorm(nrn, rmean, rsd)) # GENERATE BOOKING LIMITS bl <- round(rnorm(nrn, rmean, rsd)) # GENERATE OBSERVED DEMAND demand <- rdemand * (rdemand <= bl) + bl * (rdemand > bl) # IDENTIFIED PERIODS WITH CONSTRAINED DEMAND: 1 - CONSTRAINED DEMAND names(demand) <- as.character(as.numeric(rdemand>bl)) demand # UNTRUNCATE DEMAND PD(demand) PD(demand, tau=0.5, eps=0.005) PD(demand, tau=0.5, eps=0.00005) # MODIFY DEMAND VECTOR - NO CONSTRAINED INSTANCES ARE OBSERVED names(demand) <- rep(0, length(demand)) # ATTEMPT TO UNTRUNCATE THE DEMAND PD(demand, tau=0.5, eps=0.005)