Refine
Language
- English (5)
Keywords
- Airline revenue management (1)
- Chance-Constrained-Programming (1)
- Hydro-Reservoir-Management (1)
- Joint-Chance-Constraints (1)
- Multistage stochastic programming (1)
- Scenario tree generation (1)
- Seat inventory control (1)
- Stochastic optimization, probabilistic constraints, mixed-integer nonlinear programming, power management (1)
- Stochastic-Inflows (1)
A multistage stochastic programming approach to airline network revenue management is presented. The objective is to determine seat protection levels for all itineraries, fare classes, point of sales of the airline network and all data collection points of the booking horizon such that the expected revenue is maximized. While the passenger demand and cancelation rate processes are the stochastic inputs of the model, the stochastic protection level process represents its output and allows to control the booking process. The stochastic passenger demand and cancelation rate processes are approximated by a nite number of tree structured scenarios. The scenario tree is generated from historical data using a stability-based recursive scenario reduction scheme. Numerical results for a small hub-and-spoke network are reported.
On probabilistic constraints induced by rectangular sets and multivariate normal distributions
(2009)
In this paper, we consider optimization problems under probabilistic constraints which are defined by two-sided
inequalities for the underlying normally distributed random vector. As a main step
for an algorithmic solution of such problems, we derive a derivative formula for (normal) probabilities
of rectangles as functions of their lower or upper bounds. This formula allows to reduce the calculus
of such derivatives to the calculus of (normal) probabilities of rectangles themselves thus generalizing a
similar well-known statement for multivariate normal distribution functions. As an application, we consider
a problem from water reservoir management. One of the outcomes of the problem solution is that the
(still frequently encountered) use of simple individual probabilistic can completely fail. In contrast, the
(more difficult) use of joint probabilistic constraints which heavily depends on the derivative formula mentioned
before yields very reasonable and robust solutions over the whole time horizon considered.
O&D revenue management (RM)
– either leg-based or PNR-based – has become
a standard in the airline industry. In this paper,
we present a new approach to O&D RM which
does not make any assumptions on demand distributions
or on the correlations of the booking
process. Protection levels are determined for all
origin destination itineraries, fare classes, points
of sale and data collection points (DCPs). This
approach to the seat inventory problem is modelled
as a multistage stochastic program, where
its stages correspond to the DCPs of the booking
horizon. The stochastic passenger demand
process is approximated by a scenario tree generated
from historical data by a recursive scenario
reduction procedure. The stochastic program
represents a specially structured large scale
LP that may be solved by standard LP software
(e.g. CPLEX). Preliminary numerical experience
is reported.
In this paper, we deal with a hydraulic reservoir optimization problem with uncertainty on
inflows in a joint chance constrained programming setting. In particular, we will consider inflows with
a persistency effect, following a causal time series model, and examine the impact of the ”Gaussian”
assumption for such inflows. We present an iterative algorithm for solving similarly structured joint
chance constrained programming problems that requires a Slater point and the computation of gradients.
Several alternatives to the joint chance constraint problem are presented. In particular, we present an
individual chance constraint problem and a robust model. We illustrate the interest of joint chance
constrained programming by comparing results obtained on a realistic hydro-valley with those obtained
from the alternative models. Despite the fact that the alternative models often require less hypothesis
on the law of the inflows, we show that they yield conservative and costly solutions. The simpler models,
such as the individual chance constraint one, are shown to yield insufficient robustness and are therefore
not useful. We therefore conclude that Joint Chance Constrained programming appears as a technique
offering a good trade-off between cost and robustness and can be tractable for complex realistic models.
A mixed-integer stochastic nonlinear optimization problem with joint probabilistic constraints
(2013)
We illustrate the solution of a mixed-integer stochastic nonlinear optimization problem in an application of power management. In this application, a coupled system consisting of a hydro power station and a wind farm is considered. The objective is to satisfy the local energy demand and sell any surplus energy on a spot market for a short time horizon. Generation of wind energy is assumed to be random, so that demand satisfaction is modeled by a joint probabilistic constraint taking into account the multivariate distribution. The turbine is forced to either operate between given positive limits or to be shut down. This introduces additional binary decisions. The numerical solution procedure is presented and results are illustrated.