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 stochasti...

SETSTOCH is a tool for linking Algebraic Modeling Languages (AMLs) with Specialized Stochastic Programming Solvers (SSPSs). Its main role is to retrieve from the AML a dynamically ordered core model (baseline scenario) that is then sent automatically to the SSPS. The user is then able to take full advantage of speci c SSPS features. The current implementation of SETSTOCH enables to access the S...

We introduce the Stochastic multistage fixed charge transportation problem in which a producer has to ship an uncertain load to a customer within a deadline. At each time period, a fixed transportation price can be paid to buy a transportation capacity. If the transportation capacity is used, the supplier also pays an uncertain unit transportation price. A unit inventory cost is charged for the...

In this paper, in a Model Predictive Control problem, we tackle the integration of uncertain constraints that belong to discrete set. We propose controller offers solution reformulate stochastic avoid exponential growth scenario tree experienced by existing controllers. The proposed controller’s efficiency is shown benchmarking and comparing it with Multistage Stochastic Programming algorithm c...

In this paper, we consider a stochastic programming approach to multi-stage posttax portfolio optimization. Asset performance information is speci ed as a scenario tree generated by two alternative methods based on simulation and optimization. We assume three tax wrappers involving the same instruments for an eÆcient investment strategy and determine optimal allocations to di erent instruments ...

Decomposition and Monte Carlo sampling-based algorithms hold much promise for solving stochastic programs with many scenarios. A critical component of such algorithms is a stopping criterion to ensure the quality of the solution. In this paper, we develop a stopping rule theory for a class of algorithms that estimate bounds on the optimal objective function value by sampling. We provide rules f...

We consider the problem of efficient resource allocation in a grid computing environment. Grid computing is an emerging paradigm that allows the sharing of a large number of a heterogeneous set of resources. We propose an auction mechanism for decentralized resource allocation. The problem is modeled as a multistage stochastic programming problem. Convergence of the auction allocations to the s...

In the present paper, the approximate computation of a multistage stochastic programming problem (MSSPP) is studied. First, the MSSPP and its discretization are defined. Second, the expected loss caused by the usage of the “approximate” solution instead of the “exact” one is studied. Third, new results concerning approximate computation of expectations are presented. Finally, the main results o...

In this work, we address the modeling and solution of mixed-integer linear multistage stochastic programming problems involving both endogenous and exogenous uncertain parameters. We first propose a composite scenario tree that captures both types of uncertainty, and we exploit its unique structure to derive new theoretical properties that can drastically reduce the number of non-anticipativity...

Stochastic optimization problems pose unique challenges in how they are represented mathematically. These problems arise in a number of different communities, often in the context of problems that introduce specific computational characteristics. As a result, a number of contrasting notational styles have evolved, which complicate our ability to communicate research across communities. This is ...