Horand I. Gassmann

MSLiP: a computer code for the multistage stochastic linear programming problem

This paper describes an efficient implementation of a nested decomposition algorithm for the multistage stochastic linear programming problem. Many of the computational tricks developed for deterministic staircase problems are adapted to the stochastic setting and their effect on computation times is investigated. The computer code supports an arbitrary number of time periods and various types of random structures for the input data. Numerical results compare the performance of the algorithm to MINOS 5.0.

A Comprehensive Input Format for Stochastic Linear Programs

Based on the MPS standard for linear programs, data conventions for the description of multistage stochastic linear programs were described by Birge et al. [3]. This paper proposes extensions to the so-called SMPS standard, in order to address known shortcomings and to extend the range of problems that can be expressed within the standard.

Scenario formulation in an algebraic modelling language

Algebraic modelling languages have simplified management of many types of large linear programs but have not specifically supported stochastic modelling. This paper considers modelling language support for multistage stochastic linear recourse problems with finite distributions. We describe basic language requirements for formulation of finite event trees in algebraic modelling languages and show representative problems in AMPL using three commonly used scenario types.

On the formulation of stochastic linear programs using algebraic modelling languages

This paper considers extensions to algebraic modelling languages to support formulation, instantiation and solver integration for stochastic linear programs (SLPs). We present a taxonomy of SLP problem types and analyze formulation requirements including distribution handling by class of problem. We demonstrate suggested formulations for most problem classes, show solver input in the S-MPS standard, and propose consistency checks for constraints involving stochastic data items. Some unresolved difficulties are identified.

Solving linear programs with multiple right-hand sides: Pricing and ordering schemes

This paper discusses the use of different pricing and ordering schemes when solving many linear programs that differ only in the right-hand sides. This is done in a setting of what has become known as bunching or trickling down. The idea is to collect (bunch) all right-hand sides that have the same optimal basis, and to organize the search for these bases efficiently. We demonstrate that the choice of pricing rule is indeed very important, but we were not able to make conclusions regarding ordering schemes. Numerical results are given.

AN XML-BASED SCHEMA FOR STOCHASTIC PROGRAMS

This paper describes a proposed format to record instances of stochastic programs. It forms part of a larger XML-based schema that is designed to allow the expression of essentially any type of mathematical program within a unifying framework. A wide variety of different linear and nonlinear stochastic programs can be handled, and the paper describes in some detail how this is done. Screen captures and sample problems illustrate the use of the schema.

Stochastic programming : applications in finance, energy, planning and logistics

This book shows the breadth and depth of stochastic programming applications. All the papers presented here involve optimization over the scenarios that represent possible future outcomes of the uncertainty problems. The applications, which were presented at the 12th International Conference on Stochastic Programming held in Halifax, Nova Scotia in August 2010, span the rich field of uses of these models. The finance papers discuss such diverse problems as longevity risk management of individual investors, personal financial planning, intertemporal surplus management, asset management with benchmarks, dynamic portfolio management, fixed income immunization and racetrack betting. The production and logistics papers discuss natural gas infrastructure design, farming Atlantic salmon, prevention of nuclear smuggling and sawmill planning. The energy papers involve electricity production planning, hydroelectric reservoir operations and power generation planning for liquid natural gas plants. Finally, two telecommunication papers discuss mobile network design and frequency assignment problems.

On stages and consistency checks in stochastic programming

This paper gives a rigorous definition of a stage, usable for dynamic stochastic programs with both recourse and probabilistic constraints. Algebraic modelling languages can make use of this definition for automatic consistency checks.

Modelling support for stochastic programs

In many decision problems, some of the factors considered are subject to significantuncertainty, randomness, or statistical fluctuations: these circumstances motivate the studyof stochastic models. The paper is intended to provide an overview of modelling toolsavailable for the development, analysis, solution and maintenance of stochastic programs.A brief introduction to some important model forms is followed by a review of suitablemodelling and computational environments, including algebraic modelling languages.Aspects of problem description, solution methodology, report generation, and visual problemrepresentation, as well as certain auxiliary tools and diagnostics are discussed. An extensivelist of references is provided, to give further pointers into a challenging field of greatpractical importance.