Mathematical programming in the Netherlands

Results of an exhaustive survey of mathematical programming in the Netherlands held in 1982 are presented and, where applicable, compared to a survey held in 1976. It appears that the growth rate has levelled off, that about half of the largest one hundred industrial firms in the Netherlands now apply MP and that the users are quite satisfied with LP programs except for input, output and documentation.     

Mathematical programming and electricity markets

The electric power industry in Europe and all over the world is undertaking major regulatory and operational changes. The underlying rationale behind all these changes is to move from a centralized operation approach to a competitive one. That is, the understanding of power supply as a public service is being replaced by the notion that a competitive market is a more appropriate framework to supply reliable and cheap electric energy to consumers. In some cases, the aforementioned transition process has included the privatization of power utilities. This new framework requires new tools and procedures, and some of these procedures drastically differ from traditional ones. Therefore, new challenging mathematical programming and operations research problems naturally arise in this context. This paper provides a review of some of these problems, particularly operational problems spanning a time horizon from one day to one year. The approach adopted emphasizes mathematical programming issues, describing the structure and characteristics of these problems and suggesting appropriate solution techniques. Relevant comments and suggestions were provided by Alexis Motto from McGill University, Montréal, Québec, Canada.     

Mathematical programming via the least-squares method

The least-squares method is used to obtain a stable algorithm for a system of linear inequalities as well as linear and nonlinear programming. For these problems the solution with minimal norm for a system of linear inequalities is found by solving the non-negative least-squares (NNLS) problem. Approximate and exact solutions of these problems are discussed. Attention is mainly paid to finding the initial solution to an LP problem. For this purpose an NNLS problem is formulated, enabling finding the initial solution to the primal or dual problem, which may turn out to be optimal. The presented methods are primarily suitable for ill-conditioned and degenerate problems, as well as for LP problems for which the initial solution is not known. The algorithms are illustrated using some test problems.     

Mathematical programming study 4

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Mathematical programming study 4Computational Practice in Mathematical Programming     

Simulation techniques for the sensitivity analysis of multi-criteria decision models

This paper presents a simulation approach for high dimensional sensitivity analysis of the weights of multi-criteria decision models. This approach allows simultaneous changes of the weights and generates results that can easily be analyzed statistically to provide insights into multi-criteria model recommendations. In this study we consider three cases: no information, order information, and partial information regarding the weights. Our approach also allows investigation of sensitivity to the form of multi-criteria decision models. The simulation procedures we propose can also be used to aide in the actual decision process, particularly when the task is to select a subset of superior alternatives.