Fuzzy linear programming problems : models and solutions

We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, alpha-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately

Models for Oil Refinery Waste Management Using Determined and Fuzzy Conditions

This study developed models to solve problems of optimisation, production, and consumption in waste management based on methods of system analysis. Mathematical models of the problems of optimisation and sustainable waste management in deterministic conditions and in a fuzzy environment were formulated. The income from production was maximised considering environmental standards that apply to the field of macroeconomics and microeconomics. The proposed approach used MANAGER software to formalise and solve the problem of revenue optimisation with production waste management to optimise the production of oil products with waste management at a specific technological facility of the Atyrau oil refinery in Kazakhstan. Based on the combined application of the principles of maximin and Pareto optimality, a formulation of the problem of production optimisation with waste management was obtained and a heuristic algorithm for solving the formulated fuzzy optimisation problem with waste management was developed.info:eu-repo/semantics/publishedVersio

FINANCIAL STRUCTURE OPTIMIZATION BY USING A GOAL PROGRAMMING APPROACH

This paper proposes a new methodology for solving the multiple objective fractional linear programming problems using Taylor’s formula and goal programming techniques. The proposed methodology is tested on the example of company\u27s financial structure optimization. The obtained results indicate the possibility of efficient application of the proposed methodology for company\u27s financial structure optimization as well as for solving other multi-criteria fractional programming problems

Enhancing Evacuation Planning in Public Buildings: Optimising Egress Location and Protection

Effective evacuation strategies are crucial for ensuring the safety of individuals during emergencies and disasters. Despite significant progress in evacuation planning, the intricate dynamics of disaster scenarios and uncertainties inherent in such situations need to be better incorporated in planning egress locations to enhance safety in buildings. This work focuses on strategically locating egress points within public buildings, acknowledging their pivotal role in facilitating secure evacuations. Optimising egress points improves evacuation efficiency and minimises associated risks, significantly improving evacuation. This research introduces an innovative approach that integrates optimisation models, addresses decision-making complexities, explores practical applications, and considers potential attack scenarios. The study explores evacuation dynamics across diverse scenarios, elevating preparedness, and safety protocols to protect public assets and lives. Developing mixedinteger programming models establishes a foundation for optimising egress locations. MCDM is then employed, leveraging the F-AHP to address uncertainties in egress selection. Practicality is realised through integrating Revit and AnyLogic software, facilitating assessment through BIM and ABM. A stochastic BP model is formulated, addressing both Defender and Attacker perspectives for enhanced egress strategies. This model strategically allocates resources to fortify egresses, ensuring occupant safety during evacuations. Contributions further optimisation approaches, fortification strategies, and progressive enhancements in evacuation planning. These collectively address key challenges and gaps in existing literature, enhancing evacuation efficiency and public safety during emergencies. The research bridges gaps in existing approaches, providing a framework for future investigations into optimising evacuation strategies, enhanced disaster preparation, and further advancements in the field

Domination and Decomposition in Multiobjective Programming

During the last few decades, multiobjective programming has received much attention for both its numerous theoretical advances as well as its continued success in modeling and solving real-life decision problems in business and engineering. In extension of the traditionally adopted concept of Pareto optimality, this research investigates the more general notion of domination and establishes various theoretical results that lead to new optimization methods and support decision making. After a preparatory discussion of some preliminaries and a review of the relevant literature, several new findings are presented that characterize the nondominated set of a general vector optimization problem for which the underlying domination structure is defined in terms of different cones. Using concepts from linear algebra and convex analysis, a well known result relating nondominated points for polyhedral cones with Pareto solutions is generalized to nonpolyhedral cones that are induced by positively homogeneous functions, and to translated polyhedral cones that are used to describe a notion of approximate nondominance. Pareto-oriented scalarization methods are modified and several new solution approaches are proposed for these two classes of cones. In addition, necessary and sufficient conditions for nondominance with respect to a variable domination cone are developed, and some more specific results for the case of Bishop-Phelps cones are derived. Based on the above findings, a decomposition framework is proposed for the solution of multi-scenario and large-scale multiobjective programs and analyzed in terms of the efficiency relationships between the original and the decomposed subproblems. Using the concept of approximate nondominance, an interactive decision making procedure is formulated to coordinate tradeoffs between these subproblems and applied to selected problems from portfolio optimization and engineering design. Some introductory remarks and concluding comments together with ideas and research directions for possible future work complete this dissertation

Methodology and Software for Interactive Decision Support

These Proceedings report the scientific results of an International Workshop on "Methodology and Software for Interactive Decision Support" organized jointly by the System and Decision Sciences Program of IIASA and The National Committee for Applied Systems Analysis and Management in Bulgaria. Several other Bulgarian institutions sponsored the workshop -- The Committee for Science to the Council of Ministers, The State Committee for Research and Technology and The Bulgarian Industrial Association. The workshop was held in Albena, on the Black Sea Coast. In the first section, "Theory and Algorithms for Multiple Criteria Optimization," new theoretical developments in multiple criteria optimization are presented. In the second section, "Theory, Methodology and Software for Decision Support Systems," the principles of building decision support systems are presented as well as software tools constituting the building components of such systems. Moreover, several papers are devoted to the general methodology of building such systems or present experimental design of systems supporting certain class of decision problems. The third section addresses issues of "Applications of Decision Support Systems and Computer Implementations of Decision Support Systems." Another part of this section has a special character. Beside theoretical and methodological papers, several practical implementations of software for decision support have been presented during the workshop. These software packages varied from very experimental and illustrative implementations of some theoretical concept to well developed and documented systems being currently commercially distributed and used for solving practical problems

A review of portfolio planning: Models and systems

In this chapter, we first provide an overview of a number of portfolio planning models which have been proposed and investigated over the last forty years. We revisit the mean-variance (M-V) model of Markowitz and the construction of the risk-return efficient frontier. A piecewise linear approximation of the problem through a reformulation involving diagonalisation of the quadratic form into a variable separable function is also considered. A few other models, such as, the Mean Absolute Deviation (MAD), the Weighted Goal Programming (WGP) and the Minimax (MM) model which use alternative metrics for risk are also introduced, compared and contrasted. Recently asymmetric measures of risk have gained in importance; we consider a generic representation and a number of alternative symmetric and asymmetric measures of risk which find use in the evaluation of portfolios. There are a number of modelling and computational considerations which have been introduced into practical portfolio planning problems. These include: (a) buy-in thresholds for assets, (b) restriction on the number of assets (cardinality constraints), (c) transaction roundlot restrictions. Practical portfolio models may also include (d) dedication of cashflow streams, and, (e) immunization which involves duration matching and convexity constraints. The modelling issues in respect of these features are discussed. Many of these features lead to discrete restrictions involving zero-one and general integer variables which make the resulting model a quadratic mixed-integer programming model (QMIP). The QMIP is a NP-hard problem; the algorithms and solution methods for this class of problems are also discussed. The issues of preparing the analytic data (financial datamarts) for this family of portfolio planning problems are examined. We finally present computational results which provide some indication of the state-of-the-art in the solution of portfolio optimisation problems