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Book part
Publication date: 6 November 2013

Bartosz Sawik

This chapter presents the survey of selected linear and mixed integer programming multi-objective portfolio optimization. The definitions of selected percentile risk…

Abstract

This chapter presents the survey of selected linear and mixed integer programming multi-objective portfolio optimization. The definitions of selected percentile risk measures are presented. Some contrasts and similarities of the different types of portfolio formulations are drawn out. The survey of multi-criteria methods devoted to portfolio optimization such as weighting approach, lexicographic approach, and reference point method is also presented. This survey presents the nature of the multi-objective portfolio problems focuses on a compromise between the construction of objectives, constraints, and decision variables in a portfolio and the problem complexity of the implemented mathematical models. There is always a trade-off between computational time and the size of an input data, as well as the type of mathematical programming formulation with linear and/or mixed integer variables.

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Article
Publication date: 5 May 2020

Moinak Maiti, Victor Krakovich, S.M. Riad Shams and Darko B. Vukovic

The paper introduces a resource-based linear programming model for resource optimization in small innovative enterprises (SIE).

Abstract

Purpose

The paper introduces a resource-based linear programming model for resource optimization in small innovative enterprises (SIE).

Design/methodology/approach

The model is grounded on resource-based view on the firm and dynamic capabilities approach. Linear programming technique is used to provide the actual framework to the resource-based model.

Findings

The paper introduces a new resource-based linear programming model for resource optimization in small innovative enterprises. The conceptual model is grounded on resource-based view (RBV) and dynamic capabilities strategy. The RVB of firm and firm strategy is based on the concept of economic rent. Linear programming technique is used to provide the actual framework to the resource-based model. In developing the versatility concept, study suggests a distinct sight regarding resource fungibility. Study classifies resources into multipliable, rentable and expendable resources to increases adequacy of the model. The developed model includes both tangible and intangible assets such as human capital. The survival rate of SIE in the early stages of life cycle is very low due to the competition among SIEs. In this regard, the greatest advancement of the developed resource-based linear programming model is its simplicity and versatility which is much desirable for the SIE especially in their initial stages of the life cycle. Kelliher and Reinl (2009) argued that micro firms have unique advantage over bigger firms in following term: rate of learning or redeployment of strategy in micro firms is faster than the rate of change in their environment. One very significant feature of the developed resource-based linear programming model is that mathematically the proposed model could easily be transformed into mixed integer or stochastic linear programming models to meet the time variant requirement of small firms especially when it expands its operation.

Research limitations/implications

The survival rate of SIE in the early stages of life cycle is very low due to the competition among SIEs. In this regard, the greatest advancement of the developed resource-based linear programming model is its simplicity and versatility which is much desirable for the SIE especially in their initial stages of the life cycle. Kelliher and Reinl (2009) argued that micro firms have unique advantage over bigger firms in following term: rate of learning or redeployment of strategy in micro firms is faster than the rate of change in their environment. One very significant feature of the developed resource-based linear programming model is that mathematically the proposed model could easily be transformed into mixed integer or stochastic linear programming models to meet the time variant requirement of small firms especially when it expands its operation.

Originality/value

One very significant contribution of the present study is that the study develops a new resource-based model for SIE especially for the SIE in the initial stages of the life cycle, to gain competitive advantages. Furthermore, the present study contributes to the existing literature in strategy at least in three senses as mentioned below: 1. further addition of SIE research based on the RBV and dynamic capabilities in the strategy literature 2. in developing the versatility concept, the study suggests a distinct sight regarding resource fungibility and it classifies resources into three categories as follows: multipliable, rentable and expendable resources to increases adequacy of the model. 3. Finally, the study introduces a new resource-based linear programming model for SIE resources allocation. To the best of author’s knowledge, no such similar model is introduced by any previous studies for small firm. The greatest advancement of the developed resource-based linear programming model is its simplicity and versatility.

Details

Management Decision, vol. 58 no. 8
Type: Research Article
ISSN: 0025-1747

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Article
Publication date: 1 May 1990

Usha Sharma and K.B. Misra

A large number of research articles have appeared in the literature during the last two decades on the subject of system reliability optimisation, each with a view to…

Abstract

A large number of research articles have appeared in the literature during the last two decades on the subject of system reliability optimisation, each with a view to providing simple, exact and efficient techniques. Here, an efficient, fast and exact technique is proposed for solving integerprogramming problems that normally arise in optimal reliability design problems. The algorithm presented is superior to any of the earlier methods available so far, being based on functional evaluations and a limited systematic search close to the boundary of resources. Thus it can quickly solve even very large system problems. It can also be effectively used with other operations research problems involving integerprogramming formulations.

Details

International Journal of Quality & Reliability Management, vol. 7 no. 5
Type: Research Article
ISSN: 0265-671X

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Book part
Publication date: 1 January 1991

Abstract

Details

Operations Research for Libraries and Information Agencies: Techniques for the Evaluation of Management Decision Alternatives
Type: Book
ISBN: 978-0-12424-520-4

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Article
Publication date: 1 April 1981

Arthur Meidan

Introduction Operations research, i.e. the application of scientific methodology to operational problems in the search for improved understanding and control, can be said…

Abstract

Introduction Operations research, i.e. the application of scientific methodology to operational problems in the search for improved understanding and control, can be said to have started with the application of mathematical tools to military problems of supply bombing and strategy, during the Second World War. Post‐war these tools were applied to business problems, particularly production scheduling, inventory control and physical distribution because of the acute shortages of goods and the numerical aspects of these problems.

Details

Management Decision, vol. 19 no. 4/5
Type: Research Article
ISSN: 0025-1747

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Article
Publication date: 10 August 2010

Alain Billionnet

Negative effects of habitat isolation that arise from landscape fragmentation can be mitigated, by connecting natural areas through a network of habitat corridors. To…

Abstract

Purpose

Negative effects of habitat isolation that arise from landscape fragmentation can be mitigated, by connecting natural areas through a network of habitat corridors. To increase the permeability of a given network, i.e. to decrease the resistance to animal movements through this network, often many developments can be made. The available financial resources being limited, the most effective developments must be chosen. This optimization problem, suggested in Finke and Sonnenschein, can be treated by heuristics and simulation approaches, but the method is heavy and the obtained solutions are sub‐optimal. The aim of the paper is to show that the problem can be efficiently solved to optimality by mathematical programming.

Design/methodology/approach

The moves of the individual in the network are modeled by an absorbing Markov chain and the development problem is formulated as a mixed‐integer quadratic program, then this program is linearized, and the best developments to make are determined by mixed‐integer linear programming.

Findings

First, the approach allows the development problem to be solved to optimality contrary to other methods. Second, the definition of the mathematical program is relatively simple, and its implementation is immediate by using standard, commercially available, software. Third, as it is well known with mixed‐integer linear programming formulation it is possible to add new constraints easily if they are linear (or can be linearized).

Research limitations/implications

With a view to propose a simple and efficient tool to solve a difficult combinatorial optimization problem arising in the improvement of permeability across habitat networks, the approach has been tested on simulated habitat networks. The research does not include the study of some precise species movements in a real network.

Practical implications

The results provide a simple and efficient decision‐aid tool to try to improve the permeability of habitat networks.

Originality/value

The joint use of mathematical programming techniques and Markov chain theory is used to try to lessen the negative effects of landscape fragmentation.

Details

Management of Environmental Quality: An International Journal, vol. 21 no. 5
Type: Research Article
ISSN: 1477-7835

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Article
Publication date: 1 October 1995

B.A. Murtagh and J.W. Sims

Describes a procedure for modelling the costs of production anddistribution between several production facilities with economies ofscale and many customers who are widely…

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Abstract

Describes a procedure for modelling the costs of production and distribution between several production facilities with economies of scale and many customers who are widely dispersed. The problem takes the form of a large transportation problem on which is superimposed a cost minimization problem involving variable production quantities. These costs involve fixed costs for initiating production and variable costs with diminishing returns to scale. Models the problem as a non‐linear integer programming problem and then solves it using a recently developed non‐linear integer algorithm. Describes two applications in Australia and New Zealand and illustrates how comparison with a mixed‐integer linear programming formulation shows a significant improvement.

Details

International Journal of Physical Distribution & Logistics Management, vol. 25 no. 8
Type: Research Article
ISSN: 0960-0035

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Article
Publication date: 17 June 2020

Davood Darvishi, Sifeng Liu and Jeffrey Yi-Lin Forrest

The purpose of this paper is to survey and express the advantages and disadvantages of the existing approaches for solving grey linear programming in decision-making problems.

Abstract

Purpose

The purpose of this paper is to survey and express the advantages and disadvantages of the existing approaches for solving grey linear programming in decision-making problems.

Design/methodology/approach

After presenting the concepts of grey systems and grey numbers, this paper surveys existing approaches for solving grey linear programming problems and applications. Also, methods and approaches for solving grey linear programming are classified, and its advantages and disadvantages are expressed.

Findings

The progress of grey programming has been expressed from past to present. The main methods for solving the grey linear programming problem can be categorized as Best-Worst model, Confidence degree, Whitening parameters, Prediction model, Positioned solution, Genetic algorithm, Covered solution, Multi-objective, Simplex and dual theory methods. This survey investigates the developments of various solving grey programming methods and its applications.

Originality/value

Different methods for solving grey linear programming problems are presented, where each of them has disadvantages and advantages in providing results of grey linear programming problems. This study attempted to review papers published during 35 years (1985–2020) about grey linear programming solving and applications. The review also helps clarify the important advantages, disadvantages and distinctions between different approaches and algorithms such as weakness of solving linear programming with grey numbers in constraints, inappropriate results with the lower bound is greater than upper bound, out of feasible region solutions and so on.

Details

Grey Systems: Theory and Application, vol. 11 no. 1
Type: Research Article
ISSN: 2043-9377

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Article
Publication date: 19 June 2007

Ralf Östermark

To propose a new algorithmic platform (minlp_machine) for complex mixed‐integer non‐linear programming (MINLP) problems.

Abstract

Purpose

To propose a new algorithmic platform (minlp_machine) for complex mixed‐integer non‐linear programming (MINLP) problems.

Design/methodology/approach

The platform combines features from classical non‐linear optimization methodology with novel innovations in computational techniques. The system constructs discrete search zones around non‐integer discrete‐valued variables of local solutions, which reduces the search process significantly. In complicated problems fast feasibility restoration is achieved through concentrated Hessians. The system is programmed in strict ANSI C and can be run either stand alone or as a support library for other programs. File I/O is designed to recognize possible usage in both single and parallel processor environments.

Findings

The system has been tested on Alpha and Sun mainframes and – as a support library for a Genetic Hybrid Algorithm (GHA()) – in Linux and IBM parallel supercomputer environments. The constrained problem can, for example, be solved through a sequence of first order Taylor approximations of the non‐linear constraints and occasional feasibility restoration through Hessian information of the Lagrangian of the MINLP problem, or by invoking a nonlinear solver like SQP directly in the branch and bound tree. The system has been successfully tested on a small sample of representative continuous‐valued non‐linear programming problems.

Originality/value

It is demonstrated that – through zone‐constrained search – minlp_machine() outperforms some recent competing approaches with respect to the number of nodes in the branch and bound tree.

Details

Kybernetes, vol. 36 no. 5/6
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 5 March 2018

Vincent Reinbold, Van-Binh Dinh, Daniel Tenfen, Benoit Delinchant and Dirk Saelens

This paper aims to present two mathematical models to solve the Energy Management problem of a building microgrid (MG). In particular, it proposes a deterministic mixed…

Abstract

Purpose

This paper aims to present two mathematical models to solve the Energy Management problem of a building microgrid (MG). In particular, it proposes a deterministic mixed integer linear programming (MILP) and non-linear programming (NLP) formulations. This paper focuses on the modelling process and the optimization performances for both approaches regarding optimal operation of near-zero energy buildings connected to an electric MG with a 24-h time horizon.

Design/methodology/approach

A general architecture of a MG is detailed, involving energy storage systems, distributed generation and a thermal reduced model of the grid-connected building. A continuous non-linear model is detailed along with linearizations for the mixed-integer liner formulation. Multi-physic, non-linear and non-convex phenomena are detailed, such as ventilation and air quality models.

Findings

Results show that both approaches are relevant for solving the energy management problem of the building MG.

Originality/value

Introduction and modelling of the thermal loads within the MG. The resulting linear program handles the mutli-objective trade-off between discomfort and the cost of use taking into account air quality criterion. Linearization and modelling of the ventilation system behaviour, which is generally non-linear and non-convex equality constraints, involving air quality model, heat transfer and ventilation power. Comparison of both MILP and NLP methods on a general use case provides a solution that can be interpreted for implementation.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 37 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

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