共查询到20条相似文献,搜索用时 31 毫秒
1.
N. C. Steele K.‐J. Backstrom 《International Journal of Mathematical Education in Science & Technology》2013,44(5):693-695
In the past decade there have been significant developments in computer technology and solution techniques for analysing business and industrial decision problems. In recent years good modelling systems have become available to ease the burden of model communication. Currently the single most important barrier to increased use of structured approaches to decision modelling is the acquisition of the necessary skills to initially develop models of complex decision systems. This paper examines the modelling process with reference to linear programming. Two related production planning problems are presented and their associated models developed. The relationship between the two problems is such that student modellers are forced to become involved in the important details of the problems and, by examining the nature of solution spaces in constrained optimisation, students are able to rapidly gain confidence and skills in modelling. 相似文献
2.
Nuno P. Faísca Pedro M. Saraiva Berç Rustem Efstratios N. Pistikopoulos 《Computational Management Science》2009,6(4):377-397
In this paper, we outline the foundations of a general global optimisation strategy for the solution of multilevel hierarchical
and general decentralised multilevel problems, based on our recent developments on multi-parametric programming and control
theory. The core idea is to recast each optimisation subproblem, present in the hierarchy, as a multi-parametric programming
problem, with parameters being the optimisation variables belonging to the remaining subproblems. This then transforms the
multilevel problem into single-level linear/convex optimisation problems. For decentralised systems, where more than one optimisation
problem is present at each level of the hierarchy, Nash equilibrium is considered. A three person dynamic optimisation problem
is presented to illustrate the mathematical developments. 相似文献
3.
4.
A study was made on the existing practices of production planning, scheduling and prevailing constraints in the six plants of a lube oil section in a petroleum refinery. Based on the data collected from these plants, some generative and evaluative models were developed. The generative models developed were flow network optimisation (FNO) model and binary integer linear programming (BILP) model. The evaluative model developed was simulation. The optimal results obtained from the generative model were fed to the evaluative model to derive the measure of performance. This integration of generative and evaluative models offers an opportunity for better understanding of the subsystem and appropriate decision making. 相似文献
5.
Xiaobo Li Karthik Natarajan Chung-Piaw Teo Zhichao Zheng 《European Journal of Operational Research》2014
In this paper, we review recent advances in the distributional analysis of mixed integer linear programs with random objective coefficients. Suppose that the probability distribution of the objective coefficients is incompletely specified and characterized through partial moment information. Conic programming methods have been recently used to find distributionally robust bounds for the expected optimal value of mixed integer linear programs over the set of all distributions with the given moment information. These methods also provide additional information on the probability that a binary variable attains a value of 1 in the optimal solution for 0–1 integer linear programs. This probability is defined as the persistency of a binary variable. In this paper, we provide an overview of the complexity results for these models, conic programming formulations that are readily implementable with standard solvers and important applications of persistency models. The main message that we hope to convey through this review is that tools of conic programming provide important insights in the probabilistic analysis of discrete optimization problems. These tools lead to distributionally robust bounds with applications in activity networks, vertex packing, discrete choice models, random walks and sequencing problems, and newsvendor problems. 相似文献
6.
《European Journal of Operational Research》1996,89(2):408-422
In the past two decades, there has been a significant increase in the number of interactive algorithms proposed for solving multiple objective mathematical programming (MOMP) problems. Most of these procedures have neither been tested in real decision making situations, nor compared to each other. In this study, we emphasize the importance of comparative studies of interactive MOMP procedures and present a state of the art review. Our scope is limited to the comparisons of interactive procedures for solving deterministic, linear, integer or nonlinear constrained multiple objective optimization problems involving a single decision maker. 相似文献
7.
8.
In this paper we develop an algorithm to optimise a nonlinear utility function of multiple objectives over the integer efficient set. Our approach is based on identifying and updating bounds on the individual objectives as well as the optimal utility value. This is done using already known solutions, linear programming relaxations, utility function inversion, and integer programming. We develop a general optimisation algorithm for use with k objectives, and we illustrate our approach using a tri-objective integer programming problem. 相似文献
9.
Yinyu YE 《Annals of Operations Research》1990,25(1):59-73
We describe recent developments in interior-point algorithms for global optimization. We will focus on the algorithmic research for nonconvex quadratic programming, linear complementarity problem, and integer programming. We also outline directions in which future progress might be made. 相似文献
10.
Parametric global optimisation for bilevel programming 总被引:2,自引:2,他引:0
Nuno P. Faísca Vivek Dua Berç Rustem Pedro M. Saraiva Efstratios N. Pistikopoulos 《Journal of Global Optimization》2007,38(4):609-623
We propose a global optimisation approach for the solution of various classes of bilevel programming problems (BLPP) based
on recently developed parametric programming algorithms. We first describe how we can recast and solve the inner (follower’s)
problem of the bilevel formulation as a multi-parametric programming problem, with parameters being the (unknown) variables
of the outer (leader’s) problem. By inserting the obtained rational reaction sets in the upper level problem the overall problem
is transformed into a set of independent quadratic, linear or mixed integer linear programming problems, which can be solved
to global optimality. In particular, we solve bilevel quadratic and bilevel mixed integer linear problems, with or without
right-hand-side uncertainty. A number of examples are presented to illustrate the steps and details of the proposed global
optimisation strategy. 相似文献
11.
A I Marqués V García J S Sánchez 《The Journal of the Operational Research Society》2013,64(9):1384-1399
The last years have seen the development of many credit scoring models for assessing the creditworthiness of loan applicants. Traditional credit scoring methodology has involved the use of statistical and mathematical programming techniques such as discriminant analysis, linear and logistic regression, linear and quadratic programming, or decision trees. However, the importance of credit grant decisions for financial institutions has caused growing interest in using a variety of computational intelligence techniques. This paper concentrates on evolutionary computing, which is viewed as one of the most promising paradigms of computational intelligence. Taking into account the synergistic relationship between the communities of Economics and Computer Science, the aim of this paper is to summarize the most recent developments in the application of evolutionary algorithms to credit scoring by means of a thorough review of scientific articles published during the period 2000–2012. 相似文献
12.
This paper is on fuzzy stochastic optimisation, an area that is quickly coming to the forefront of mathematical programming under uncertainty. An even stronger motivating factor for the growing interest in this area can be found in the ubiquitous nature of decision problems involving hybrid imprecision. More precisely, we consider a range of situations in which random factors and fuzzy information co-occur in an optimisation setting. Related hybrid optimisation models are discussed and converted into deterministic terms through appropriate tools like probabilistic set, uncertain probability, and fuzzy random variable, making good use of uncertainty principles. We also discuss ways to deal with the resulting problems. Numerical examples carried out using class optimisation software demonstrate the efficiency of the proposed approaches. We shall end this article by pointing out some of the challenges that currently occupy researchers in this emerging field. 相似文献
13.
An approach to the valuation and decision of ERP investment projects based on real options 总被引:1,自引:0,他引:1
The risks and uncertainties inherent in most enterprise resources planning (ERP) investment projects are vast. Decision making
in multistage ERP projects investment is also complex, due mainly to the uncertainties involved and the various managerial
and/or physical constraints to be enforced. This paper tackles the problem using a real-option analysis framework, and applies
multistage stochastic integer programming in formulating an analytical model whose solution will yield optimum or near-optimum
investment decisions for ERP projects. Traditionally, such decision problems were tackled using lattice simulation or finite
difference methods to compute the value of simple real options. However, these approaches are incapable of dealing with the
more complex compound real options, and their use is thus limited to simple real-option analysis. Multistage stochastic integer
programming is particularly suitable for sequential decision making under uncertainty, and is used in this paper and to find
near-optimal strategies for complex decision problems. Compared with the traditional approaches, multistage stochastic integer
programming is a much more powerful tool in evaluating such compound real options. This paper describes the proposed real-option
analysis model and uses an example case study to demonstrate the effectiveness of the proposed approach. 相似文献
14.
《Applied Mathematical Modelling》2014,38(21-22):5334-5346
The determination of a single efficient decision making unit (DMU) as the most efficient unit has been attracted by decision makers in some situations. Some integrated mixed integer linear programming (MILP) and mixed integer nonlinear programming (MINLP) data envelopment analysis (DEA) models have been proposed to find a single efficient unit by the optimal common set of weights. In conventional DEA models, the non-Archimedean infinitesimal epsilon, which forestalls weights from being zero, is useless if one utilizes the well-known two-phase method. Nevertheless, this approach is inapplicable to integrated DEA models. Unfortunately, in some proposed integrated DEA models, the epsilon is neither considered nor determined. More importantly, based on this lack some approaches have been developed which will raise this drawback.In this paper, first of all some drawbacks of these models are discussed. Indeed, it is shown that, if the non-Archimedean epsilon is ignored, then these models can neither find the most efficient unit nor rank the extreme efficient units. Next, we formulate some new models to capture these drawbacks and hence attain assurance regions. Finally, a real data set of 53 professional tennis players is applied to illustrate the applicability of the suggested models. 相似文献
15.
Stackelberg solutions for fuzzy random two-level linear programming through probability maximization with possibility 总被引:1,自引:0,他引:1
This paper considers Stackelberg solutions for decision making problems in hierarchical organizations under fuzzy random environments. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced into the formulated fuzzy random two-level linear programming problems. On the basis of the possibility and necessity measures that each objective function fulfills the corresponding fuzzy goal, together with the introduction of probability maximization criterion in stochastic programming, we propose new two-level fuzzy random decision making models which maximize the probabilities that the degrees of possibility and necessity are greater than or equal to certain values. Through the proposed models, it is shown that the original two-level linear programming problems with fuzzy random variables can be transformed into deterministic two-level linear fractional programming problems. For the transformed problems, extended concepts of Stackelberg solutions are defined and computational methods are also presented. A numerical example is provided to illustrate the proposed methods. 相似文献
16.
Renata Mansini Wlodzimierz Ogryczak M. Grazia Speranza 《European Journal of Operational Research》2014
Markowitz formulated the portfolio optimization problem through two criteria: the expected return and the risk, as a measure of the variability of the return. The classical Markowitz model uses the variance as the risk measure and is a quadratic programming problem. Many attempts have been made to linearize the portfolio optimization problem. Several different risk measures have been proposed which are computationally attractive as (for discrete random variables) they give rise to linear programming (LP) problems. About twenty years ago, the mean absolute deviation (MAD) model drew a lot of attention resulting in much research and speeding up development of other LP models. Further, the LP models based on the conditional value at risk (CVaR) have a great impact on new developments in portfolio optimization during the first decade of the 21st century. The LP solvability may become relevant for real-life decisions when portfolios have to meet side constraints and take into account transaction costs or when large size instances have to be solved. In this paper we review the variety of LP solvable portfolio optimization models presented in the literature, the real features that have been modeled and the solution approaches to the resulting models, in most of the cases mixed integer linear programming (MILP) models. We also discuss the impact of the inclusion of the real features. 相似文献
17.
In this paper, we present a new preference disaggregation method for multiple criteria sorting problems, called DIS-CARD. Real-life experience indicates the need of considering decision making situations in which a decision maker (DM) specifies a desired number of alternatives to be assigned to single classes or to unions of some classes. These situations require special methods for multiple criteria sorting subject to desired cardinalities of classes. DIS-CARD deals with such a problem, using the ordinal regression approach to construct a model of DM’s preferences from preference information provided in terms of exemplary assignments of some reference alternatives, together with the above desired cardinalities. We develop a mathematical model for incorporating such preference information via mixed integer linear programming (MILP). Then, we adapt the MILP model to two types of preference models: an additive value function and an outranking relation. Illustrative example is solved to illustrate the methodology. 相似文献
18.
A penalty function approach for solving bi-level linear programs 总被引:8,自引:0,他引:8
The paper presents an approach to bi-level programming using a duality gap—penalty function format. A new exact penalty function exists for obtaining a global optimal solution for the linear case, and an algorithm is given for doing this, making use of some new theoretical properties. For each penalty parameter value, the central optimisation problem is one of maximising a convex function over a polytope, for which a modification of an algorithm of Tuy (1964) is used. Some numerical results are given. The approach has other features which assist the actual decisionmaking process, which make use of the natural roles of duality gaps and penalty parameters. The approach also allows a natural generalization to nonlinear problems. 相似文献
19.
Multilevel programming is characterized as mathematical programming to solve decentralized planning problems. The models partition control over decision variables among ordered levels within a hierarchical planning structure of which the linear bilevel form is a special case of a multilevel programming problem. In a system with such a hierarchical structure, the high-level decision making situations generally require inclusion of zero-one variables representing ‘yes-no’ decisions. We provide a mixed-integer linear bilevel programming formulation in which zero-one decision variables are controlled by a high-level decision maker and real-value decision variables are controlled by a low-level decision maker. An algorithm based on the short term memory component of Tabu Search, called Simple Tabu Search, is developed to solve the problem, and two supplementary procedures are proposed that provide variations of the algorithm. Computational results disclose that our approach is effective in terms of both solution quality and efficiency. 相似文献
20.
《Mathematical and Computer Modelling》2000,31(10-12):89-98
Stochastic programming is concerned with practical procedures for decision making under uncertainty, by modelling uncertainties and risks associated with decision in a form suitable for optimization. The field is developing rapidly with contributions from many disciplines such as operations research, probability and statistics, and economics. A stochastic linear program with recourse can equivalently be formulated as a convex programming problem. The problem is often large-scale as the objective function involves an expectation, either over a discrete set of scenarios or as a multi-dimensional integral. Moreover, the objective function is possibly nondifferentiable. This paper provides a brief overview of recent developments on smooth approximation techniques and Newton-type methods for solving two-stage stochastic linear programs with recourse, and parallel implementation of these methods. A simple numerical example is used to signal the potential of smoothing approaches. 相似文献