In this paper, nonsmooth univex, nonsmooth quasiunivex, and nonsmooth pseudounivex functions are introduced. By utilizing these new concepts, sufficient optimality conditions for a weakly efficient solution of the non...
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In this paper, nonsmooth univex, nonsmooth quasiunivex, and nonsmooth pseudounivex functions are introduced. By utilizing these new concepts, sufficient optimality conditions for a weakly efficient solution of the nonsmooth multiobjective programming problem are established. Weak and strong duality theorems axe also derived for Mond-Weir type multiobjective dual programs.
In this paper, we are concerned with a vector reverse convex minimization problem (P). For such a problem, by means of the so-called Fenchel-Lagrange duality, we provide nec-essary optimality conditions for proper eff...
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In this paper, we are concerned with a vector reverse convex minimization problem (P). For such a problem, by means of the so-called Fenchel-Lagrange duality, we provide nec-essary optimality conditions for proper efficiency in the sense of Geoffrion. This duality is used after a decomposition of problem (P) into a family of convex vector minimization sub-problems and scalarization of these subproblems. The optimality conditions are expressed in terms of subdifferentials and normal cones in the sense of convex analysis. The obtained results are new in the literature of vector reverse convex programming. Moreover, some of them extend with improvement some similar results given in the literature, from the scalar case to the vectorial one.
In this paper, a new pair of higher-order nondifferentiable multiobjective mixed symmetric dual programs over arbitrary cones is formulated, where each of the objective functions contains a support function of a compa...
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In this paper, a new pair of higher-order nondifferentiable multiobjective mixed symmetric dual programs over arbitrary cones is formulated, where each of the objective functions contains a support function of a compact convex set. Usual duality theorems are established under higher-order K-(F,alpha,rho,d)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(F,\alpha ,\rho ,d)$$\end{document}-convexity assumptions. Also, the example of a higher-order dual pair, which shows that higher-order provides tighter bounds for the value of the objective function of the primal and dual problem, is given in the paper. Several known results are also discussed as special cases.
Relief activities are complicated when multiple disasters take place simultaneously at different locations. Designing effective relief networks for these instances involves managing the priorities among regions and pr...
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Relief activities are complicated when multiple disasters take place simultaneously at different locations. Designing effective relief networks for these instances involves managing the priorities among regions and products, developing the capacity to share limited resources and facilities, and engaging with multiple suppliers over several periods. Unfortunately, even after recent experiences in different countries, the management of simultaneous disasters is still understudied. This article introduces a two-stage dynamic formulation for logistics decisions in instances caused by simultaneous disasters. It guides supplier selection, facility location, stock prepositioning, and resource allocation at the first stage, whereas relief distribution, postdisaster procurement, and inventory management are addressed at the second stage. The model minimizes cost and the maximum shortage. Results of numerical experiments show the way the model considers the characteristics of each situation to dispatch limited shared resources. The experiments show that planning for single disasters has a negative impact on performance when faced with situations caused by simultaneous disasters. That is confirmed by findings from the case study in Mexico, which also highlights the preference for prepositioning stock using a mix of different kind of suppliers, and the importance of developing a reliable network of facilities and suppliers to handle simultaneous disasters effectively.
The most important factor affecting efficiency and ergonomic risk levels in an assembly line design is the problem of assigning certain tasks to certain stations, namely the assembly line balancing problem. In the lit...
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The most important factor affecting efficiency and ergonomic risk levels in an assembly line design is the problem of assigning certain tasks to certain stations, namely the assembly line balancing problem. In the literature, assembly line balancing problem has often been studied, but studies that consider ergonomic risks are deficient. Recently, it has been one of the issues that have started to attract great attention with the realization of health problems caused by assembly lines. To this end, in this study, a bi-objective mathematical model is developed that considers balancing assembly line station time and ergonomic risk levels, simultaneously. It is aimed to minimize both station time and the total deviations of ergonomic risk scores for the stations. Weighted sum and conic scalarization methods are applied to solve the bi-objective model. To analyze the outcomes of the developed model, an application is proposed and tested on a real industrial case, at a home appliance assembly line. The deployment of the OMAX method is a contribution to the literature since it shows an analysis tool which evaluates the results of assembly line balancing. This method evaluates the performance of the stations based on different criteria such as station time and ergonomic risk. The number of high-risk stations is obtained as 13 in the single-objective model aiming to minimize the station time, while it is found to be nine in the bi-objective model solved with CSM, without an increase in the total number of stations.
In this paper, we focus on multiobjective two-level simple recourse programming problems with discrete-type LR fuzzy random variables, in which each of the decision makers called the leader and the follower optimizes ...
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In this paper, we focus on multiobjective two-level simple recourse programming problems with discrete-type LR fuzzy random variables, in which each of the decision makers called the leader and the follower optimizes his/her multiple objective functions independently, shortages and excesses arising from the violation of the constraints with discrete-type LR fuzzy random variables are penalized, and the sum of the objective function and the expectation of the amount of the penalties is minimized. To deal with such problems, we introduce a new solution concept called an estimated Pareto Stackelberg solution for the leader. To obtain a candidate of a satisfactory solution for the leader from among an estimated Pareto Stackelberg solution set, using the Kuhn-Tucker approach and the transformation technique for complementarity conditions, an original problem is transformed into a mixed integer programming problem. Then, we propose an interactive algorithm to obtain a satisfactory solution of the leader from among an estimated Pareto Stackelberg solution set. A numerical example illustrates the proposed algorithm for a multiobjective two-level fuzzy random simple recourse programming problem under the hypothetical leader.
Optimizing a function over the efficient set of a multiojective problem plays an important role in many fields of application. This problem arises whenever the decision maker wants to select the efficient solution tha...
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Optimizing a function over the efficient set of a multiojective problem plays an important role in many fields of application. This problem arises whenever the decision maker wants to select the efficient solution that optimizes his utility function. Several methods are proposed in literature to deal with the problem of optimizing a linear function over the efficient set of a multiobjective integer linear program MOILFP. However, in many real-world problems, the objective functions or the utility function are nonlinear. In this paper, we propose an exact method to optimize a quadratic function over the efficient set of a multiobjective integer linear fractional program MOILFP. The proposed method solves a sequence of quadratic integer problems. Where, at each iteration, the search domain is reduced s6uccessively, by introducing cuts, to eliminate dominated solutions. We conducted a computational experiment, by solving randomly generated instances, to analyze the performance of the proposed method.
An accurate prediction of asset prices is perhaps the biggest challenge of any study in portfolio optimization. Asset prices are affected by several random and nonrandom factors, which makes them difficult to forecast...
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An accurate prediction of asset prices is perhaps the biggest challenge of any study in portfolio optimization. Asset prices are affected by several random and nonrandom factors, which makes them difficult to forecast. This paper proposes a two-phase dynamic portfolio optimization approach. In the first phase, assets are clustered into buy, sell, and hold groups using technical indicators. We provide a methodology to integrate the investor attitude (optimistic, pessimistic, or neutral) during the clustering phase. In the second phase, we input the clustered groups into a portfolio optimization model to obtain the optimum asset allocations. We use coherent fuzzy numbers to model the asset returns to integrate the investor attitude in this phase. The optimization model is solved using a genetic algorithm. The portfolios are rebalanced at regular intervals as new data becomes available. We illustrate the proposed methodology on a 100-asset problem of the US stock market. We analyze the real-world performance of the obtained portfolios. We compare the performance of the proposed approach with the mean-variance model, and other portfolios, such as the naive portfolio and the NASDAQ-100 index.
In this paper,we point out some deficiencies in a recent paper(Lee and Kim in *** Convex Anal.13:599–614,2012),and we establish strong duality and converse duality theorems for two types of nondifferentiable higher-...
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In this paper,we point out some deficiencies in a recent paper(Lee and Kim in *** Convex Anal.13:599–614,2012),and we establish strong duality and converse duality theorems for two types of nondifferentiable higher-order symmetric duals multiobjective programming involving cones.
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