Food industry is one of the fastest growing industry. With the development of varieties in this industry, the need for revenue management is vital. Revenue management is a technique to optimize the income by selling t...
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Food industry is one of the fastest growing industry. With the development of varieties in this industry, the need for revenue management is vital. Revenue management is a technique to optimize the income by selling the right product to right customer at right time which is done by using data driven tactics and strategies. In this paper, a revenue management problem is formulated as multi-objective programming problem in an uncertain environment. As in real life situations most of the parameters are generally uncertain, therefore cost parameter considered as triangular fuzzy numbers. Fuzzy problem is converted into deterministic problem by alpha-cut method and then the algorithm is developed to solve the multi-objective linear programmingproblem to optimize revenue as well as cost simultaneously. To demonstrate and justify the formulated problem a numerical illustration has been considered and solved. All the mathematical problems are solved through an optimisation software LINGO-13.
The paper presents the solution methodology of a multi-objective probabilistic fractional programmingproblem, where the parameters of the right hand side constraints follow Cauchy distribution. The proposed mathemati...
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The paper presents the solution methodology of a multi-objective probabilistic fractional programmingproblem, where the parameters of the right hand side constraints follow Cauchy distribution. The proposed mathematical model can not be solved directly. The solution procedure is completed in three steps. In first step, multi-objective probabilistic fractional programmingproblem is converted to deterministic multi-objective fractional mathematical programmingproblem. In the second step, it is converted to its equivalent multi-objective mathematical programmingproblem. Finally, epsilon-constraint method is applied to find the best compromise solution. A numerical example and application are presented to demonstrate the procedure of proposed mathematical model.
The growing dependence on optimization models in decision-making has created a demand for tools that can facilitate the formulation and resolution of a broader range of real-world processes and systems associated with...
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The growing dependence on optimization models in decision-making has created a demand for tools that can facilitate the formulation and resolution of a broader range of real-world processes and systems associated with human activity. These situations often involve assumptions that diverge from traditional optimization methodologies. One viable approach for addressing optimization problems in real-life scenarios with uncertainty is interval-valued optimization. Taking into account the significance of interval-valued optimization, in this paper, we derive first and second order necessary optimality conditions for a multi-objective programming problem with interval-valued objective functions defined on a Riemannian manifold. To establish these conditions, we consider the objective functions to be weakly differentiable and twice weakly differentiable for first and second order, respectively. Additionally, we assume that the constraints, both equality and inequality constraints, are differentiable and twice differentiable for first and second order conditions respectively. The first order as well as second order necessary conditions are derived under two types of constraint qualifications. Furthermore, we provide illustrative examples to demonstrate the application of the established results.
The objective of this paper is to introduce a method for computing weights of attributes in a decision making problem under intuitionistic fuzzy environment. Many weight generation methods exist in the literature unde...
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The objective of this paper is to introduce a method for computing weights of attributes in a decision making problem under intuitionistic fuzzy environment. Many weight generation methods exist in the literature under intuitionistic fuzzy setting, but they have some limitations which can be pointed out as: the entropy measures used in entropy weight methods are invalid in many situations and also there are lots of entropy formulae for intuitionistic fuzzy sets, which will be better to use, and thus a confusion may arise;the other weight generation methods may lose some information since it needs to transform the intuitionistic fuzzy decision matrix into an interval-valued decision matrix. This conversion distorts experts original opinions. In this point of view, to overcome these demerits, we develop a weight generation method without changing the original decision information. The proposed method maximizes the average degree of satisfiability and minimizes the average degree of non-satisfiability of each alternative over a set of attributes, simultaneously. This leads to formulate a multi-objective programming problem (MOPP) to compute the final comprehensive value for each alternative. The scenario of an MOPP itself is subjective and can be modeled by fuzzy decision making problem due to the conflicting objectives and the way of human choice on conflict resolution. This problem is solved by using particle swarm optimization scheme, and the evaluation procedure is illustrated by means of a numerical example. This work has also justified the proposed approach by analyzing a comparative study.
This paper demonstrates a satisfaction-based method for solving multi-objective programming problems in a multi-level decision structure through the renewed use of a weighted additive fuzzy goal programming (weighted ...
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This paper demonstrates a satisfaction-based method for solving multi-objective programming problems in a multi-level decision structure through the renewed use of a weighted additive fuzzy goal programming (weighted additive-FGP) approach. The weighted additive-FGP enables us to indicate decision maker's preferences toward the unit's goals and decision vectors that are controlled by the decision maker in the pth-level. This paper presents the algorithm reflecting the influence of a higher-level decision on the decision of a lower level, with the respective decision maker having the authority to place emphasis on certain decision variables. A numerical example clearly illustrates the proposed solution procedure.
In this paper, multi-objectiveprogramming (MOP) approaches are proposed to deal with the feasible Vertical Block Linear Complementarity problems (VLCP) and to look into the solvability and unsolvability of the VLCP. ...
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In this paper, multi-objectiveprogramming (MOP) approaches are proposed to deal with the feasible Vertical Block Linear Complementarity problems (VLCP) and to look into the solvability and unsolvability of the VLCP. The characterization of an unsolvable VLCP is obtained via the existence of nonzero efficient point of the MOP problem. Also a perturbed problem is proposed if the VLCP is unsolvable for small disturbances in data. This perturbed problem is useful to construct the solvable VLCP corresponding to the original unsolvable VLCP. Examples are given to demonstrate the effectiveness of the results.
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