In this study, we consider the linearprogramming problem with the objective of the investment discounted value, where the interest rate is imprecise and has a triangular possibilistic distribution. An (crisp) auxilia...
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In this study, we consider the linearprogramming problem with the objective of the investment discounted value, where the interest rate is imprecise and has a triangular possibilistic distribution. An (crisp) auxiliary bi-objective linearprogramming model is proposed to resolve this possibilistic nature. Furthermore, we develop an extended Zimmermann approach, called augmented max-min approach, for solving this auxiliary bi-objective linearprogramming problem and other multiple objective linearprogramming problems. Finally, a numerical bank balance sheet problem, where interest rates, price of futures contract, loan demand, deposit supply and ratio of desired loan to deposit are assumed to be fuzzy, is solved for illustrating the new approach.
In this paper, a robust optimization approach to possibilistic linear programming problems is studied. After necessity measures and generation processes of logical connectives are reviewed, the necessity tractile opti...
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ISBN:
(纸本)9783642225888
In this paper, a robust optimization approach to possibilistic linear programming problems is studied. After necessity measures and generation processes of logical connectives are reviewed, the necessity tractile optimization model of possibilistic linear programming problem is introduced as a robust optimization model. This problem is reduced to a linear semi-infinite programming problem. Assuming the convexity of the right parts of membership functions of fuzzy coefficients and the concavity of membership functions of fuzzy constraints, we investigate conditions on logical connectives for the problems to be reduced to linearprogramming problems. Several examples are given to demonstrate that necessity tractile optimization models are often reduced to linearprogramming problems.
In this paper, we develop a possibilistic linear programming model for supply chain network design with imprecise inputs: market demands, supplied quantities, transportation costs, opening costs, treatment and storage...
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In this paper, we develop a possibilistic linear programming model for supply chain network design with imprecise inputs: market demands, supplied quantities, transportation costs, opening costs, treatment and storage costs are modelled as fuzzy numbers. An efficient possibilisticlinear programme is constructed with fuzzy objective function that minimizes the sum of investment costs and operating costs of the supply chain. A method for solving the programming problem with fuzzy parameters is proposed. Application to a supply chain problem at a European textile company illustrates our methodology. Numerical results show that the performance of the proposed model in handling data uncertainty is better when compared to a classical deterministic model.
In practice, the unit costs/profits of new products or new projects, the lending and borrowing interest rates, and cash flows are always imprecise. We provide an auxiliary multiple objective linearprogramming model t...
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In practice, the unit costs/profits of new products or new projects, the lending and borrowing interest rates, and cash flows are always imprecise. We provide an auxiliary multiple objective linearprogramming model to solve a linearprogramming problem with imprecise objective and/or constraint coefficients. Our strategy is to maximize the most possible value of the imprecise profit. At the same time, we would like to minimize the risk of obtaining lower profit and maximize the possibility of obtaining higher profit. This strategy is equivalent to the practical considerations of financial problems. In this paper, a numeric investment problem is solved for illustrating the new approach.
This work presents a novel interactive possibilistic linear programming (PLP) approach for solving the multi-product aggregate production planning (APP) problem with imprecise forecast demand, related operating costs,...
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This work presents a novel interactive possibilistic linear programming (PLP) approach for solving the multi-product aggregate production planning (APP) problem with imprecise forecast demand, related operating costs, and capacity. The proposed approach attempts to minimize total costs with reference to inventory levels, labor levels, overtime, subcontracting and backordering levels, and labor, machine and warehouse capacity. The proposed approach uses the strategy of simultaneously minimizing the most possible value of the imprecise total costs, maximizing the possibility of obtaining lower total costs, and minimizing the risk of obtaining higher total costs. An industrial case demonstrates the feasibility of applying the proposed approach to real APP decision problems. Consequently, the proposed PLP approach yields an efficient APP compromise solution and overall degree of decision maker (DM) satisfaction with determined goal values. Particularly, several significant management implications and characteristics of the proposed PLP approach that distinguish it from the other APP decision models are presented. (c) 2004 Elsevier B.V. All rights reserved.
Aggregate production planning (APP) addresses matching supply to forecast demand, with varying customer orders over the intermediate planning horizon. In real-world APP problems, input data and related parameters are ...
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Aggregate production planning (APP) addresses matching supply to forecast demand, with varying customer orders over the intermediate planning horizon. In real-world APP problems, input data and related parameters are commonly imprecise because information is incomplete or unavailable, and the decision maker (DM) must simultaneously consider conflicting objectives. This study develops an interactive possibilistic linear programming (i-PLP) approach to solve multi-product and multi-time period APP problems with multiple imprecise objectives and cost coefficients by triangular possibility distributions in uncertain environments. The imprecise multi-objective APP model designed here seeks to minimise total production costs and changes in work-force level with reference to imprecise demand, cost coefficients, available resources and capacity. Additionally, the proposed i-PLP approach provides a systematic framework that helps the decision-making process to solve fuzzy multi-objective APP problems, enabling a DM to interactively modify the imprecise data and parameters until a set of satisfactory solutions is derived. An industrial case demonstrates the feasibility of applying the proposed approach to a practical multi-objective APP problem.
A system of linear constraints in the form of inequalities with possibilistic coefficients is investigated. A method is obtained for constructing a deterministic system of linear constraints that is equivalent to the ...
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A system of linear constraints in the form of inequalities with possibilistic coefficients is investigated. A method is obtained for constructing a deterministic system of linear constraints that is equivalent to the original system. The results obtained are illustrated with a model example.
A production management system contains many imprecise natures. The conventional deterministic and/or stochastic model in a computer integrated production management system (CIPMS) may not capture the imprecise nature...
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A production management system contains many imprecise natures. The conventional deterministic and/or stochastic model in a computer integrated production management system (CIPMS) may not capture the imprecise natures well. This study examines how the imprecise natures in the CIPMS affect the planning results. possibilistic linear programming models are also proposed for the aggregate production planning problem with imprecise natures. The proposed model can adequately describe the imprecise natures in a production system and, in doing so, the CIPMS can adapt to a variety of non-crisp properties in an actual system. For comparison, the classic aggregate production planning problem given by Holt, Modigliani, and Simon (HMS) is solved using the proposed possibilistic model and the crisp model of Hanssmann and Hess (HH). Perturbing the cost coefficients and the demand allows one to simulate the imprecise natures of a real world and evaluate the effect of the imprecise natures to production plans by both the possibilistic and the crisp HH approaches. Experimental results indicate that the possibilistic model does provide better plans that can tolerate a higher spectrum of imprecise properties than those obtained by the crisp HH model.
In this paper, several kinds of possibility distributions of fuzzy variables are studied in possibilistic linear programming problems to reflect the inherent fuzziness in fuzzy decision problems. Interval and triangul...
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In this paper, several kinds of possibility distributions of fuzzy variables are studied in possibilistic linear programming problems to reflect the inherent fuzziness in fuzzy decision problems. Interval and triangular possibility distributions are used to express the non-interactive cases between the fuzzy decision variables, and exponential possibility distributions are used to represent the interrelated cases. possibilistic linear programming problems based on exponential possibility distributions become non-linear optimization problems. In order to solve optimization problems easily, algorithms for obtaining center vectors and distribution matrices in sequence are proposed. By the proposed algorithms, the possibility distribution of fuzzy decision variables can be obtained. (C) 2000 Elsevier Science B.V. All rights reserved.
The relative modalities defined by possibility, necessity, impossibility and contingency of fuzzy sets in modal semantics are investigated. Decision procedures based on the modal concept are introduced and classified ...
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The relative modalities defined by possibility, necessity, impossibility and contingency of fuzzy sets in modal semantics are investigated. Decision procedures based on the modal concept are introduced and classified into eight classes. The relation between each decision procedure and the attitude of the decision maker toward uncertainty is discussed. Lastly, possibilistic linear programming relying on these decision procedures is formulated and a solution algorithm is proposed. A numerical example is given.
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