Search

The parameters of decision models are not clearly known and they are not exact for most real-life problems. Therefore, this article presents a model of linear programming with grey interval numbers for right-hand-side parameters under an uncertainty case. The purpose of this article is to compare the results of a fuzzy linear programming model and those of four proposed grey linear programming models and to find effective solutions for alternative production planning. The results produced a more effective plan to use as an industrial solution according to a fuzzy linear programming model. The objective function value is about 3% more effective than with the fuzzy linear programming method, and the customer satisfaction of total demand is about 25% more effective for the number of served customers. [ABSTRACT FROM AUTHOR]

Uncertainties in quantities of work items and vagueness in unit price boundaries have mainly been disregarded in unbalanced bidding models. This article presents a fuzzy linear programming (FLP) model which treats the quantities of works and unit price limitations as fuzzy numbers. Fuzzy constraints are used to define upper and lower bounds on the unit prices proposed by the contractor. The uncertainties in quantities of works are addressed through fuzzy coefficients with asymmetric fuzziness ratio in the objective function. Therefore, the problem lends itself to an FLP model with fuzzy coefficients in the objective function and fuzzy constraints. To account for these uncertainties, two different approaches are proposed and tested. Performance of the model is demonstrated using three hypothetical case examples and the results are discussed and compared with those of a deterministic model. [ABSTRACT FROM AUTHOR]

A semi-infinite analysis-based inexact two-stage stochastic fuzzy linear programming approach is proposed for water resources management problems. Semi-infinite analysis is incorporated into the modelling framework to handle infinite α -cuts to the membership functions of fuzzy parameters. Compared to the existing methods in which only limited α -cuts are divided under an assumption that these could represent all fuzzy information of the function, the proposed approach could be more reliable in terms of full consideration of fuzzy membership functions. The obtained optimal results from this approach present robustness according to a case study. By assigning different confidence levels, five groups of optimal solutions are obtained. It is indicated that higher confidence levels would relate to more reliable allocation strategies, as well as higher and more stable system benefits. However, with the increases in violation risks, the intervals of the optimal system benefit become wider, reflecting the impact of high risks combined with high benefits. [ABSTRACT FROM AUTHOR]

It is well known that optimization problems for the decision-making process in real environments should consider uncertainty to attain robust solutions. Although this uncertainty has been usually modelled using probability theory, assuming a random origin, possibility theory has emerged as an alternative uncertainty model when statistical information is not available, or when imprecision and vagueness have to be considered. This article proposes two different criteria to obtain robust solutions for linear optimization problems when the objective function coefficients are modelled with possibility distributions. To do so, chance constrained programming is used, leading to equivalent crisp optimization problems, which can be solved by commercial optimization software. A simple case example is presented to illustrate the use of the proposed methodology. [ABSTRACT FROM AUTHOR]