Many authors have presented studies of multi-choice stochastic transportation problem (MCSTP) where availability and demand parameters follow a particular probability distribution (such as exponential, weibull, cauchy or extreme value). In this paper an MCSTP is considered where availability and demand parameters follow general form of distribution and a generalized equivalent deterministic model (GMCSTP) of MCSTP is obtained. It is also shown that all previous models obtained by different authors can be deduced with the help of GMCSTP. MCSTP with pareto, power function or burr-XII distributions are also considered and equivalent deterministic models are obtained. To illustrate the proposed model two numerical examples are presented and solved using LINGO 13.0 software package.
In this paper a new method, namely the MMK-method is proposed for finding non-degenerate compromise optimal solution for Bi-objective transportation problem (BTP). The MMK-method derives the set of all possible non-degenerate efficient solutions and it uses the concept of the distance between two points in (x, y) coordinate for finding non-degenerate compromise optimal solution to BTP. A numerical example is given to illustrate the proposed method. A comparative study has also been made between the existing methods and the proposed method.
This study extends the BSMAP (Biobjective Selective Maintenance AllocationProblem) from deterministic to fuzzy cases, where the cost of maintaining a component, total failed component cost within a subsystem, and the total cost of maintaining the whole system are considered to be fuzzy numbers. The BSMAP has been modified as a BFSMAP (Biobjective fuzzy selective maintenance allocation problem), where the fuzzy and crisp number of failed items are repaired and replaced to achieve the maximum reliability of a system in a cost-effective manner using a fuzzy programming approach. Numerical examples are used to illustrate the method for solving BFSMAP.
Goal programming (GP) is a powerful method to solve multi-objective programming problems. In GP the preferential weights are incorporated in different ways into the achievement function. The problem becomes more complicated if the preferences are imprecise in nature, for example ‘Goal A is slightly or moderately or significantly important than Goal B’. Considering such type of problems, this paper proposes standard goal programming models for multi-objective decision-making, where fuzzy linguistic preference relations are incorporated to model the relative importance of the goals. In the existing literature, only methods with linear preference relations are available. As per our knowledge, nonlinearity was not considered previously in preference relations. We formulated fuzzy preference relations as exponential membership functions. The grades or achievement function is described as an exponential membership function and is used for grading levels of preference toward uncertainty. A nonlinear membership function may lead to a better representation of the achievement level than a linear one. Our proposed models can be a useful tool for different types of real life applications, where exponential nonlinearity in goal preferences exists. Finally, a numerical example is presented and analyzed through multiple cases to validate and compare the proposed models. A distance measure function is also developed and used to compare proposed models. It is found that, for the numerical example, models with exponential membership functions perform better than models with linear membership functions. The proposed models will help decision makers analyze and plan real life problems more realistically.
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