We develop in this article a geometric approach to duality in Multiple Objective Linear Programming. This approach is based on a very old idea, the duality of polytopes, which can be traced back to the old Greeks. We show that there is an inclusion reversing one-to-one map between the minimal faces of the image of the primal objective and the maximal faces of the image of the dual objective map.

Many real-world decision problems require making tradeoffs among multiple objectives. However, in some cases, the relative importance of these objectives is not known when the problem is solved, precluding the use of single-objective methods. Instead, multi-objective methods, which compute the set of all potentially useful solutions, are required. This paper proposes variable elimination linear...

The application of fuzzy approach models to forecast has been drawing a lot of attention. This study proposes a fuzzy approach to forecasting using a financial data set. The methodology used is multiple objective linear programming (MOLP). Selecting an individual forecast based upon a single objective may not make the best use of available information for a variety of reasons. Combined forecast...

We discuss two approaches to duality for multiple objective linear problems. The first approach is based on a duality relation between a set and its complement in the outcome space. It allows us to obtain a number of known duality constructions. The second approach utilizes polarity between a polyhedral set and the epigraph of its support function. It leads to a parametric dual problem which is...

classical deterministic inventory models consider the demand rate to be either constant or time-dependent but independent from the stock status. however, for a certain type of inventory, the demand rate may be in-fluenced by the stock level. also in many real-life problems, some products such as fruits, vegetables, phar-maceuticals and volatile liquids continuously deteriorate to evaporation, o...

in this paper, the researchers present a multi-objective linear fractional inventory model using fuzzy pro-gramming. the proposed method in this paper is applied to a problem with two objective functions. the re-sulted fuzzy model is transformed into an ordinary linear programming. the implementation of the develop-ing model presented in this paper is demonstrated through the use of some numeri...

in this paper imprecise target models has been proposed to investigate the relation between imprecise data envelopment analysis (idea) and mini-max reference point formulations. through these models, the decision makers' preferences are involved in interactive trade-off analysis procedures in multiple objective linear programming with imprecise data. in addition, the gradient projection type me...

data envelopment analysis operates as a tool for appraising the relative efficiency of a set of homogenous decision making units. this methodology is applied widely in different contexts. regarding to its logic, dea allows each dmu to take its optimal weight in comparison with other dmus while a similar condition is considered for other units. this feature is a bilabial characteristic which opt...