Application of Fuzzy Sets to Aggregate Production Planning With Multiproducts and Multitime Periods

IEEE Transactions on Fuzzy Systems (Impact Factor: 8.75). 07/2011; 19(3):465 - 477. DOI: 10.1109/TFUZZ.2011.2114668
Source: IEEE Xplore


The objective of this study is to develop a fuzzy mathematical programming method to solve aggregate production planning (APP) decision problems that involve multiproducts and multitime periods in a fuzzy environment. The fuzzy APP model that is developed here attempts to minimize total cost with respect to inventory carrying levels, available labor levels, machine capacity and warehouse space, and the constraint of available budget. The proposed APP method evaluates monetary interest of related operating cost categories and provides greater computational efficiency and flexibility by adopting triangular fuzzy numbers and piecewise linear membership functions to represent both imprecise data and fuzzy goals. The actual performance of an industrial company was used to demonstrate the feasibility of applying the proposed method to real-world APP decisions. The proposed method yields an efficient solution and presents overall decision-maker satisfaction with the given goal values. This paper also presents several significant management implications that are related to the practical application of the proposed method.

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    ABSTRACT: Mathematical programming approach has been employed extensively as a means to enhance the decision-making process in science and engineering. One of the fields that has been benefiting from the employing mathematical programming is the production planning and scheduling in both the industry and service sectors. Most of these applications assume deterministic situations in which the parameters used to develop the model are known in advanced and will remain unchanged. Undesirably, real-world decision-making problems are not deterministic, and in fact; they are fuzzy in nature. This research work is mainly concerned with enhancing the decision-making in production planning through adaptation of the concept of fuzzy programming. This paper reports on the development of a mathematical programming model that involves fuzzy parameters. In addition and besides presenting the fuzzy mathematical model, our paper will present, compare and discuss among two solution procedures that can deal with the fuzzy multi-objective linear programming problems.
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    ABSTRACT: This paper introduces a fuzzy mixed-integer linear programming (FMILP) model to solve the aggregate production planning (APP) problem. The FMILP formulation is developed in which both fuzzy and possibilistic uncertainties appear in the same model. The main objective of this paper is to investigate the benefits of adopting fuzzy mathematical programming approach to model APP problems. To achieve the objective of this paper, a real industrial data from a resin manufacturing plant (see Omar and Teo [1]) were used to develop the proposed FMILP. In addition, the results of the FMILP were compared with the results from the deterministic model proposed by Omar and Teo [1]. The findings indicate that significant cost savings were achieved by adopting the fuzzy programming approach.
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