Abstract
This paper deals with the modeling and optimization of a bi-level multi-objective production planning problem, where some of the coefficients of objective functions and parameters of constraints are multi-choice. A general transformation technique based on a binary variable has been used to transform the multi-choices parameters of the problem into their equivalent deterministic form. Finally, two different types of secularization technique have been used to achieve the maximum degree of individually membership goals by minimizing their deviational variables and obtained the most satisfactory solution of the formulated problem. An illustrative real case study of production planning has been discussed and, also compared to validate the efficiency and usefulness of the proposed work.
Highlights
Bi-level programming (BLP) is considered as the advanced form of mathematical programming.It has been applied to many real-life problems, such as agriculture, production, economic systems, finance, engineering, banking, management sciences, industrial problems, and transportation problems, and so on
Based on the above assumptions and notations, the mathematical model of the production planning problem is formulated: The objective function I is related to maximizing the profit: Every company wants to remain in business for a longer period, and this can be achieved by only making a profit
We have constructed a new mathematical model for the production planning problem with some we realistic constructed model has been formulated as aplanning bi-level
Summary
Bi-level programming (BLP) is considered as the advanced form of mathematical programming. Real-life multi-objective problems can be formulated as a bi-level multi-level programming problem in which two decision-makers (DM’s)make decisions successively, without affecting the decisions of the others DM’s. In many real-life situations, the DM has multiple information available about the parameters of the optimization problem In such situations, parameters of the problem become a multi-choice type. The decision-maker has the set of multi-choices of the parameters out of which only one choice is to be selected to optimize the problem This type of mathematical problem is known as a multi-choice programming problem. Such kinds of situations of multiple numbers of choices for a parameter occurs in several decision-making problems. Before going to formulate the problem, the following literature has been reviewed, which are discussed
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