In real-world problems, the parameters of optimization problems are uncertain. A class of multilevel linear programming (MLLP) with uncertainty problem models cannot be determined exactly. Hence, in this paper, we are concerned with studying the uncertainty of MLLP problems. The main motivation of this paper is to obtain the solution to a multilevel rough interval linear programming (MLRILP) problem. To obtain that, we start turning the problem into its competent crisp equivalent using the interval method. Moreover, we rely on three methods to address the problem of multiple levels. First, by applying the constraint method in which upper levels give satisfactory solutions that are reasonable in rank order to the lower levels, second, by an interactive approach that uses the satisfaction test function, and third, by the fuzzy approach that is based on the concept of the tolerance membership function. A numerical example is given for illustration and to examine the validity of the approach. An application to deduce the optimality for the cost of the solid MLLP transportation problem in rough interval environment is presented.
This paper focuses on the solution of fully fuzzy multi-level linear programming (FFMLLP) Problem, where all of its decision parameters and variables are fuzzy numbers. An algorithm depending on the fuzzy decision approach and bound and decomposition method will be developed to find a fuzzy optimal solution for the problem under consideration. The main results obtained in this paper will be clarified by an illustrative numerical example.
KeywordsMulti-level programming; Fuzzy decision approach; Bound and decomposition method; Fuzzy linear programming.
Due to the importance of the multi-level fully rough interval linear programming (MLFRILP) problem to address a wide range of management and optimization challenges in practical applications, such as policymaking, supply chain management, energy management, and so on, few researchers have specifically discussed this point. This paper presents an easy and systematic roadmap of studies of the currently available literature on rough multi-level programming problems and improvements related to group procedures in seven basic categories for future researchers and also introduces the concept of multi-level fully rough interval optimization. We start remodeling the problem into its sixteen crisp linear programming LP problems using the interval method and slice sum method. All crisp LPs can be reduced to four crisp LPs. In addition, three different optimization techniques were used to solve the complex multi-level linear programming issues. A numerical example is also provided to further clarify each strategy. Finally, we have a comparison of the methods used for solving the MLFRILP problem.
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