Three different optimization techniques for solving the fully rough interval multi-level linear programming problem

Abstract

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.