Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80884120140823Enhancing the solution method of linear Bi – level programming problem based on enumeration method and dual methodEnhancing the solution method of linear Bi – level programming problem based on enumeration method and dual method275311214FAIsaNakhai KamalabadiDepartment of Industrial Engineering, University of KurdistanEghbalHosseiniPayamenur University of Tehran, Department of MathematicsMohammadFathiDepartment of Power Engineering, University of KurdistanJournal Article20140724In the recent years, the bi-level programming problem (BLPP) is known as an appropriate approach for solving the real problems in applicable areas such as traffic, transportation, economics and supply chain management. There are several known algorithms to solve BLPP as an NP-hard problem. Almost all proposed algorithms in references have been used the Karush-Kuhn–Tucker to convert the BLPP into the single level problem which the obtained problem is complicated. In this paper, we attempt to develop two effective approaches, one based on enumeration method and the other based on duality characteristic for solving the linear BLPP. In these approaches, the BLPP is solved without using the Karush-Kuhn–Tucker conditions. The presented approaches achieve an efficient and feasible solution in an appropriate time which has been evaluated by comparing to references and test problems.In the recent years, the bi-level programming problem (BLPP) is known as an appropriate approach for solving the real problems in applicable areas such as traffic, transportation, economics and supply chain management. There are several known algorithms to solve BLPP as an NP-hard problem. Almost all proposed algorithms in references have been used the Karush-Kuhn–Tucker to convert the BLPP into the single level problem which the obtained problem is complicated. In this paper, we attempt to develop two effective approaches, one based on enumeration method and the other based on duality characteristic for solving the linear BLPP. In these approaches, the BLPP is solved without using the Karush-Kuhn–Tucker conditions. The presented approaches achieve an efficient and feasible solution in an appropriate time which has been evaluated by comparing to references and test problems.https://jamm.scu.ac.ir/article_11214_7e521bae700ef0bc5815247aceba9186.pdf