A linear fractional bilevel programming problem with multichoice parameters
A bilevel programming problem (BLPP) is a hierarchical optimization problem where the constraint region of the upper level is implicitly determined by the lower level optimization problem. In this paper, a bilevel programming problem is considered in which the objective functions are linear fraction...
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| Format: | Article |
| Language: | English |
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Croatian Operational Research Society
2017-01-01
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| Series: | Croatian Operational Research Review |
| Online Access: | http://hrcak.srce.hr/file/285661 |
| _version_ | 1819057186556346368 |
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| author | Ritu Arora Kavita Gupta |
| author_facet | Ritu Arora Kavita Gupta |
| author_sort | Ritu Arora |
| collection | DOAJ |
| description | A bilevel programming problem (BLPP) is a hierarchical optimization problem where the constraint region of the upper level is implicitly determined by the lower level optimization problem. In this paper, a bilevel programming problem is considered in which the objective functions are linear fractional and the feasible region is a convex polyhedron. Linear fractional objectives in BLPP are useful in production planning, financial planning, corporate planning and so forth. Here, the cost coefficient of the objective functions are multi-choice parameters. The multi-choice parameters are replaced using interpolating polynomials. Then, fuzzy programming is used to find a compromise solution of the transformed BLPP. An algorithm is developed to find a compromise solution of BLPP. The method is illustrated with the help of an example. |
| first_indexed | 2024-12-21T13:35:18Z |
| format | Article |
| id | doaj.art-8b07041b684643e783162feb05d8ebb0 |
| institution | Directory Open Access Journal |
| issn | 1848-0225 1848-9931 |
| language | English |
| last_indexed | 2024-12-21T13:35:18Z |
| publishDate | 2017-01-01 |
| publisher | Croatian Operational Research Society |
| record_format | Article |
| series | Croatian Operational Research Review |
| spelling | doaj.art-8b07041b684643e783162feb05d8ebb02022-12-21T19:02:11ZengCroatian Operational Research SocietyCroatian Operational Research Review1848-02251848-99312017-01-018249951310.17535/crorr.2017.0032193639A linear fractional bilevel programming problem with multichoice parametersRitu Arora0Kavita Gupta1Department of Mathematics, Keshav Mahavidyalaya, University of Delhi, Delhi, IndiaDepartment of Mathematics, Kirori Mal College, University of Delhi, Delhi, IndiaA bilevel programming problem (BLPP) is a hierarchical optimization problem where the constraint region of the upper level is implicitly determined by the lower level optimization problem. In this paper, a bilevel programming problem is considered in which the objective functions are linear fractional and the feasible region is a convex polyhedron. Linear fractional objectives in BLPP are useful in production planning, financial planning, corporate planning and so forth. Here, the cost coefficient of the objective functions are multi-choice parameters. The multi-choice parameters are replaced using interpolating polynomials. Then, fuzzy programming is used to find a compromise solution of the transformed BLPP. An algorithm is developed to find a compromise solution of BLPP. The method is illustrated with the help of an example.http://hrcak.srce.hr/file/285661 |
| spellingShingle | Ritu Arora Kavita Gupta A linear fractional bilevel programming problem with multichoice parameters Croatian Operational Research Review |
| title | A linear fractional bilevel programming problem with multichoice parameters |
| title_full | A linear fractional bilevel programming problem with multichoice parameters |
| title_fullStr | A linear fractional bilevel programming problem with multichoice parameters |
| title_full_unstemmed | A linear fractional bilevel programming problem with multichoice parameters |
| title_short | A linear fractional bilevel programming problem with multichoice parameters |
| title_sort | linear fractional bilevel programming problem with multichoice parameters |
| url | http://hrcak.srce.hr/file/285661 |
| work_keys_str_mv | AT rituarora alinearfractionalbilevelprogrammingproblemwithmultichoiceparameters AT kavitagupta alinearfractionalbilevelprogrammingproblemwithmultichoiceparameters AT rituarora linearfractionalbilevelprogrammingproblemwithmultichoiceparameters AT kavitagupta linearfractionalbilevelprogrammingproblemwithmultichoiceparameters |