Title: On solving multi-objective linear bi-level multi-follower programming problem

Authors: Kailash C. Lachhwani

Addresses: Department of Mathematics, Government Engineering College, Bikaner, Rajasthan – 334 004, India; Department of Applied Sciences, National Institute of Technical Teachers Training and Research (NITTTR), Chandigarh – 160 019, India

Abstract: Multi-objective linear bi-level multi-follower programming problem (MOBLMFPP) is a special case of two level hierarchical programming problems in which the second level hierarchy includes multiple followers. This paper presents an alternate method based on fuzzy goal programming approach for the solution of multi-objective linear bi-level multi-follower programming (MOLBMFP) problem in which there is no sharing of information among followers. In the proposed FGP model formulation, each of objective functions of each level (leader and follower's level of MOLBMFPP) as well as decision variables at each level are characterised into fuzzy goals. Suitable linear membership functions are defined for each objective function and decision variables. Then minimising the sum of the negative deviational variables of both levels, the highest membership value of each of fuzzy goals is obtained. Existence of compromise optimal solution for MOLBMFPP is established in context of proposed approach. A numerical example is illustrated in support of proposed methodology. A comparative analysis is also carried out in order to show efficiency of proposed method over earlier method for the solution of MOLBMFPP.

Keywords: bi-level programming; BLP; multi-objective linear bi-level multi-follower programming; fuzzy goal programming; FGP; membership function; compromise optimal solution.

DOI: 10.1504/IJOR.2018.090426

International Journal of Operational Research, 2018 Vol.31 No.4, pp.442 - 460

Received: 22 Aug 2014
Accepted: 12 Jun 2015
Published online: 19 Mar 2018 *

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