Affiliations: [a] Statistical Quality Control & Operations Research Unit, Indian Statistical Institute, Delhi Centre, 7, S.J.S. Sansanwal Marg, New Delhi, India | [b] Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, India
Correspondence:
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Corresponding author. Dipti Dubey, Statistical Quality Control & Operations Research Unit, Indian Statistical Institute, Delhi Centre, 7, S.J.S. Sansanwal Marg, New Delhi-110016, India. Tel.: +91 8130254720; Fax: +91 1141493968; E-mail: [email protected].
Abstract: The aim of this paper is twofold. Firstly, to define a solution concept of Pareto-optimality for a multi-objective flexible linear programming (MOFLP) problem (or multi-objective fuzzy linear programming problem) and design a method to extract a Pareto-optimal solution of MOFLP problem from the set of optimal solutions of equivalent optimization problem formulated by Dubey and Mehra (2013). Secondly, to extend this study to multi-objective linear programming problem involving hard and flexible constraints with interval uncertainty. A flexible constraint with interval uncertainty generalizes a flexible constraint by allowing preferences to be expressed in the form of intervals. An optimistic-pessimistic approach is proposed to solve multi-objective flexible linear programming with interval uncertainty (MOFLPIU) using an interval-valued fuzzy set representation and the Hurwicz optimism-pessimism criterion.
