Title: An extended multi-objective capacitated transportation problem with mixed constraints in fuzzy environment

Authors: Srikant Gupta; Irfan Ali; Aquil Ahmed

Addresses: Jaipuria Institute of Management, Jaipur, India ' Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh-202002, Uttar Pradesh, India ' Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh-202002, Uttar Pradesh, India

Abstract: In this paper, we study a multi-objective capacitated transportation problem (MOCTP) with mixed constraints. This paper is comprised of the modelling and optimisation of an MOCTP in a fuzzy environment in which some goals are fractional and some are linear. In real life application of the fuzzy goal programming (FGP) problem with multiple objectives, it is difficult for the decision maker(s) to determine the goal value of each objective precisely as the goal values are imprecise or uncertain. Also, we developed the concept of linearisation of fractional goal for solving the MOCTP. In this paper imprecision of the parameter is handled by the concept of fuzzy set theory by considering these parameters as a trapezoidal fuzzy number. α-cut approach is used to get the crisp value of the parameters. Numerical examples are used to illustrate the method for solving MOCTP.

Keywords: capacitated transportation problem; multi objective linear programming; multi-objective fractional programming; mixed constraints; trapezoidal fuzzy number; fuzzy goal programming; FGP.

DOI: 10.1504/IJOR.2020.105443

International Journal of Operational Research, 2020 Vol.37 No.3, pp.345 - 376

Received: 09 Jan 2017
Accepted: 11 Apr 2017
Published online: 02 Mar 2020 *

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