Journal
PAKISTAN JOURNAL OF STATISTICS AND OPERATION RESEARCH
Volume 18, Issue 1, Pages 151-166Publisher
UNIV PUNJAB
DOI: 10.18187/pjsor.v18i1.3889
Keywords
Linear Fractional Programming; Fractional Transportation Problem; Iterative Method; Mixed Constraints; Optimization
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This paper presents a novel algorithm based on the traditional definition of continuity to solve the linear fractional transportation problem (LFTP), and discusses the asymptotic solution for LFTP for the first time. Numerical examples are used to illustrate the method and compare it with existing methods. Additionally, an application with an environmentalist objective is solved using real case data.
The linear fractional transportation problem (LFTP) is widely encountered as a particular type of transportation problem (TP) in real-life. In this paper, a novel algorithm, based on the traditional definition of continuity, is presented to solve the LFTP. An iterative constraint is constructed by combining the objective function of the LFTP and the supply-demand condition since the fractional objective function is continuous at every point of the feasible region. By this constraint obtained, LFTP is converted into an iterative linear programming (LP) problem to reach the optimum solution. In this study, the case of asymptotic solution for LFTP is discussed for the first time in the literature. The numerical examples are performed for the linear and asymptotic cases to illustrate the method, and the approach proposed is compared with the other existing methods to demonstrate the efficiency of the algorithm. Also, an application had environmentalist objective is solved by proposed mathematical method using the software general algebraic modeling system (GAMS) with data set of the real case. Finally, some computational results from tests performed on randomly generated large-scale transportation problems are provided.
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