Title: On logarithmic fixed-charge transportation problem

Authors: Debiprasad Acharya; Manjusri Basu; Atanu Das

Addresses: Department of Mathematics, N.V. College, Nabadwip, Nadia, W.B., India ' Department of Mathematics, University of Kalyani, Kalyani-741235, India ' Department of Mathematics, University of Kalyani, Kalyani-741235, India

Abstract: The fixed-charge transportation problem (FCTP) is still a challenging problem in the field of mathematical programming. In this paper, we consider fixed-charge transportation problem with logarithmic objective function. In the absence of any suitable algorithm to obtain the solution of this type of nonlinear transportation problem, we discuss the advantage of polynomial approximation. There exists a major difference between the two problems that the variables in the polynomial transportation problem have no upper bound but in the logarithmic transportation problem they are bounded. Using the expansion of logarithm we show the resemblance between the structural behaviour of linear and fixed-charge transportation problems. We illustrate a numerical example in support of the developed method.

Keywords: transportation problem; fixed cost; logarithm modelling.

DOI: 10.1504/IJMOR.2018.092108

International Journal of Mathematics in Operational Research, 2018 Vol.12 No.4, pp.532 - 541

Received: 04 Aug 2016
Accepted: 12 Nov 2016
Published online: 04 Jun 2018 *

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