(Stellenbosch : Stellenbosch University, 2019-04) Dikgale, Rarang Phillemon; Visagie, S. E.; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Logistics. Logistics.

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ENGLISH SUMMARY : The classical transportation problem is concerned with the distribution of a single commodity
from a group of supply centres or sources, to a group of demand centres or destinations. The amount of commodity available at any source is limited, and the demand for the commodity at each destination is finite. Transportation cost functions may be non-linear because of quantity discounts, or price breaks, etc. Also, a fixed charge may be incurred every time units of commodity are sent from a given source to a given destination. The fixed charge transportation problems
(FCTP) differs from the standard linear transportation problem (TP) only in the nonlinearity (caused by die fixed charge) in the objective function.
Different heuristic methods were developed to generate initial solutions. The stepping stone method and tabu search algorithm are used to attempt to solve this problem. The algorithms are
evaluated according to their efficiency (computational runtime and solution quality) for solving FCTP problems. Comparisons are made using randomly generated benchmark instances from
the literature. The instances contain different sizes and different ranges of magnitude of fixed costs relative to variable costs. The primal-dual algorithm was also considered in finding good
solutions to be FCTP.
The results (for small instances) obtained for the proposed algorithm have been compared with that for an exact algorithm based on an integer programming formulation available in the literature.
The results from computational experiments show that the proposed algorithms yield near optimal solution to most instances. The primal-dual algorithm demonstrate significant
improvement over the proposed heuristic methods for small FCTPs, although it could not find feasible solutions to some instances.