Theoretical Comparison, Computational and Practical Experience with Some Transportation Type Algorithms

The development of efficient algorithms for the solution of commercial transportation type problems was an active research stimulant for the last two decades or so. The shape of the cost functions usually dictates the solution procedure to be followed. However for some procedures there may be more than one algorithm available and a choice has to be made. This paper considers problems with three classes of cost functions, viz (a) linear, (b) concave, (c) convex, Although the bulk of research in the field of transportation planning deals with class (a), interest in the other classes is growing. In this paper, theoretical comparisons between the three classes are made and difficulty of handling each are cited. Some of the available algorithms of class (a) are summarized and the main differences pinpointed. Experience with several existing codes in the solution of 200 randomly generated problems covering large ranges of sizes, costs and quantities transported is described, Some of these algorithms were used to solve many real problems and the experience shows that the efficiency of the algorithms depend on the nature of the problems to which they are applied.