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This paper presents a mathematical model for the cost varying transportation problem (CVTP) in which cost is varied due to the capacity of vehicles as well as amount of transport quantity. The main purpose is to develop a bi-level mathematical model. This model determines the minimum total transportation cost by determining minimum cost of the transportation at the route (i, j). This model is also a mixed-integer mathematical model. To tackle sucha problem, a genetic algorithm (GA) based on the spanning tree hasbeen proposed. We focus on the use of Prufer number encoding based on a spanning tree, which is adopted because it is capable of equally and uniquely representing all possible trees. From this point, the criteria by which chromosomes can always be converted to a CVTP tree is design. The procedures of crossover and mutation operators are newly designed. Numerical examples arepresented to illustrate the problem with some conclusions.
How to Cite this Article:
Chandan Bikash Das, Solving cost varying transportation problems by genetic algorithm based on a spanning tree and prufer number, Communications in Optimization Theory 2016 (2016), Article ID 22.