Abstract
This paper deals with two different public transport problems, in which the same phenomenon of waiting time occurs. In the past, both the problems were solved in the same way, which included rearrangement of the original problems to simpler max-min problems. These simplified approaches were used due to that time state of optimization software. In connection with building new computational laboratories equipped with new optimization environment, we want to come back to the more precise original quadratic models of the problems and explore new possibilities in obtaining the optimal solution of the original problems. We have done an analysis of those quadratic programming problems, worked out a linearized model and completed the computational study to compare the max-min and quadratic approaches.
Highlights
A series of mathematical programming models of transportation problems were formulated and solved in the several last decades to obtain solution of the transportation problems
Regular distribution of time intervals was taken as a quality criterion of searched solutions, even if the original objective was to minimize the total waiting time of passengers or cars in traffic flows
We present two transportation problems with the original and surrogate objective functions and compare the results obtained by solving a simplified model with the max-min criterion and a more precise and larger model, which respects the quadratic criterion
Summary
A series of mathematical programming models of transportation problems were formulated and solved in the several last decades to obtain solution of the transportation problems In those models, regular distribution of time intervals was taken as a quality criterion of searched solutions, even if the original objective was to minimize the total waiting time of passengers or cars in traffic flows. We present two transportation problems with the original and surrogate objective functions and compare the results obtained by solving a simplified model with the max-min criterion and a more precise and larger model, which respects the quadratic criterion This comparison including the inevitable large problem solving is enabled by exploitation of optimization environment called XPRESS-IVE. Abilities of this tool are studied in this paper in connection with the necessity to solve much larger linear problems to comply with the quadratic criteria
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