Nonlinear Transportation Problems
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Date
2007-08
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Addis Ababa University
Abstract
Some times there may be many di®erent ways to model a particular problem,
choosing the best one minimizes the complexity of the problem and time to solve.
Since, as we have said earlier, any programming problem with constraint matrix
structure the same as the transportation problem is regarded as a transportation
problem regardless of it's physical meaning and because of it's simple structure,
modeling problems as transportation problems requires much less e®ort to solve
than that of modeling it di®erently.
In this thesis the nonlinear transportation problem is considered as nonlinear pro-
gramming problem and algorithms to solve this particular problem are given. The
¯rst algorithm is similar to that of the transportation simplex algorithm except
the nonlinearity assumption. The second algorithm is dependent on the simplex
algorithm of Zangwill [32] that we modi¯ed it to use the special property of the
coe±cient matrix of the transportation problem so that we may take shortcuts to
make problem solving simple. However the algorithms are not been compered to
other previous algorithms. Therefore in the future further work must be done :
1. To measure the e±ciency of the algorithm.
2. To check how near the solution of the approximated problem of the piece-
wise linear transportation problem is to the optimal solution of the original
problem. And ¯nally
3. to implement the algorithm to the real world problem.
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Keywords
Nonlinear Transportation Problems