Abstract
This paper investigates the solution for an inverse of a parametric nonlinear transportation problem, in which, for a certain values of the parameters, the cost of the unit transportation in the basic problem are adapted as little as possible so that the specific feasible alternative become an optimal solution. In addition, a solution stability set of these parameters was investigated to keep the new optimal solution (feasible one) is unchanged. The idea of this study based on using a tuning parameters lambda is an element of R-m in the function of the objective and input parameters upsilon is an element of R-l in the set of constraint. The inverse parametric nonlinear cost transportation problem P(lambda,upsilon), where the tuning parameters lambda is an element of R-m in the objective function are tuned (adapted) as less as possible so that the specific feasible solution x degrees has been became the optimal ones for a certain values of upsilon is an element of R-l, then, a solution stability set of the parameters was investigated to keep the new optimal solution x degrees unchanged. The proposed method consists of three phases. Firstly, based on the optimality conditions, the parameter lambda is an element of R-m are tuned as less as possible so that the initial feasible solution x degrees has been became new optimal solution. Secondly, using input parameters upsilon is an element of R-l resulting problem is reformulated in parametric form P(upsilon). Finally, based on the stability notions, the availability domain of the input parameters was detected to keep its optimal solution unchanged. Finally, to clarify the effectiveness of the proposed algorithm not only for the inverse transportation problems but also, for the nonlinear programming problems; numerical examples treating the inverse nonlinear programming problem and the inverse transportation problem of minimizing the nonlinear cost functions are presented.