On studying monotonicity in the parameter of optimal solutions for one class of the parametric optimization problems

Consideration was given to minimization of a nonnegative nondecreasing function under the linear constraints comprising a scalar parameter $t$ of the right side of the constraints. Monotonicity in the parameter $t$ of the optimal solutions of the considered problem plays an important part in some applied optimization models such as static optimization of the transportation systems with the linear constraints $x\geq0$, $Ax=tb$. Some possible interpretations (economic, transport-economic, and investment) of the considered mathematical problem were presented, and the problem history was outlined. Relatively simple, yet hard, sufficient conditions for monotonicity were obtained. Simple examples demonstrating that this property may be violated already in the simplest cases were presented.