The paper deals with the following (P-production) problem: Let \(P=(<_ p,Y)\) be a partial order on a set \(Y=\{y_ 1,y_ 1,...,y_ n\}\) of n elements. Given an input of n distinct numbers \(x_ 1,x_ 2,...,x_ n\) find a permutation \(\sigma\) of \(\{\) 1,2,...,n\(\}\) such that \(y_ i<_ Py_ j\) implies \(x_{\sigma (i)}<_ Px_{\sigma (j)}\). The author proves by clear and systematical way the following results on worst-case (C(P)) and average-case \((\tilde C(P))\) complexities of this problem under the decision-tree model of computations: 1) For all P, \(\tilde C(P)=\Omega(n-\beta (P)+\log_ 2(n!/\mu (P)))\) 2) For all P, \(C(P)=0(n-\beta(P)+\log_ 2(n!/\mu (P)))\) (i.e. for all P, \(C(P)=\theta(\tilde C(P)))\) where \(\mu(P)\) is the number of permutations consistent with P and \(\beta(P)\) denotes the number of connected components of P.