### Refine

#### Keywords

- Diskrete Optimierung (1)
- Ressourcenallokation (1)
- Stabilität (1)
- Standardisierung (1)
- Trajektorie (Mathematik) (1)

We consider the standardization problem (SP) which can be formulated as follows. It is known demand bi in each type i in {1, 2, ..., n} of items. Production of yi items of the ith type brings a profit fi (yi), where fi is a nondecreasing concave function for each i in {1, 2, ..., n}.It is necessary to satisfy the demand and to maximize the total profit provided that there exist >standardization possibilities< . These possibilities means that some types of items can be replaced by some another types. We introduce generalized standardization problem (GSP) in which titems demand is given as the set of admissible demand vectors. We show that GSP and SP are special cases of the resource allocation problem over a network polymatroid. Ibasing on this observation we propose a polynomial time solution algorithm for GSP and SP.

This work was partially supported by DAAD, Fundamental Researches Foundation of Belarus and International Soros Science Education Program We consider a vector discrete optimization problem on a system of non- empty subsets (trajectories) of a finite set. The vector criterion of the pro- blem consists partial criterias of the kinds MINSUM, MINMAX and MIN- MIN. The stability of eficient (Pareto optimal, Slater optimal and Smale op- timal) trajectories to perturbations of vector criterion parameters has been investigated. Suficient and necessary conditions of eficient trajectories local stability have been obtained. Lower evaluations of eficient trajectories sta- bility radii, and formulas in several cases, have been found for the case when l(inf) -norm is defined in the space of vector criterion parameters.