The classical problem of scheduling theory 1|r_j| L max is considered. New properties of optimal schedules are found.

In november-december new Information System for constructing companies 1C:USO will be presented. Our group take a part in this project. We have adapted algorithms for Resource Constrainted Project Scheduling Problems for real-world tasks. By results of our experiments our solution is more effective than solutions used in MS Project, Primavera.

On the "Operation Research 2006" conference (Karlsruhe, Germany 6 sep-9 sep) we have presented two papers with our recent results for scheduling and combinatorial problems.

An Preprint has been printed (our recent results for the total tardiness problem).

Algorithms based on this method have following properties: used for Integer Partitioning problem, Knapsack, total tardiness and other,the run time less or equal run time corresponding algorithm of dynamical programming,by results of experiments we have polynomial run time O(n^3) for great part of instances, we can decide not-integer instances

For NP-hard in the ordinary sense total tardiness problem 1||sum T_j new Hybrid algorithm has been constructed based on the idea of well-known meta-heuristic algorithm Ant Colony Optimization (ACO) and combinatorial properties of Elimination Rules 1-4. We compare its efficiency with efficiency of ACO.

A pseudo-polynomial algorithm O(n^2 \sum p_j) time is constructed.

In this paper we show that the special case B-1 of the single machine total tardiness problem 1||\sum T_j is NP-hard in ordinary sense. For the case there exist pseudo-polynomial algorithm O(n \sum p_j) time.

The son of Alexander Kvarazheliya has born in 12th November, 2005

In this paper we show that the run time of well known algorithms (Szwarc, Lazarev, Chang) for the problem 1||\sum T_j is exponential for canonical DL instances and for the special case BF. For this cases we present two new algorithms.