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In the paper [2] a calculus for solving integer optimization problems which can arithmetico proposition logical was developed. In the present paper these studies are used to obtain procedures for solving integer linear optimization problems based on switching algebra algorithms. These procedures differ both from cutting methods and also the known combinational methods. Three procedures, which may allow further modifications, are considered.

This paper studies a single server queuing model wherein arrivals are in groups following a time homogeneous POISSON process with the group size being a random variable and the server being available intermittently. Using the LAPLACE transform and the probability generating functions, the transient and the stationary distribution of queue size are discussed and in the steady state case various means are obtained explicitly.

Approximate algorithms for the travelling salesman problem, which is in a direct relationship to the transportation problem, use expedient the reduced cost matrix. This paper deals with a similar fundamental property for the classical job scheduling problem making use of a special formula for the make-span.

In this paper we make a qualitative investigation of a special class of linear one parameter (twice on parameter) optimization problems, i.e. we consider optimization problems of the form with the constraints .

Scheduling problems can be formulated as mathematical programs with integrity requirement on some variables. In this paper some properties of linearly solvable mixed integer programing are discussed, and experiments are reported where integer solutions have been obtained by linear programming.

The choice of the abscissa-values in linear regression is considered as a decision problem and it is treated in the present paper for the case that this choice is connected with given costs and that the risk is calculable by means of a given quadratic lossfunction. Three optimisation problems are formulated: i) minimal costs with bounded risk - ii) minima! risk with bounded costs - iii) minimal s u n of costs and risk. For these problems the existence of solutions is proved under assumptions concerning the cost function, assumptions being always satisfied in practice. For the first two problems alternative theorems are stated facilitating their treatment essentially.

In this paper special min-max problems are reduced to a certain type of problem in which a concave function is to be minimized over a convex set. On the basis of the extension principle a solution procedure for this problem is developed and the first feasible solution yields a t the same time the global minimum. Since the feasible set is defined by linear constraints, the algorithm consists essentially in the application of the simplex transformation.

As a part of investigations about flight operating scheduling of airlines there results the problem how to attach the individual aircrafts to te turns of a gicen time table and which of several variants of a time table is the best for attaching the aircrafts to the turns of these time table variants. For this aircraft scheduling the present paper gives an optimazation approach which takes into account the necessary maintenance but does not take into account unforeseen defects of aircrafts. Solving this optimization problem by traditional methods is too expensive. Therefore a method of blind search is used. Stopping the search follows a stopping rule based of a modification of BAYES principle and meaning that the search is cut off if the cost of one additional trial is greater than the expected payoff from it. At the end, the free changeable parameters of the stopping rule are discussed, and about an example is reported.

One possible way of solving a constrained optimization problem consists in its transformation into a sequence of unconstrained problems. In this paper is presented the connection between three of this methods; namely the method of centers (Huard), the SUMT (sequential unconstrained minimization technique) without parameters (Fiacco and Mccormick) and the method of barycenters (Lommatzsch). For the metyhod of centers is presented a simple proof of convergence without convexity assumptions, developed from an idea of Huard Further are given relations between some regularity conditions, which were used for this methods.