Abstract. Linear unconditional problem of combinatorial optimization on arrangements under stochastic uncertainty is solved. The minimum is defined as the result of consecutive comparison of numerical characteristic of random variables. The properties of the solution of the considered optimization problem are obtained. These properties use the properties of special constructed deterministic problems. We also propose the reducing method of solution of linear unconditional problem of combinatorial stochastic optimization, which is based on obtained solution’s properties.

Keywords: Euclidian combinatorial optimization problem, optimization on arrangements, stochastic uncertainty, stochastic optimization, stochastic combinatorial optimization.