On a routing problem with constraints that include dependence on a task list

We consider the solution of a routing problem complicated by constraints and by a possible dependence of the cost function on a task list. In addition, the statement admits that some of the constraints may be formed depending on a current list of tasks. Possible applications of this problem include routing the workers' movements under increased radiation in the process of dismantling radiation sources as well as steering a numerically controlled machine tool during the sheet cutting of parts. We propose a modification of widely understood dynamic programming and use it to design two versions of an algorithm, which are implemented as computer programs.