An extremal constrained routing problem with internal losses

We consider the following problem: one has to visit a finite number of sets and perform certain work on each of them. The work is accompanied by certain (internal) losses. The movements from some set to another one are constrained and accompanied by external (aggregated additively) losses. We propose a “through” variant of the dynamic programming method, formulate an equivalent reconstruction problem, and develop an optimal algorithm based on an efficient dynamic programming method technique.