Initial states and transitional expenses in production and transport systems optimization

The production and transport systems optimization models, as well as classical transport or distributive problems, mainly concentrate on finding of the plan, optimum according to own characteristics, and don't take into account costs on system transition from its given (initial) state to defined as optimum. The neglect of such transitional expenses leads to certain losses of the corresponding models’ adequacy and to obtaining the absolutely-optimal solution, which is invariant to initial system state. In our paper we introduce and investigate the notion of relatively-optimal plans. The basic types of dependences of relatively-optimal plans and maximum achievable profit on the production and transport system initial state under the different functions of transitional expenses are determined. Corresponding computer calculations are also carried out and confirmed our theoretical results and conclusions. From the mathematical point of view, the accounting of initial states and the transitional expenses, on the one hand, complicates the corresponding models and computing processes, however on the other hand – does the models even more interesting, creates additional non-trivial effects