As the parameters of the state will take stock of goods at the beginning of a k-step. Control variables are the size of the replenishment (xk) and flow (yh) stocks at ku step.
The main characteristic of the equipment is its age. Depend on the age of the equipment operating costs, production costs, performance and liquidity costs. These figures vary, given the technological progress, not just replacing old equipment with new, with new technical and economic characteristics, but also new of the same type is not used. In the latter case, the change is due to obsolescence.
Aging equipment includes its wear and tear, resulting in rising production costs for the output on the old equipment, increase the cost of its repair and maintenance, and at the same time reduce the performance and cost of the so-called liquidity.
There comes a time when the old equipment is more profitable to "sell, replaced by a new, than operate at great cost. This equipment can be replaced either with new equipment of the same type, or a new, more advanced technically, to technical progress.
The optimal strategy of replacement is to determine the optimal timing of replacement. Optimality criterion in determining the timing of replacement can be either profit from the operation of the equipment, which should be maximized, or the total cost of ownership during the reporting period to be minimized. It is known that for a given production plan to maximize profits is equivalent to minimization of costs. Almost more convenient to use the second criterion, introducing to address performance degradation conditionally reduced expenditures.
We assume that the decision to replace the equipment taken periodically at the beginning of each period (year, month, week, etc.), which are divided into the planning period. Assume also that the equipment can be used indefinitely, if you spend enough money on its repair.