Next, we plan to Step 4, by analyzing each state in which the system may be at the end of the 4 th step, given the optimal continuation to the end of the process.
If the beginning of the 5 th step corresponds to the point (4, 0), used in the management of the system goes to the point (5, 0), the cost of this step is 7.2, and the total cost of the last two steps are 7.2 9 , 1 = 16. In managing the M3 cost is 3.1 + 3.2 = 6.3, and the flow of funds in the last two steps is 6.3 4.4 = 10.7. Choosing a minimum flow of 10.7, put it in a circle of points (4, 0), and the appropriate management of this step is labeled by an arrow leading from the state (4, 0) to state (5, 1).
Determine the optimum time replacement for an unlimited period of use, if known: p - the initial cost; r (t) - the operational costs of maintaining the equipment t years of age within the next year, f (£)-realizable value of equipment age t years.
In the problem will minimize costs. The state variable is the time: g = f. The process is never-ending, so the relatively minimal cost of Zu * (t) for all time to come, starting with a k-year, depend only on ik-i - i do not depend on k.
When considering the infinite process to introduce the so-called discount factor 0 <a <1, allowing the amount of lead in the future. time to date, taking into account annual growth according to the rule of compound interest.
Aware of the difficulties encountered in the solution of linear problems, even if the model includes the requirement of integer variables. For example, the method of Gomori sections related to the construction of the sequence of simplex table and requires a rather cumbersome calculations. If the objective function is nonlinear, then the use of the method of sections impossible. In contrast, the computational methods suggest discrete DP, and an appropriate change of scale - an integer variable, and almost indifferent to the form of the objective function.