
Optimality criterion, the total cost of delivery, stockpiling and production rate change due to variations in demand.
Stocks may be seasonal goods, the remaining stock of limited capacity. Goods can be bought and sold in different quantities at prices that are changing over time. The task is to determine the policy of buying and selling, providing maximum total profit, and is an example of the problem storage.
The number of such examples could be multiplied. However, in this section we consider only some simple dynamic model of inventory management tasks.
If the problem initial data are uniquely defined, the problem is called deterministic, but if at least some of the data is random and given by a probability distribution, the corresponding problems are called stochastic. In this chapter we restrict ourselves to examples of deterministic inventory control problems.
A feature of these problems is the presence of two control variables (twodimensional model). However, the solution of these problems is much easier with a linear objective function.
Task 4. Storage capacity for storing supplies are limited to a certain size. In each of the n periods stocks can be replenished with ak cost per unit and spent incomepk per unit, and the decision on the replenishment of inventories or the expenditure made once in each period of time. Determine the optimal strategy in terms of inventory management to maximize the total profit for a given initial stock levels.
Let us define the problem. There are three options in order to replenish and utilization of stocks in each of the periods of time: I variant  recruitment precedes consumption; II version  consumption prior replenishment and III variant  any sequence.
In III choices optimalnoy4 strategy does not only determine the amount of recharge and flow, but the selection of the optimum order in each of the periods of time.
The versions of conditions affect the form of the model constraints of the problem.
Form the dynamic model of the problem. Consider the Istep process, meaning the step ku gap of time in which a decision on the replenishment of reserves or spending (k = I, 2, ..., n). 