2.Kantorovich's view plan theory

Let M be an input matrix, x be an activity level, and B be an output matrix.The amount of inputs Mx is not supplied other than an initial value.If an initial value is made into d（0）, then

In the mid-term plan, we introduce the resource constraint condition that the amount of the required inputs of a certain term does not exceed the quantity of the outputs of the previous term.Therefore, if the output Bx（t）of the t term becomes the next input, the input Mx（t+1）of the t+1 term must be represented by the following formula.Namely,

In the mid-term, only these constraints are effective.Maximization by the predetermined ratio a=t（α1, …, αr）of an additional.Additional product is given as the last term of a plan.

However, k is the number of groups of additional product.

We can thus summarize the above conditions until the last term in order to obtain

The coefficient matrix of（4）, a variable vector, and the constant vector of the righthand side are set to G, x（t）, and d, respectively.In this way, the constraints can be written as follows:

Since an objective function is k, let v be

concerning a variable vector, then an objective function can be expressed as vx（t）.

Therefore, the following linear programming problems are acquired:

In terms of the economic meaning of this problem, the maintenance plan of future capital equipment and the social-capital infrastructure improvement that influences consumption habits can be considered.The dual problem of（7）is therefore set to

where u（t）is a dual variable.This elucidates the meaning of the so-called shadow price, which allows us to judge the degree of achievement of a plan.