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## 数学代写|最优化理论作业代写optimization theory代考|The creation of a mathematical model of the strategic plan

A mathematical model of the strategic plan is created, taking into account extensive and intensive factors regarding the development of the firm, based on information collected from its management accounting processes [79-82].

We will take a model of an annual plan as an example (8.2.25)-(8.2.30), and include extensive and intensive factors regarding the development of the firm.

Extensive factors are connected, first of all, with production expansion. It is supposed that depreciation charges will come from part of the profit and go towards reproduction. This is understood, first, as the restoration of worn-out equipment and, secondly, after a miscalculation of the annual plan, as restrictions (8.2.27) that increase on those resources for which equality or an inequality is carried out. It would then be the case that restrictions on these resources $b_i(t), i=\overline{1, M}$ in the planned year $(t+1) \in T$ increase by the size $\Delta b_i(t), i=\overline{1, M}$ and will assume the form:
$$b_i(t+1)=b_i(t)+\Delta b_i(t), i=\overline{1, M},(t, t+1) \in T \text {. }$$
Intensive factors are defined by labour productivity growth, a decrease in material input, an increase in capital productivity and an improvement in the quality of production. All these factors have to be obviously or implicitly reflected in a mathematical model of a corporation’s long-term development plan.

In a mathematical model of the annual plan (8.2.25)-(8.2.30), with restrictions $(8.2 .27)$, coefficients of $a_{i j}(t), i=\overline{1, M} j=\overline{1, N}, j=$ $\overline{1, N}, t \in T$ define labour, material input and capacity.

The size at which labour costs are lowered by the production of a unit of a $j$-th type, determines the growth of labour productivity in an enterprise.
$$\Delta a_{i j}(t+1)=a_{i j}(t)-a_{i j}(t+1), i=\overline{1, M_{t r}}, M_{t r} \subset M, j=\overline{1, N}, j=$$
$\overline{1, N}, t \in T$
Similarly, a decrease in the material capacity of a product in an enterprise $i=\overline{1, M_{\text {mat }}}, M_{\text {mat }} \subset M$ is defined.

When assessing capacity, it is necessary to consider the wear and tear of $\Delta b_l^{f o n d}(t+1), i=\overline{1, M_{\text {fond }}}, M_{\text {fond }} \subset M$ and the increase in $\Delta b_l^{f o n d}(t+1)$ due to any investment into the enterprise’s capacity.

## 数学代写|最优化理论作业代写optimization theory代考|The algorithm for modelling the strategic plan

The algorithm for modelling the strategic plan includes a solution to a vector problem in mathematical programming (8.5.1)-(8.5.6) and is realized in two stages.

Stage 1. We solve a VPMP (8.5.1)-(8.5.6) with equivalent criteria for the first planning period of $t \in T$. During this period, intensive and extensive components are equal to zero:
$$\Delta a_{i j}(t+1)=0, \Delta b_i(t+1)=0, i=\overline{1, M}, j=\overline{1, N} .$$
As a result we will obtain an optimum set of products released by the enterprises, $X^o=\left{X_q^o, q=\overline{1, Q}\right}$, and the maximum relative assessment of $\lambda^0$ for which equality is carried out:
$$\lambda^o=\lambda_q\left(X_q^o\right), q=\overline{1, Q}, Q \subset K, X(t) \subset S .$$
For other criteria the ratio is applied:
In other words, $\lambda^o$ is the maximum lower level for all relative estimates of $\lambda_k\left(X^o(t)\right), k=\overline{1, K} \lambda_k\left(X^o(t)\right)$ or the guaranteed result at relative units.
At each calculation, along with obtaining technical and economic indicators (8.5.1)-(8.5.2), distribution of a global resource (8.5.3)-(8.5.4) between the different sections of a firm according to (8.3.7) is carried out: $r_i^q(t)=A^q X_q^o, i=\overline{1, M}, q=\overline{1, Q}$ and we also calculate in general for the firm (8.3.8):
$$R_i(t)=\sum_{q=1}^Q r_i^q=A X^o, i=\overline{1, M}, t=\overline{1, T} .$$
The remaining resources are defined from ratios:
$$\Delta R_i(\mathrm{t})=b_i(t)-R_i(t), i=\overline{1, M} .$$
Stage 2. We solve a VPMP (8.5.1)-(8.5.6) with equivalent criteria for the following planning period: $(t+1) \in T$. During this period, it is supposed that depreciation charges discerned at stage $t \in T$ will be addressed with part of the profit, which will go towards reproduction of the enterprise’s fixed business assets, manpower etc., at the expense of extensive and intensive components which, in this case, amounts to more than zero:
$$\Delta a_{i j}(t+1) \geq 0, \Delta b_i(t+1)=0, i \in M, j=\overline{1, N} .$$
As a result, in period $t=2$ we will obtain: $X^o(t)=\left{X_q^o(t), q=\right.$ $\overline{1, Q}}, t=2 \in T}$, a maximum relative assessment of $\lambda^o(t)$ and the distribution of a global resource (8.5.3)-(8.5.4).

# 最优化理论代写

## 数学代写|最优化理论作业代写optimization theory代考|The creation of a mathematical model of the strategic plan

$$b_i(t+1)=b_i(t)+\Delta b_i(t), i=\overline{1, M},(t, t+1) \in T .$$

$$\Delta a_{i j}(t+1)=a_{i j}(t)-a_{i j}(t+1), i=\overline{1, M_{t r}}, M_{t r} \subset M, j=\overline{1, N}, j=$$
$1, N, t \in T$

## 数学代写|最优化理论作业代写optimization theory代考|The algorithm for modelling the strategic plan

$$\Delta a_{i j}(t+1)=0, \Delta b_i(t+1)=0, i=\overline{1, M}, j=\overline{1, N} .$$

$$\lambda^o=\lambda_q\left(X_q^o\right), q=\overline{1, Q}, Q \subset K, X(t) \subset S .$$

$r_i^q(t)=A^q X_q^o, i=\overline{1, M}, q=\overline{1, Q}$ 我们还对公司 (8.3.8) 进行了一般计算:
$$R_i(t)=\sum_{q=1}^Q r_i^q=A X^o, i=\overline{1, M}, t=\overline{1, T} .$$

$$\Delta R_i(\mathrm{t})=b_i(t)-R_i(t), i=\overline{1, M} .$$

$$\Delta a_{i j}(t+1) \geq 0, \Delta b_i(t+1)=0, i \in M, j=\overline{1, N} .$$

，最大相对评估 $\lambda^o(t)$ 以及全球资源的分布 (8.5.3)-(8.5.4)。

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