Posted on Categories:Operations Research, 数学代写, 运筹学

# 数学代写|运筹学代写Operations Research代考|OPR561 CONTINUOUS DEMAND INSTANTANEOUS REPLENISHMENT MODEL

avatest™

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 数学代写|运筹学代写Operations Research代考|CONTINUOUS DEMAND INSTANTANEOUS REPLENISHMENT MODEL

The inventory-time behaviour is given in Figure 13.1. We place order for $Q$ items when the stock reaches zero and the inventory is instantaneously replenished. Inventory is consumed continuously at the rate of $D$ year.
The coefficients are:
Annual demand $=D /$ year
Order cost $=C_o$
Carrying cost $=C_c$
Order quantity $=Q$
Number of orders $/$ year $=\frac{D}{Q}$

Annual order cost $=\frac{D C_o}{Q}$
Average inventory in the system $=\frac{Q}{2}$
Annual inventory carrying cost $=\frac{Q C_c}{2}$
Total cost $(T C)=\frac{D C_o}{Q}+\frac{Q C_c}{2}$
The value of $Q$ that minimizes the total cost is obtained by setting the first derivative to zero. We get
$$\frac{-D C_o}{Q^2}+\frac{C_c}{2}=0$$
from which
$$Q^=\sqrt{\frac{2 D C_o}{C_c}}$$ and substituting $Q^$ in $T C$, we get
$$T C^*=\sqrt{2 D C_o C_c}$$

## 数学代写|运筹学代写Operations Research代考|ONSIDERING BACKORDERING

In this model, we allow a backorder of $s$ units every cycle and as soon as the order quantity $Q$ arrives, we issue the backordered quantity. Figure $13.3$ shows the model. The maximum inventory held is $I_m=Q-s$. There is an inventory period of $T_1$ per cycle and a backorder period of $T_2$ per cycle.

The coefficients are:
Annual demand $=D /$ year
Order cost $=C_o$
Carrying cost $=C_c$
Shortage (backorder) $\operatorname{cost}=C_s$
Order quantity $=Q$
Backorder quantity $=s$
Maximum inventory in a cycle $=I_m$
Number of orders/year $=\frac{D}{Q}$
Annual order cost $=\frac{D C_o}{Q}$
Average inventory in the system $=\frac{I_m}{2}$
Annual inventory carrying cost $=\frac{I_m C_c}{2}$
Average shortage in the system $=\frac{s}{2}$

Annual shortage cost $=\frac{s C_s}{2}$
Total cost $T C=\frac{D C_o}{Q}+\frac{I_m C_c}{2} \times \frac{T_1}{\left(T_1+T_2\right)}+\frac{s C_s}{2} \times \frac{T_2}{\left(T_1+T_2\right)}$
From similar triangles, we get
and
Substituting, we get
$$T C=\frac{D C_o}{Q}+\frac{(Q-s)^2 C_c}{2 Q}+\frac{s^2 C_s}{2 Q}$$
The values of $Q$ and $s$ that minimize the total cost are obtained by setting the first partial derivative with respect to $Q$ and $s$ to zero. Partially differentiating with respect to $s$ and setting to zero, we get
$$s=\frac{Q C_c}{\left(C_c+C_s\right)}$$
Partially differentiating with respect to $Q$ and substituting for $s$, we get
$$Q^*=\sqrt{\frac{2 D C_o\left(C_c+C_s\right)}{C_c C_s}}$$

## 数学代写|运筹学代写Operations Research代考|CONTINUOUS DEMAND INSTANTANEOUS REPLENISHMENT MODEL

$$\frac{-D C_o}{Q^2}+\frac{C_c}{2}=0$$
M中
$$Q^{=} \sqrt{\frac{2 D C_o}{C_c}}$$

$$T C^=\sqrt{2 D C_o C_c}$$

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。