# 数学代写|运筹学作业代写operational research代考|General Modeling Tricks

## 数学代写|运筹学作业代写operational research代考|General Modeling Tricks

In this section, we discuss a number of generally applicable modeling tricks to model “almost-linear” programming problems as (mixed) ILP problems. Some of these tricks have already been used in the examples in Section 2.2. Other tricks will come back in the exercises.
Almost-Linear Objective Function
Suppose that a production-stock problem is given, with aim to minimize the costs, and the objective function contains an almost-linear term $P(x)$, where $P(x)$ represents the production costs of $x$ units. The following three cases are of interest for applications:
(a) variable production costs plus fixed setup cost:
$$P(x)=\left{\begin{array}{cc} K+c x & \text { for } x>0 \ 0 & \text { for } x=0 \end{array}\right.$$
where $K$ and $c$ are constants with $K>0$ and $x$ is a variable;
(b) piecewise-linear production costs:
$$P(x)=\left{\begin{array}{cl} c_1 x & \text { for } 0 \leq x \leq a_1, \ c_1 a_1+c_2\left(x-a_1\right) & \text { for } x>a_1, \end{array}\right.$$

## 数学代写|运筹学作业代写operational research代考|The Branch-and-Bound Method

• 上限与拆分（分支）过程中创建的每个解决方案子集相关联。给定解决方案子集的上限是一个数字，使得子集中每个可行解决方案的目标值都小于或等于该数字。
• 下界是目前已知的最佳可行解的目标值。

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