LP Formulaiton Guidelines
Guidelines for formulation:
- Understand the problem
- ask the following three questions:
- decision variables
- what measure should we use to ompare alternative sets of decisions
- what restrictions
- mathematical representation of the objective function in terms of the decision variables
- write the constraints in terms of the decision vatiables
- check your formulation!
- Does it make sense?
- Is there any data in the problem you haven’t used?
Post Office
- The number of full-time employees needed on each day is as follows:
- 7,3,5,9,4,6,1分别对应周一到周日
- 公会要求，每个全职雇员应该连续工作五天并且连续休息两天
- 邮局必须满足需求，使用全职雇员
- 目标：最小化使用的雇员数量
- 题目说明：
解答：
- 另外讨论两种Alternative Question
- 如果有临时工：
- 目标：$min(\sum^{7}_{i=1}[c_ix_i+c_i’y_i])$
- s.t.: Example of Monday: $x_1+x_4+x_5+x_6+x_7+y_1 == 7$
Blending
- three basic blends in 1 pound bags: special, mountain dark, mil regular
- two different types of beans to produce the blends: brazilian and mild
- blend recipe:
| Blend | Mix requirements | selling price(dollar/LB) |
|---|---|---|
| special | 40% brazilian, no more than 30% mild | 6.5 |
| dark | 60% Brazilian, no more than 10% mild | 5.25 |
| regular | no more than 60% brazilian, at least 30% brazilian | 3.75 |
- brazilian coffee beans: 2 dollar/pound, while mild is 1.25/pound
- brazilian <= 210 pounds and mild coffee <= 300 pounds
To maximize the profit
解答：
投资组合：
- 不去管下面的示例表
- 本质上要最小化专款专用的投入额
解答：
生产问题：
解答：
- 不是说变量越少越好，有时候多一些变量会更好
路径问题：
解答：
- 每条线一个变量
分配问题：
