A case study~

This week I passed the driving license computer test, so I will get my car right now , lol , means I will see goodbye to bieber~

I work for the case study of the operations management theory & practice class, here it is, please give me some advices on it, actually this is my first english case study.

Linear programming

Definition

Linear programming is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear equations.

Linear programming is heavily used in microeconomics and company management, such as planning, production, transportation, technology and other issues. Although the modern management issues are ever-changing, most companies would like to maximize profits or minimize costs with limited resources. Therefore, many issues can be characterized as linear programming problems.

Importance

Almost every companies want to get the maximize profits with minimize costs, today company’s labor costs became one of the major costs. So how to deal with the labor costs is really a complicated affair for modern manager. For example, the HONG KONG bank find that their labor costs remain at a high level, at the same time their profit became lower. The manager find the bank do not need keep whole tellers in service through their office hours. Because the consumers always come to  the bank at some regular time. If the bank make a new schedule that let the number of tellers needed varies by time of day, it must reduce the labor costs. So Linear programming can be used to make a new suitable schedule, therefore, this issue could be characterized as a linear programming problem.

Application

Linear programming is a considerable field of optimization for several reasons. Many practical problems in operations research can be expressed as linear programming problems. In the case of HONG KONG bank, first manager calculated the minimum number tellers per time period.( table 1), than he knew the total minimum daily requirement is 112 hours. There are two kinds of tellers. One is full time tellers, they work from 9AM-5PM with $90 a day, and currently there are only 12 tellers are available. And the other kind tellers are part time workers. They work 4 consecutive hours with $7 per hour, can begin work at 9,10,11,noon,or 1. And the Hongkong’s law ordered that part time employees cannot exceed 50% of the day’s minimum requirement.(56 hours). Than manager use the Linear programming tool to calculate the minimum number thellers needed by a formula :

Table 1

Time Period	Min Num. Tellers
9-10	10
10-11	12
11-12	14
12-1	16
1-2	18
2-3	17
3-4	15
4-5	10

Min 90F(full time teller)+ 28(P1+P2+P3+P4+P5) ( part time tellers work at 9,10,11,12,1)

subject to the constraints

Part Time Hours Cannot Exceed 56 Hours

4(P1+P2+P3+P4+P5) ≤≤ 56

Finally, the manager made a schedule minimize the labor costs.

Relationship

The manager of the HONG KONG bank may want to just have the part time employees because they are with the low cost, but there a law that ordered the minimum numbers of the part time employees. So he must to made a economic schedule to reach the law’s minimum permit, and achieve the goal that to reduce the labor cost at the same time. Linear programming help him to do the job easily and efficiency. From this case, we can find how Linear programming react on the company’s management.