The main goal is to find the most cost-effective mix of teachers who can collectively cover all the required subjects, thereby minimizing the monthly salary expenditure.
A headteacher is looking for new teachers in the following subjects: mathematics, statistics, programming, English, data science, and software engineering.
- She has six qualified applicants for the jobs.
- Some can only work part-time and the monthly wage for this is £480.
- The others are paid on one of two scales, depending on their experience.
This problem setup uses binary variables for each teacher's hiring decision and seeks an optimal hiring configuration that minimises total salary while meeting the staffing requirements for all subjects.
- This configuration optimises costs while maintaining coverage for all subjects, suggesting hiring more expensive teachers or more teachers than necessary is unnecessary, even if they can teach multiple subjects.
- This highlights the importance of proper resource allocation, ensuring hiring decisions are based on qualification coverage and cost efficiency.
- This underscores your responsibility and accountability in ensuring all subjects are adequately staffed, but it only solves the problem with one dimension: the 'cost'.