I have a project and I want to minimize the costs. I am are responsible for the inspection of 1000 kilometers of sewer grid in Canada. My goal is to provide time high quality inspection reports. I tried to define the problem using optimization but I haven't used for a year. I want to know what would be the optimised number of people I should hire.
The people I have to pay are robots drivers and inspectors.
- I have a $\$90000$ budget, two months on site and two weeks off site before.
- robots drivers take 6 pictures of every pole under different point of views and upload them on my cloud. The drivers upload their pics once a week.
- A well trained driver can inspect 15miles of sewer grid per day. Training lasts for one day, you can train two pilots in parallel.
- A photo inspector performs a quality check of the pictures on the Sterblue cloud. Sterblue asks the drone pilots to reinspect any poles not passing the quality checks. You can assume 10% of the poles have to be re-inspected.
- My AI on the cloud detects the defects. The customer expects 95% accuracy.
- The inspector performs a quality check of the detections found by the AI. They cost $300 a day and can handle 30miles/day for image quality review, 30miles/day to review the work of the AI.
- I have a free operations team that generates the inspection reports. 0,5 day is needed to prepare a report for 100 miles of grid.
Where x_1 is the number of robots drivers, x_2 the number of inspectors, y_1 the time spent by robot drivers, y_2 the time spent by inspectors.
I know that inspection can't start before reports, and that I haven't found a way to write the 95% accuracy constraints.
Can you help me improve the problem so I take into account every constraints to determine the number of people I should hire ?
I know I should do a Gantt diagram as well but I don't know yet where the major steps and dependencies are.