How to determine the human resources I need given financial and operational constraints?

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.

• Can you create separate resource groups for each type of worker (men, machines) and convert their productivity into FTE? I think that would allow you to track their work load so you can distribute it more evenly or find spots where certain resource will be overloaded. Epicflow does that sort of analysis, but I'm not sure if it fits your situation. – Igor Gorbenko Jun 25 '19 at 10:36