I want to know if there is any already defined problem that could give me a hint on how should I approach the following task.
There are N tasks that should be accomplished, each task requires different amount of time to complete. On the other hand we have X persons to take care of the tasks but their speed of execution may vary per task. One restriction here is that each person should be designated to a single task. The goal here is to meet the demand of the tasks but also total duration should be kept as low as possible.
An easy way to proceed is to set a weight on meet the demand and also reduce the time of execution.(e.g 0.7 for demand and 0.3 for duration). I need to get the optimal weights.
Demand: total number of tasks: 1000
3 different tasks with the following distribution of demand T1: 20%, T2: 40%, T3: 40%
How should I formulate the problem so as weights can get into the game?