There are N person. Each person has a strength Si to perform tasks .
There are T tasks. Each task consumes energy ej
We have to assign the tasks to the persons such that the distribution is balanced.
For e.g if there are 4 person with Strengths 100, 50, and 30, 20 and there are 10 tasks with energy weight as 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 (No need to be same). Here I want to assign the tasks such that maximum tasks can be done without exhausting any person.
So,I would assign 6 tasks to the first one, 2, 1, 1 to second, third and fourth respectively.
I tried solving the problem with OR tools https://developers.google.com/optimization/bin/multiple_knapsack but the solver assigns all the 10 tasks to the first person exhausting it immediately.
Here is a question with similar
problem but it is different from mine because I have different capacity of bags https://math.stackexchange.com/questions/1833651/is-there-a-balanced-knapsacks-problem-with-a-known-result
Is it a known problem?
Am I wrong by calling it a Multiple Knapsack?
Is there a way to solve this using the OR tools or any other way is much appreciated?