I have to solve a problem from industry where there are a number of machines which should be assigned to a number of tasks. The difference from the general assignment problem is tough, that the decision variable x is not a binary, it is a value between [0,1]. So that one machine can do 0.5(50%) of the task and another one can complete the task,does that make sense? I definied the problem like this:
When I program this problem in python with docplex, the solver is giving me only values of 1. Why there are no continuous values like 0.5 etc. Is there even a possibility that the mathematical optimal solution is a continuous value, or will this model always give binary results because there is a mathematical reason and maybe proof to that? So Does it even make sense to declare the decision variable as contionuous rather than binary?