The solver output gives negative values even after applying necessary constraints.

I've attached the problem in the file below. I need to optimize resource allocation across projects. I've decided to use binary variables to indicate whether a project is assigned to a particular resource or not. I've done the necessary formatting in data validation as well.

However, instead of giving me binary values, the solver keeps giving me negative values as output.

Objective as stated in earlier thread:

I have ten projects to be completed. 5 of them are short term which take 6 months to complete and the other 5 are long term projects which take 12 months to complete. I have three resources available with me. One resource is enough to complete one project. However, one resource can only be engaged with one project at a time. As soon as a project is completed the resource can be engaged in the next project. Write a linear program in excel to optimize resource allocation and start stop times of the ten projects to ensure that all the ten projects get completed within the least amount of time.

This is the same file you attached in your other thread. Does this thread supersede the first thread? I am inclined to close the other as a duplicate, as this one is more specific about your question.

If you want to use binary variables, you must add a constraint in the range B4:K6, and choose "bin" as option.

Moreover, you can simplify the constraint in row 8 selecting the range B8:K8 and setting it equal to 1.

Finally, change the engine to Simplex LP.

I doubt this approach will give you the minimum amount of time required to complete all the projects, though.

HTH,

Francesco