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Up until this point I have only solved simple LPP problems with maybe 2 to 3 variables that looked like this, using pen and paper.

simple lpp

I need to solve This Problem using Simplex, Dual Simplex, Big M and 2 Phase. I can use a solver for this problem, but I don't know how to start.

In the PDF above it looks like it has all the constraints and the objective function, I assume I will have to substitute the above values and make a massive objective function. But I don't know what I even need to do.

I have downloaded GAMS and modeled a simple problem in it, but I am not understanding how to start modelling this one in it. So can someone help me on how to start? I have not solved these types of problems before, so which program should I use? Any tutorials maybe on how to model my problem in it.

Other than GAMS I checked and their is an Excel Solver, some libraries for python. I am fine with any of these.

Adding a few images from the PDF:

Cons Cons1 Objective Objective 2

HABIL BHAGAT
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    If you can use Gurobi as your solver, I refer you to the following question on a complete implementation of an scheduling example in Python: https://or.stackexchange.com/questions/797/how-to-model-a-mixed-integer-linear-programming-formulation-in-python-using-guro – Mostafa Apr 01 '20 at 07:50
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    @Habil, Welcome to OR.SE. First of all, what you need to formulate a MP in an algebraic modelling language like GAMS is, every MP does have a standard notation to define sets, indices, parameters/data, variables and equations. All of the modern solvers and frameworks have such capabilities. If you are new and interested in programming in the framework or the solver through an algebraic or APIs, I recommend you start with a simple and basic example such as transportation problem which can be found on all of the optimization programs. In GAMS you can find this on its host easily. – A.Omidi Apr 01 '20 at 08:34
  • Thanks @Mostafa , I will see check that post and try and use Gurobi. Can I solve my problem using Simplex, Dual Simplex, Big M and 2 Phase? – HABIL BHAGAT Apr 02 '20 at 08:12
  • @A.Omidi I solved a simple problem in Gams, like the first image I have sent. But I can't understand how to model this problem with summation equations. Plus there are 5 objective functions, which I don't understand how to handle that. I saw the other post that Mostafa sent and I am understanding a bit. I am guessing I will have to simplify my objective function before trying anything but. – HABIL BHAGAT Apr 02 '20 at 08:24
  • @Habil, as per your previous question, by using a solver like Gurobi or Cplex, trough an API or framework, it does automatically and you do not need to perform it yourself. (I mean simplex or dual simplex.). About the big M or two phases and based on your problem formulation you will have to do that yourself. Would you please, do you see the transportation problem coding in GAMS as I said in the previous comment? If you are new in the MP or programming and you would need to use an MP solver, I really recommended you to use an algebraic modelling language like GAMS. – A.Omidi Apr 02 '20 at 13:29
  • Ah, about your multi-objective problem, first you will need to formulate and write the problem in your favourite framework/API, then by using some methods like the sum of weighted objects, lexicograph and etc, you can solve the problem. Would you try writing your problem in GAMS? – A.Omidi Apr 02 '20 at 13:48

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