implement the mathematical model in part a in python and solve with Gurobi

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

a. [20 points] Provide the mathematical model that would determine the optimal schedule for these 6 orders throughout the half year that minimizes the total costs. Indicate the parameters, decision variables, objective function and constraints clearly with their definitions and explanations. Note: If the mathematical model has fundamental flaws at this stage the rest of the assignment may not be evaluated.

b. [20 points] Implement the mathematical model in part a in python and solve with Gurobi. Provide the optimal solution. By the optimal solution it is meant that you need to provide the optimal objective function value, the separate costs components and a clear overview of all the related decision variables. Note: You are expected to have the implementation in the matrix form and if the implementation fails that, the rest of the assignment may not be evaluated. Moreover, make sure that model and data are separated. This is required to enable experiments with the same model but other data-sets; or with the same data but other model choices. Now consider that there is a monthly production capacity limit. The maximum production each month is 75 ton (bruto, before electrolysis).

c. [10 points] What would change in the formulation? Provide the new additions/changes to the mathematical model. What would be the new optimal solution? Discuss the changes in the results (compared to part b) together with your reasoning.

d. [15 points] Verify the mathematical formulation (part c) with a number of verification tests that cover different types of parameters used in the model. Provide a discussion on the verification experiments and their results with your justifications. 

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