TIME (Hours) Task 1 Task 2 Task 3 Task 4 Machine 1 130 40 70 60 Machine 2 10 110 50 40 Machine 3 60 70 20 80 Machine 4 10 30 50 90
Assignment Problem:
An iron & steel plant company has 4 machines available for assignment to 4 tasks in one of its production lines. Any machine can be assigned to any task, and each task requires processing by one machine. The time required to set up each machine for the processing of each task is given in the table below.
(a) Formulate an assignment problem that could be used to determine how to minimize the total setup time needed for the processing of all four tasks. The formulation should be in algebraic closed form.
(b) Use LINGO/OPL/EXCEL to solve your model. Write down the results of the decision variables and the objective function. Explain the value of the decision variables. What do they mean? (You can code your model either in the open form or in the closed form, it depends on you).
(c) Use the Hungarian method to solve the problem. Find the optimal assignment and the total setup time required.
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