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hw1.sol[1]

hw1.sol[1] - IE 335 Operations Research Optimization...

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Unformatted text preview: IE 335 Operations Research - Optimization Solutions to Homework 1 Fall 2011 Problem 2. Rardin, Exercise 1-3 1-3.a Decision variables represent the decision to be taken in the optimization model. Since we need to decide on the quantities produced, this implies that x 1 and x 2 are the decision variables for this problem. 1-3.b Input parameters are quantities in the model not affected by decisions. Therefore, the input parameters in this problem are t 1 ,t 2 ,T,c 1 ,c 2 and b . 1-3.c It would be advantageous to minimize production cost. Since c i is the cost of producing a lot in production line i , the total cost is c 1 x 1 + c 2 x 2 and therefore the objective function is: minimize c 1 x 1 + c 2 x 2 (1) 1-3.d We identify the constraints on the decision variables from the problem statement: Statement Constraint b lots in total x 1 + x 2 = b in a total of at most T hours x 1 t 1 + x 2 t 2 ≤ T integer number x 1 & x 2 x 1 ,x 2 integer Since production quantities cannot be negative, we add nonnegativity constraints on...
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hw1.sol[1] - IE 335 Operations Research Optimization...

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