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hw1.sol - IE 335 Operations Research Optimization Solutions...

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IE 335 Operations Research - Optimization Solutions to Homework 1 Spring 2012 Problem 2. Rardin, Exercise 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. (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 . (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 (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 x 1 and x 2 . The
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