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Unformatted text preview: IE 335 Operations Research  Optimization Solutions to Homework 1 Fall 2011 Problem 2. Rardin, Exercise 13 13.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. 13.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 . 13.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) 13.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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 Fall '08
 Jeanphilippe,R
 Operations Research, Optimization, $1, 1 j, 10 310 secs, 15 315 secs, 16.40 hours

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