Fixed Charge Constraints (Binary Variables) - Cal Poly Pomona固定费用约束（二进制变量）-加州波莫纳.pptVIP

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Fixed Charge Constraints (Binary Variables) - Cal Poly Pomona固定费用约束（二进制变量）-加州波莫纳.ppt

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Fixed Charge Constraints (Binary Variables) - Cal Poly Pomona固定费用约束（二进制变量）-加州波莫纳

Fixed Charge Constraints(Binary Variables) Henry C. Co Technology and Operations Management, California Polytechnic and State University Decision variables x1 = number of shirts to produce x2 = number of shorts to produce x3 = number of pants to produce At most 150 labor hours and 160 square yards of cloth are available. Without looking at the fixed cost, and ignoring the fact that the number of shirts, shorts, and pants to produce must be integers, this simplifies to an LP problem: The LP Solution Question: How can we model the fixed costs? We do this by using binary variables. Integer (Binary) Variables Introduce a set of integer (binary) variables as follows: y1 = 1 if we produce shirts (i.e., if x1 0), otherwise, y1 = 0. Y2 = 1 if we produce shorts (i.e., if x2 0), otherwise, y2 = 0. Y3 = 1 if we produce pants (i.e., if x3 0), otherwise, y3 = 0. How do we model this? A Useful Trick Let M = a reasonably large constant. For example, M=the most number of shirts you may want to produce. If we state: x1≤ M y1 or equivalently, x1- My1 ≤ 0, then If x1 0, y1 can not be 0. In other words, if we produce shirts, y1 = 1. What is M? If we ALL the labor is used to produce shirts, we can produce 150/3 = 50 shirts (note: there are 150 available and each shirt takes 3 hours to make). If all the cloth is used to produce shirts, we can produce 160/4 = 4 shirts (i.e., there are 160 sq. yd of cloth and each shirt need 4 sq. yd). Thus, the most shirts we can produce is Minimum (50,40) = 40. Following the same argument, the most pants we can produce = 53, and the most pants we can produce = 25. Fixed Cost in the Objective Function Add the following fixed costs to the objective function: $200 y1 + $150 y2 + $100 y3 Plus 3 additional constraints: x1- 40y1 ≤ 0 x2- 53y2 ≤ 0 x3- 25y3 ≤ 0 Binary Variables in Solver Declare y1, y2, and y3 as binary variables by adding the following constraints in Solver: Integer Variables in Solver If needed, you may also declare x1, x2,