# Goal Programming Models: Rigid Constraints

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Goal Programming Models SML304 Nikhil Sahu 2011CS10237 Goal Programming is a optimization methodology where there are multiple, probably conflicting goals that need to be achieved simultaneously. Rigid Constraints Goals Goal programming formulations do not contains inequalities. Every constraint is written as an equation. We introduce a extra non-negative variable to convert a inequality into a equality and that is called a slack or surplus variable. Thus any linear programming problem can be converted into a standard form: Max c1x1 + c2x2 + ........ + cnxn subject to a11x1 + a12x2 + ........ + a1nxn = b1 .... .... .... am1x1 + am2 x2 + ........ + amnxn = b2…show more content…
xn >=0 This is acheived by as following: 1. If the objective is min z , convert to max -z 2. If ineqaulity constraint is ai1x1 + ai2x2 + ........ + ainxn = bi , convert it to ai1x1 + ai2x2 + ........ + ainxn - si = bi by subtracting surplus variable. The variables which are unknown and whose solutions are to be found are called decision variables. Example 1: Two products A and B, are made out of three chemicals I,II and III. A requires 3 units of I ,5 units of II and 1 unit of III. B requires 4 units of I and 6 units of II. Profits are 70 and 80 from A and