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L18_Sensitivity analysis - Changes affecting feasibility

L18_Sensitivity analysis - Changes affecting feasibility -...

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Sensitivity Analysis The optimal solution of a LPP is based on the conditions that prevailed at the time the LP model was formulated and solved. In the real world, the decision environment rarely remains static and it is essential to determine how the optimal solution changes when the parameters of the model are changed. That is what sensitivity analysis does. It provides efficient computational techniques to study the dynamic behaviour of the optimal solution resulting from making changes in the parameters of the model.
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In studying the sensitivity analysis, we should be familiar with the lingo that is being used in LPP situations. A general LPP is of the form Maximize (or Minimize) n n x c x c x c z + + + = ... 2 2 1 1 subject to the constraints 11 1 12 2 1 1 21 1 22 2 2 2 1 1 2 2 1 2 ... ... . ... , ,..., 0 n n n n m m mn n m n a x a x a x b a x a x a x b a x a x a x b x x x + + + = + + + = + + + =
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The RHS constants of the constraints, m b b b ,..., , 2 1 are referred to resources or availabilities of the problem. The objective coefficients, n c c c ,..., , 2 1 are referred to as unit profits (or unit costs). The decision variables, n x x x ,..., , 2 1 are referred to as units of activities 1, 2, …, n .
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Dual Price of a constraint This measure actually represents the unit worth of a resource - that is it gives the contribution to the objective function resulting from a unit increase or decrease in the availability of a resource. In terms of duality theory, the dual price of a resource (=constraint) i, is precisely the value of the optimal dual variable y i associated with the constraint i . (Did you understand why it is called “dual price”?). Other non-suggestive names include shadow prices and simplex multipliers .
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Reduced cost of a variable x j (=activity j) is defined as Cost of consumed resources per unit of activity x j - profit per unit of activity x j = z j - c j
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Changes affecting feasibility The feasibility of the current optimum solution may be affected only if (1) The RHS of the constraints are changed OR (2) A new constraint is added to the model.
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