Department

Management (MGO)Course Code

MGOC10H3Professor

Vinh QuanChapter

3This

**preview**shows half of the first page. to view the full**1 pages of the document.**Chapter 3 Linear Programming: Sensitivity Analysis and Interpretation of

Solution

sensitivity analysis study of how changes in coefficients of a linear programming problem affect optimal solution

3.1 Introduction to Sensitivity Analysis

sensitivity analysis is important to decision makers because real-world problems exist in a changing environment

sensitivity analysis can also be used to determine which coefficients in a linear programming model are crucial

another aspect of sensitivity analysis concerns changes in the right-hand-side values of the constraints

3.2 Graphical Sensitivity Analysis

for linear programming problems with two decision variables, graphical solution methods can be used to perform

sensitivity analysis on the objective function coefficients and the right-hand-side values for the constraints

Objective Function Coefficients

range of optimality the range of values over which an objective function coefficient may vary without causing any

change in the values of the decision variables in the optimal solution

managerial attention should be focused on those objective function coefficients that have a narrow range of optimality

and coefficients near the end points of the range

with these coefficients, a small change can necessitate modifying the optimal solution

range of optimality for objective function coefficients is only applicable for changes made to one coefficient at a time

if two or more objective function coefficients are changed simultaneously, further analysis is necessary to determine

whether the optimal solution can change

Right-Hand Sides

dual value the change in the value of the objective function per unit increase in the right-hand side of a constraint

as more and more resources are obtained and the right-hand-side value continues to increase, other constraints will

become binding and limit the change in the value of the objective function

the dual value is the change in the objective function value per unit increase in a constraint right-hand side

3.3 Sensitivity Analysis: Computer Solution

Interpretation of Computer Output

reduced cost reduced cost of a variable is equal to the dual value on the non-negativity constraint for that variable

range of feasibility the range of values over which the dual value is applicable

Cautionary Note on the Interpretation of Dual Values

sunk cost a cost that is not affected by the decision made; it will be incurred no matter what values the decision

variables assume

relevant cost a cost that depends upon the decision made; the amount of a relevant cost will vary depending on the

values of the decision variables

when the cost of a resource is sunk, the dual value can be interpreted as the maximum amount the company should be

willing to pay for one additional unit of the resource

when the cost of a resource used is relevant, the dual value can be interpreted as the amount by which the value of the

resource exceeds its cost

thus, when the resource cost is relevant, the dual value can be interpreted as the maximum premium over the normal

cost that the company should be willing to pay for one unit of the resource

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