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Chapter 3

# MGOC10H3 Chapter Notes - Chapter 3: Sensitivity Analysis, Sunk Costs

Department
Management (MGO)
Course Code
MGOC10H3
Professor
Vinh Quan
Chapter
3

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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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