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LINEAR PROGRAMMING: SENSITIVITY ANALYSIS AND INTERPRETATION OF SOLUTION,…
LINEAR PROGRAMMING: SENSITIVITY ANALYSIS AND INTERPRETATION OF SOLUTION
3.2 GRAPHICAL SENSITIVITY ANALYSIS
:star: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
:fire:a numerical value associated with each decision variable in the objective function. It represents the contribution of one unit of that variable to the overall objective function value (e.g., profit, cost, or utility).
:fire:When you change an objective function coefficient, it essentially alters the slope of the objective function line on the graph. This can lead to a shift in the optimal solution, depending on how the slope changes relative to the feasible region.
RIGHT-HAND SIDE
:fire:It refers to the constant term in each constraint inequality. It represents the limit or capacity of a particular resource or requirement.
3.1 INTRODUCTION TO SENSITIVITY ANALYSIS
:check:Sensitivity analysis is important to decision makers because real-world problems exist in a changing environment.
:check:Linear programming models are used in such environments like prices of raw materials change, product demand changes, companies purchase new machinery, stock prices fluctuate, employee turnover occurs, and so on
:check:Coefficients in linear programming models can change over time.
:check:Sensitivity analysis helps determine how changes in coefficients affect the optimal solution.
:check:Sensitivity analysis provides information without requiring a complete re-solution of the linear program.
3.2 SENSITIVITY ANALYSIS: COMPUTER SOLUTION
:warning:it involves systematically varying parameters and observing the resulting changes in the optimal solution.
INTERPRETATION OF COMPUTER OUTPUT
:!:understanding and interpreting the computer output of sensitivity analysis, decision-makers can make informed decisions, assess the robustness of their solutions, and identify potential areas for improvement.
CAUTIONARY NOTE ON THE INTERPRETATION OF DUAL VALUES
:!:While dual values are a powerful tool for understanding the sensitivity of an optimal solution to changes in resource constraints, it's crucial to interpret them with caution. They provide marginal information and may not accurately reflect the impact of large changes or non-linear relationships.
THE MODIFIED PAR, INC., PROBLEM
:!:is a classic linear programming example. Par, Inc. produces standard and deluxe golf bags with limited resources. Sensitivity analysis helps determine how changes in resources, prices, or costs impact the optimal production plan that maximizes profit.
3.4 LIMITATIONS OF CLASSICAL SENSITIVITY ANALYSIS
:black_flag:Classical sensitivity analysis has limitations, primarily due to its reliance on linearity, certainty, and single-parameter changes. It may not accurately reflect real-world scenarios with uncertainty, nonlinear relationships, and multiple simultaneous parameter changes.
SIMULTANEOUS CHANGES
:red_flag:Real-world scenarios frequently involve simultaneous changes to multiple parameters. This limitation can hinder the accurate assessment of the impact of these changes on the optimal solution.
CHANGES IN CONSTRAINT COEFFICIENTS
:red_flag:A significant limitation of classical sensitivity analysis is its inability to directly assess the impact of changes in constraint coefficients. This limitation arises because such changes can alter the feasible region of the problem, potentially leading to a new optimal solution
NONINTUITIVE DUAL VALUES
:red_flag:One of the limitations of classical sensitivity analysis is the potential for non-intuitive dual values, especially when dealing with constraints that involve variables on both sides. This can often occur in constraints that represent percentages or ratios.
3.5 THE ELECTRONIC COMMUNICATIONS PROBLEM
:explode:The Electronic Communications problem is a classic linear programming example that involves a company producing portable radio systems. The company has various distribution channels, each with different profitability, advertising costs, and sales efforts.
PROBLEM FORMULATION
:checkered_flag:The point of the problem formulation is to mathematically represent the Electronic Communications problem in a way that can be solved using linear programming techniques.
COMPUTER SOLUTION AND INTERPRETATION
:checkered_flag:The point of the computer solution and interpretation is to use linear programming techniques to determine the optimal sales plan that maximizes profit while considering various constraints, and to analyze the sensitivity of the solution to changes in parameters.
APPENDIX 3.2 SENSITIVITY ANALYSIS WITH LINGO
:pencil2:LINGO is a good optimization software that provides robust tools for sensitivity analysis in linear programming. It offers detailed insights into how changes in model parameters affect the optimal solution.
APPENDIX 3.1 SENSITIVITY WITH EXCEL SOLVER
:recycle:Excel Solver is a good tool for solving linear programming problems. It not only provides the optimal solution but also offers valuable insights through sensitivity analysis. This analysis helps us understand how changes in the model parameters, such as objective function coefficients or constraint right-hand sides, affect the optimal solution.
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