Linear optimization: Sensibility analysis 4

Introduction

The sensibility analysis (also sensitivity analysis) determines to what extend initial data can be changed, without changing the structure and characteristics (optimality, validity) of the final solution. The modification can be caused by variation of basis and non-basis variables. Because not all variables (data) can be changed at the same time, the modification has to be “ceteris paribus” (one variable changes, all other variables stay constant). The result of the sensibility analysis will be the range in which these variables can be changed, so that we don’t have to do further iterations to get to the optimal solution.

Change of basic variables

Basic Variables
 variation interval for dual value in the initial solution is defined by the smallest negative and the smallest positive ratio of objective function (here: optimal solution) and the corresponding row element.

• • Pay attention, that the positive value has to be subtracted from the initial value. At the same time the negative value has to be added to the initial value.

• Fehler beim Erstellen des Vorschaubildes: Die Miniaturansicht konnte nicht am vorgesehenen Ort gespeichert werden
  • Interpretation: In this example (Ya) the machine capacity could decrease to 150 or increase to 210, without changing the structure. The end tableau of the optimal solution will still be the same.

Change of non-basic variables

The interval where the initial solution can be varied is defined by the smallest negative and smallest positive ratio of the RS (here: optimal solution) and the corresponding column element.

• Fehler beim Erstellen des Vorschaubildes: Die Miniaturansicht konnte nicht am vorgesehenen Ort gespeichert werden

• Fehler beim Erstellen des Vorschaubildes: Die Miniaturansicht konnte nicht am vorgesehenen Ort gespeichert werden

Sources

• W. Domschke, A. Drexl, Einführung in Operations Research, 6th edition, 2005
• Prof. Dr. O. Wendt, lecture script "Operations Research", 2013