Question

Hello I need to know how to interpret the allowable increase and decrease for both the variable cells (doors and windows produced) and the constraints (Plants 1,2, and 3). Sensitivity reports and interpretation are discussed in the text on pp. 160-162.

Answer 1

(Here i am giving you the interpretation of allowable increase and allowable decrease of the variable cell with an example. Please provide the data for variable cell in comment box if you want interpretation for your problem.)

Definition:

The allowable increase/decrease for the objective coefficient of decision variable in objective function gives the range of values for objective coefficient such that the optimal solution for decision variables remain same.

Example:

Let the objective function of a LP is defined as,

where, x1 and x2 are the decision variable.

The sensitivity report of this LP is shown below,

Variable x1

Objective function coefficient = 44000

Allowable increase = 28000

Allowable decrease = 3500

Now, if we increase the objective function coefficient value from 44000 with allowable increase such that 44000+28000 = 72000, the final value of variable x1 (=2) will be unchanged.

Similarly, if we decrease the objective function coefficient value from 44000 with allowable decrease such that 44000-3500 = 40500, the final value of variable x1 (=2) will be unchanged.