Sensitivity Analysis
We have studied how to formulate linear programming problems and how to find optimum solutions by using the graphic and simplex methods. These two phases, however, generally do not complete an LP analysis, a third phase called, sensitivity analysis or post optimality analysis is usually undertaken to explore the effect of changes in the LP parameters on the optimum solution. For example to study the effect of costs and price change. Diminishing resources becoming readily available or technological advances, on the optimum LP solution, sensitivity analysis suggest the changes in the data used to build the model.
Sensitivity analysis is concerned with the extent of sensitivity of the optimum solution to an LP for change in one or more of L: (i) the profit or cost coefficients of the objective function, (ii) the L.H.S coefficients of the variables in the constraints and (iii) the R.H S. quantities of constraints. The need for this analysis arises from reasons:
1. The aforesaid coefficients are after all estimates only and are liable to be inaccurate to some extent due to human error in observation or errors due to limited sampling. Also, in course of time, there may arise, some deviations in actual values form those estimated earlier. Such deviations or errors make it essential for the decision maker to understand their impact on the optimum solution. Some LP models may not be very sensitive to such changes and a given solution may continue to be optimum inspite of large variations in the values of the parameters. However solution, others may be very sensitive and even small changes may offset the optimum solution. in such cases the coefficients would have to be estimated after painstaking research in the relevant data.
2. The management can manipulate these coefficients and relax the constraints in several situations. For example selling prices can be increased in a product mix problem to increase the unit profit or time requirements of a product at a work centre may be diminished by improved methods or extra equipment may be installed to increase the available capacity, i.e., the R.H.S quantity. Management would then naturally be interested in knowing what effects these manipulations have on the optimum solution.
In short sensitivity Analysis is the process of investigating to what extent the numerical parameters of a LP model can be changed, before the optimum solution for a given set of parameters of a LP model can be changed before the optimum solution for a given set parameters is disturbed.
Such post optimum solution analysis can be of the following types.
Type 1. To determine the range within each of profit (or cost) coefficients can be varied without altering the basic variables though the optimum profit (or cost) would naturally vary.
Type 2. To indicate the extent of increase of R.H.S. quantities without altering the existing basic variables.
Types 3. To investigate the effect of adding or deleting constraints and or variables on the optimum product mix.
Type 4. To determine the sequence of basic situations that become optimum as the changes in the LP parameters are extended further and further.
Remark. It is easy to discern that from the management point of view the information provided by sensitively analysis may be far more useful than he single optimum result. In a way sensitivity analysis makes the static LP solution a dynamic tool that evaluate changing conditions.
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