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Description: One of a quantitative analysis method for optimizing an object function in a given constraint is called as linear programming. For this method, as the name suggests, the faction of an object must be linear in order for the linear programming to be used effectively. Problem Formulation Checklist: Problem statement gives information from which the constraints and functions of object are formulated. To minimize the errors in a problem formulation, following checklist is used:      

All the numbers in the problem statement should either be discarded or should be used. For instance sunk cost. Always remember the initial stages. For instance, the initial staff quantity present at the beginning of staffing period. Make sure that the variables that are listed in objective functions are present in constraints. If there are any non-negative constraints, they should be listed. Binary integer variables should be limited to 0,1. All the variables should be moved to left hand side of equation and should be written in order of their subscripts.

Sensitivity Analysis: Although by using deterministic objective functions the problems can be modeled, yet there is variation in the reality. This sensitivity of the solution to the changes in parameter can be determined using a process called as sensitivity analysis. Microsoft excel is very useful in generating sensitivity report, it makes the report in two parts- constraint report and changing cells report.

The increase and decrease in the changing cells depends upon the objective function decision variable coefficient change without changing the values of any decision variables. However if the coefficient changes and the corresponding decision variable does not change then the objective function value will have to change.

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The amount that would be changed by objective function value if the named constraint is changed by one unit is called as the shadow price. The amount of increase or decrease in the constraint is the shadow price. If the shadow price increases or decreases by the allowable limit then it is supposed to be unknown. But due to the laws of diminishing returns, it is less favorable than the reported value. Linearity from Non-Linear Problem: There are many problems that can be made linear from initial non-linear by formulating them carefully. For instance, avoiding the use on inequality ‘≠’, it is the same for binary integer variables ‘X+Y≠1’ or one can say ‘X=Y’. Binary variables: The following form is used when comparing binary switch variables with continuous decision variables:

Simulation: Significant randomness is not detected by the linear programming methods as they operate on certainty. To minimize random variables, following points must be considered:   

Objective function should be expressed in decision variable. For the decision variable, the incremental search value and search range should be defined. Use Monte Carlo simulator for each incremental value of decision variable.


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Linear programming  
Linear programming  

One of a quantitative analysis method for optimizing an object function in a given constraint is called as linear programming. Reference:...