Abstract
In Linear Programming (LP) applications, unexpected non binding constraints are among the “why” questions that can cause a great deal of debate. That is, those constraints that are expected to have been active based on price signals, market drivers or manager’s experiences. In such situations, users have to solve many auxiliary LP problems in order to grasp the underlying technical reasons. This practice, however, is cumbersome and time-consuming in large scale industrial models. This paper suggests a simple solution-assisted methodology, based on known concepts in LP, to detect a sub set of active constraints that have the most preventing impact on any non binding constraint at the optimal solution. The approach is based on the marginal rate of substitutions that are available in the final simplex tableau. A numerical example followed by a real-type case study is provided for illustration.
Highlights
Linear programming (LP) has found practical applications in all facets of business due to the computational efficiency of the simplex method and the availability of cheap and high-speed digital computers
In Linear Programming (LP) applications, unexpected non binding constraints are among the “why” questions that can cause a great deal of debate
This paper suggests a simple solution-assisted methodology, based on known concepts in LP, to detect a sub set of active constraints that have the most preventing impact on any non binding constraint at the optimal solution
Summary
Linear programming (LP) has found practical applications in all facets of business due to the computational efficiency of the simplex method and the availability of cheap and high-speed digital computers (for instance, see [1]). The rapid evolution of the easy-to-use software made model building and LP solving accessible to everyone. Engineers are capable to construct refinery models by drawing graphically the process models, connecting them into sophisticated external simulators (for non linear computations), designing. The commercial software imports the required input data from external sources, generates thousand of material and quality balance equations, points out data inconsistencies, debugs mathematical formulations, removes redundancies, linearizes the problem during the recursion passes (if necessary) and solves the problem in a fraction of time. Modern visualization technologies are provided to report the solution in comprehensive manners
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