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The production manager of a large Cincinnati manufacturing firm once made the statement, “I would like to use LP, but it’s a technique that operates under conditions of certainty. My plant doesn’t have that certainty; it’s a world of uncertainty. So LP can’t be used here.” Do you think this statement has any merit? Why or why not? Explain why the manager may have said it and then further substantiate his argument or compose a rebuttal.
Expert Answer
In fact a well-developed LP model can be formulated using the base case scenario or the values pertaining to the base case. The results of this base case model provides a good indicative direction towards optimizing the operations.
To take care of the uncertainty and variability, a number of scenarios can be run by varying the values of the variables, which would throw up different optimized values and different objective function values. Thus using a combination of scenario planning and LP modelling a range of feasible values can be found out which are optimal at different levels.
In fact the sensitivity output of a solved LP model in MS Excel provides the output which lends itself to such analysis. The reduced cost and the binding or non-binding constraints that is highlighted in the sensitivity analysis showcases the extent to which certain parameters can be varied without affecting the optimality of the solution.
Thus LP modelling can very well be used in conditions where there is uncertainty to build a large range of optimal solutions depending on the conditions prevailing.
