Coefficient Perturbation of a Constrained Extremum

A schedule of allocating labor (in a shipping operation) whose available amount is a function of time, to different tasks, in order to minimize the total cost, is given. The problem is cast in linear-programming form in which all the coefficients are parameterized. An illustration is given followed by a general discussion of the use and limitation of this method, which yields a correspondence between optimal solutions and ranges of time values. The dependence of the optimal value on the parameterized coefficients leads to a sensitivity study.