allowable range

The allowable range for a cost coefficient c_j (or a resource right-hand side b_i) is the interval around its current value over which today's optimal vertex remains optimal (cost case) or feasible with the same active constraints (resource case). Found by comparing the current vertex against every other candidate vertex as the coefficient is perturbed, it is the exact boundary of where a shadow price is still trustworthy -- push a coefficient past its own allowable range and a different vertex, with a different shadow price, takes over.