On Rohn's relative sensitivity coefficient of the optimal value for a linear-fractional program

summary:In this note we consider a linear-fractional programming problem with equality linear constraints. Following Rohn, we define a generalized relative sensitivity coefficient measuring the sensitivity of the optimal value for a linear program and a linear-fractional minimization problem with respect to the perturbations in the problem data. By using an extension of Rohn's result for the linear programming case, we obtain, via Charnes-Cooper variable change, the relative sensitivity coefficient for the linear-fractional problem. This coefficient involves only the measure of data perturbation, the optimal solution for the initial linear-fractional problem and the optimal solution of the dual problem of linear programming equivalent to the initial fractional problem

Non-steroidal Anti-inflammatory Drugs Ranking by Nondeterministic Assessments of Probabilistic Type

With a number of common therapeutic prescriptions, common mechanisms, common pharmacological effects - analgesic, antipyretic and anti-inflammatory (acetaminophen excepted), common side effects (SE) (platelet dysfunction, gastritis and peptic ulcers, renal insufficiency in susceptible patients, water and sodium retention, edemas, nephropathies), and only a few different characteristics – different chemical structures, pharmacokinetics and different therapeutic possibility, different selectivities according to cyclooxygenase pathway 1 and 2, non-steroidal anti-inflammatory drugs (NSAIDs) similarities are more apparent than differences. Being known that in a correct treatment benefits would exceed risks, the question “Which anti-inflammatory drug presents the lowest risks for a patient?” is just natural. By the Global Risk Method (GRM) and the Maximum Risk Method (MRM) we have determined the ranking of fourteen NSAIDs considering the risks presented by each particular NSAID. Nimesulide, Etoricoxib and Celecoxib safety level came superior to the other NSAIDs, whereas Etodolac and Indomethacin present an increased side effects risk