| # Robust LP Solution to the Drug Production Problem Return to the drug production problem described here, and the corresponding uncertainty issue discussed here. ### Robust LP model The only constraint affected by uncertainty was the active agent balance inequality. In the nominal problem, this constraint was where the nominal values of the coefficients were set to and . The uncertainty affects the coefficients , which are assumed to be only known within intervals: and . To obtain a robust solution, we can solve a new problem where we insist that the above constraint holds for every possible value of the coefficients within their respective intervals. In this problem, since the variables are non-negative, the worst-case value of the coefficients corresponds to a particular scenario where both coefficients are set to their lowest possible value: we set and and solve the corresponding LP. ### Robust LP solution The new (robust) solution is then This is to be compared with the nominal solution, which was: The profit goes down, by a relatively small amount of . This is to be compared with the expected loss of (and worst-case loss of if we had stuck to our original solution, and tried to adjust it to uncertainty (see here). Note also that the qualitative behavior of the robust solution is very different from that of the nominal one. In the latter, we only purchase the raw material II, and produce only Drug I. This makes sense as XXX. The robust solution, in contrast, recommends to purchase only raw material II and produce Drug II. This makes sense, as the uncertainty in the active ingredient amount in the raw material II is higher.