Predict-then-Optimize v/s Probabilistic Approximations: Tackling Uncertainties and Error Propagation

Proactive planning is a key necessity for busi-nesses to function efficiently under uncertain andunforeseen circumstances. Planning for the futureinvolves solving optimization problems, whichare often naturally convex or are modeled as con-vex approximations to facilitate computation. Theprimary source of uncertainties in the real worldthat business are dealing with (eg. demand) can-not be reasonably approximated by deterministicvalues. Hence deterministic convex optimizationapproximation do not not yield reasonable solu-tions. Classically, one relies on assumptions onthe data generating process (like for eg. that de-mand is log normal) to formulate as a stochasticoptimization problem. However, in today’s world,such major uncertainties are often best predictedby machine learning methods. In this paper, wepropose a novel method to integrate predictionsfrom machine learning systems and optimizationsteps for a specific context of a resource utilisa-tion problem that faces non-stationary incomingworkload. The proposed solution is robust andshows improved performance against using thetraditional point-predictions directly in the opti-mization. The proposed solution can be easilyextended to different kind of machine learningmethods and objective functions.