I haven’t been lost, but just out here in the field collecting data for this damn PhD research. The good news is that I have been cleared to collect all the data I need for my research by the management of civil aviation authority, but still going through the bureaucracies and i do hope that in a few weeks’ time i will have developed a preliminary findings report.

Alright, what is this thing called stochastic programming? Last time we saw the meaning of stochastic, it is high time we extended to stochastic programming.

Uncertainty is the key ingredient in many decision problems. Airline scheduling, financial planning at any institution, unit commitment in power systems are just few examples of areas in which ignoring uncertainty may lead to inferior or simply wrong decisions. Often there is a variety of ways in which the uncertainty can be formalized and over the years various approaches to optimization under uncertainty were developed. By averaging possible outcomes or considering probabilities of events of interest we can define the objectives and the constraints of the corresponding mathematical programming model.

Well, stochastic programming is a framework for modeling optimization problems that involve uncertainty. Whereas deterministic optimization problems are formulated with known parameters, real world problems almost invariably include some unknown parameters. When the parameters are known only within certain bounds, one approach to tackling such problems is called robust optimization. Here the goal is to find a solution which is feasible for all such data and optimal in some sense. Stochastic programming models are similar in style but take advantage of the fact that probability distributions governing the data are known or can be estimated. The goal here is to find some policy that is feasible for almost all the possible data instances and maximizes the expectation of some function of the decisions and the random variables. More generally, such models are formulated, solved analytically or numerically, and analyzed in order to provide useful information to a decision-maker.

The most widely studied and applied stochastic programming models are two-stage linear programs. Here the decision maker takes some action in the first stage, after which a random event occurs affecting the outcome of the first-stage decision. A recourse decision can then be made in the second stage that compensates for any bad effects that might have been experienced as a result of the first-stage decision. The optimal policy from such a model is a single first-stage policy and a collection of recourse decisions, a decision rule defining which second-stage action should be taken in response to each random outcome.