Challenges in Adding a Stochastic Programming/Scenario Planning Capability to a General Purpose Optimization Modeling System

We describe the stochastic programming capabilities that have recently been added to LINDO application programming interface optimization library, as well as how these stochastic programming capabilities are presented to users in the modeling systems: What’sBest! and LINGO. Stochastic programming, which might also be suggestively called Scenario Planning, is an approach for solving problems of multi-stage decision making under uncertainty. In simplest form stochastic programming problems are of the form: we make a decision, then “nature” makes a random decision, then we make a decision, etc. A notable feature of the implementation is the generality. A model may have integer variables in any stage; constraints may be linear or nonlinear. Achieving these goals is a challenge because adding the probabilistic feature makes already complex deterministic optimization problems even more complex, and stochastic programming problems can be difficult to solve, with a computational effort that may increase exponentially with the number of stages in the “we, nature” sequence of events. An interesting design decision for our particular case is where a particular computational capability should reside, in the front end that is seen by the user or in the computational engine that does the “heavy computational lifting.”