FortSP

FortSP is a solver for stochastic programming problems in which the underlying optimisation model is an LP or a very restricted class of MIP models. It is used as the solver for the SPInE system or it may be used on its own to solve problems presented in ‘SMPS’ format.

FortSP is designed to process two-stage or multi-stage recourse problems. The SP problem is to find the best values for first-stage decision variables to be chosen now, given distributions for alternative scenarios (data paths) spanning future time stages. Each uncertain value in the model data is described by a finite sampling of discrete values. In each future stage there are decision variables to correspond with each possibility (known as ‘Recourse actions’), and these are constrained by linear forms connecting that stage to previous stages. See reference [1] for detailed problem statement and mathematical background.

Three alternative algorithms are available for solving this problem referred to as the ‘Here-and-Now’ (HN) model:

• Benders Decomposition – L-shaped method (Benders)
• Deterministic Equivalent with Explicit Non-Anticipativity (Deteqe)
• Deterministic Equivalent with Implicit Non-Anticipativity (Deteqi)

In addition to finding HN ‘Here-and-Now’ values for decision variables in the first time-stage the system may extend this to recourse values for the various scenarios in future time-stages, and may also evaluate the following special models:

• WS ‘Wait and See’:- This is a family of models, one for each scenario, and the weighted average of solutions for each scenario (solved by assuming that all data were already known) gives the expected WS solution.
• EV ‘Expected Value’: - The solution based on assuming all data will take its expected value

The following stochastic measures may be derived from outputs of the three models:

• EVPI ‘Expected Value of Perfect Information’
• VSS ‘Value of Stochastic Solution’