A heuristical approach for Farmer's problem with uniform continuous random yields

Abstract

The L-shaped method is useful for solving two-stage stochastic linear programming problems which have the form of a master problem and several subproblems represented by the side model. In order to make this approach possible, the random vector ξ, which is bringing the uncertainty into the model, must have finite support. With finite support we may write the deterministic equivalent program in the extensive form which is solvable by decomposition. To avoid the problems arising from the random elements that have continuous probability distributions, an approximate discretisation is needed. In this paper, the uniform continuous probability distributions of the yields in the Farmer's problem are discretised by using one of the low-discrepancy sequences, called Faure sequence, and based on the obtained approximate discrete distribution a heuristic is proposed to approximate the solution to the problem.