Two-machine flowshop scheduling problem to minimize makespan or total completion time with random and bounded setup times.
The present paper addresses the class of two-stage robust optimization problems which can be formulated as mathematical programs with uncertainty on the right-hand side coefficients (RHS uncertainty). The wide variety of applications and the fact that many problems in the class have been shown to be NP-hard, motivates the search for efficiently solvable special cases. Accordingly, the first objective of the paper is to provide an overview of the most important applications and of various polynomial...
The paper is concerned with a parallel implementation of the progressive hedging algorithm (PHA) which is applicable for the solution of stochastic optimization problems. We utilized the Message Passing Interface (MPI) and the General Algebraic Modelling System (GAMS) to concurrently solve the scenario-related subproblems in parallel manner. The standalone application combining the PHA, MPI, and GAMS was programmed in C++. The created software was successfully applied to a steel production problem...