A branch-and-fix coordination algorithmic framework for solving some types of stochastic pure and mixed 0–1 programs

We present a framework for solving some types of 0–1 multi-stage scheduling/planning problems under uncertainty in the objective function coefficients and the right-hand-side. A sceanrio analysis scheme with full recourse is used. The solution offered for each scenario group at each stage takes into account all scenarios but without subordinating to any of them. The constraints are modeled by a splitting variables representation via scenarios. So, a 0–1 model for each scenario is considered plus the non-anticipativity constraints that equate the 0–1 variables from the same group of scenarios in each stage. The mathematical representation of the model is very amenable for the proposed framework to deal with the 0–1 character of the variables. A branch-and-fix coordination approach is introduced for coordinating the selection of the branching nodes and branching variables in the scenario subproblems to be jointly optimized. Some computational experience is reported for different types of problems.