A robust critical path in an environment with hybrid uncertainty

In this article, we consider the project critical path problem in an environment with hybrid uncertainty. In this environment, the duration of activities are considered as random fuzzy variables that have probability and fuzzy natures, simultaneously. To obtain a robust critical path with this kind of uncertainty a chance constraints programming model is used. This model is converted to a deterministic model in two stages. In the first stage, the uncertain model is converted to a model with interval parameters by alpha-cut method and distribution function concepts. In the second stage, the interval model is converted to a deterministic model by robust optimization and min–max regret criterion and ultimately a genetic algorithm with a proposed exact algorithm are applied to solve the final model. Finally, some numerical examples are given to show the efficiency of the solution procedure.

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► We consider the duration of activities as random fuzzy variables.
► We model the problem with chance constraints and a robust optimization criterion.
► An exact algorithm and genetic algorithm are used to find a robust critical path.
► Our method in comparison with simulation method, usually gives better answers.