MIP-Based Heuristics for a Robust Transfer Lines Balancing Problem.

We consider a problem of optimal allocation of processing tools to a conveyor belt with parallel execution of tasks, which is known as a Transfer Lines Balancing Problem. It requires to form a set of blocks of tasks and assign them to machines so that the cycle time constraint is satisfied. The execution times of some tasks are supposed to be uncertain. Since this uncertainty has an impact on the feasibility of the solution because of existing constraint on cycle time, it is required to find a solution with the maximum stability radius, i.e. the maximum deviation from the initial data for which the feasibility of the solution can assured. In our case, it also can be viewed as an application of the threshold robustness approach. The relations between tasks are defined by a precedence graph. In addition to the earlier formulation from the literature we extend the problem with exclusion and inclusion constraints that play an important role in the area of machining lines balancing. We propose MIP-based greedy and local search algorithms, in which a given solution is iteratively built or improved by formulating subproblems of smaller size and solving them with a MIP solver. The numerical experiments showed that our algorithms outperform the straightforward application of a MIP solver on large-scale problems.