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An effective approach for job-shop scheduling with uncertain processing requirements

This paper presents an effective approach for job-shop scheduling considering uncertain arrival times, processing times, due dates, and part priorities. A separable problem formulation that balances modeling accuracy and solution method complexity is presented with the goal to minimize expected part tardiness and earliness cost. This optimization is subject to arrival time and operation precedence constraints, and machine capacity constraints. A solution methodology based on a combined Lagrangian relaxation and stochastic dynamic programming is developed to obtain dual solutions. A good dual solution is then selected by using "ordinal optimization", and the actual schedule is dynamically constructed based on the dual solution and the realization of random events. The computational complexity of the overall algorithm is only slightly higher than the one without considering uncertainties, and a dual cost is proved to be a lower bound to the optimal expected cost for the stochastic formulation considered.