A branch-and-price algorithm for robust parallel batch scheduling problem with uncertain size

In intelligent scheduling, parallel batch processing can reasonably allocate production resources and reduce the production cost per unit product. Hence, the research on a parallel batch scheduling problem (PBSP) with uncertain job size is of great significance to realize the flexibility of product production and mass customization of personalized products.

The authors propose a robust formulation in which the job size is defined by budget constrained support. For obtaining the robust solution of the robust PBSP, the authors propose an exact algorithm based on branch-and-price framework, where the pricing subproblem can be reduced to a robust shortest path problem with resource constraints. The robust subproblem is transformed into a deterministic mixed integer programming by duality. A series of deterministic shortest path problems with resource constraints is derived from the programming for which the authors design an efficient label-setting algorithm with a strong dominance rule.

The authors test the performance of the proposed algorithm on the extension of benchmark instances in literature and compare the infeasible rate of robust and deterministic solutions in simulated scenarios. The authors' results show the efficiency of the authors' algorithm and importance of incorporating uncertainties in the problem.

This work is the first to study the PBSP with uncertain size. To solve this problem, the authors design an efficient exact algorithm based on Dantzig–Wolfe decomposition. This can not only enrich the intelligent manufacturing theory related to parallel batch scheduling but also provide ideas for relevant enterprises to solve problems.