Mixed-Integer Linear Programming, Constraint Programming and a Novel Dedicated Heuristic for Production Scheduling in a Packaging Plant

In this paper, we are discussing a research project aiming to optimize the scheduling of production orders within a real application in the packaging field. As a first approach, we model the problem as an extended version of the hybrid and flexible flowshop scheduling problem with precedence constraints, parallel machines, and sequence-dependent setups. The optimization objective considered is the minimization of the total tardiness. To tackle this problem, we use two methodologies: mixed-integer linear programming (MILP) and constraint programming (CP). These two models were further extended by adding resource calendar constraints named also availability constraints; this implies that the tasks should be scheduled only when the machine is available. The different proposed models were compared to each other on a set of generated benchmarks that reflect the specific properties of the industrial partner. Finally, as the studied configuration relies on practical real-world application, where thousands of orders are produced monthly, a novel dedicated heuristic was designed to address the need for quick solutions. The latter outperforms the other proposed algorithms for expected total tardiness minimization. The proposed problem can be readily modified to suit a wide range of real-world situations involving the scheduling of activities that share similar characteristics.