Benders Decomposition for Order Batching and Scheduling Consider Uncertainties

Under the trend of mass customization, customer orders show the characteristics of 'multi-variety, small batch', which has a great impact on the scheduling process of batch production enterprises with mass production. This paper studies the problem of order group and batch scheduling with equipment constraints, that is, the order group and batch scheduling that makes the total production cost lowest is found under the equipment and delivery time constraints. Especially, the processing time of different batch equipment is different and uncertain. Firstly, a mixed integer linear programming model is established for order group and batch scheduling problems with equipment constraints. Secondly, in order to realize the optimal decision of the model efficiently, the Benders decomposition is adopted to decompose the original model into the order group master problem and the batch scheduling problem of equipment with different capacities. In view of the uncertain parameters in the model, robust optimization is adopted to transform the uncertainty constraints into robust counterpart. For the convergence problem of decomposed model, the improved Benders cut is added to speed up the convergence. Finally, through numerical experiments, the effectiveness of the algorithm is tested, and its competitiveness is verified in solving the optimal solution of medium-sized or even larger problem cases.