Modeling And Optimization For Batch Planning Problem Of Aluminum Ingot Production

Aluminum plate is widely used in many fields such as automobile,aviation,construction,etc.The market demand shows a trend of multi-varieties and small-batch.To exploit the scale economies of large-scale facilities,aluminum factories usually organize production in batch mode in each process.The sharp conflict between customer demand and the company's production model has forced the aluminum factories to shift their production philosophy from mass production to mass customization,providing personalized and customized products at low cost,high quality and efficiency in batch production.From the perspective of mass customization,this thesis studies the planning problems existing in the aluminum ingot continuous casting production stage,and establishes the mathematical model of the batching planning problem of aluminum ingots in combination with the actual production process requirements,and proposes an optimization algorithm based on column generation.The main research contents of this thesis are as follows:(1)For the ingot batching plan problem,the ingot type selection,order allocation and plate grouping are used as decision variables.Under the premise of considering the technological constraints of the alloy consistency,the width,thickness and weight limit between the order and the ingot type,and the number limit of standard ingot type,a novel integer programming model is formulated with the objective of minimizing trim loss and residual material generation.Combining the actual production data of aluminum factories to design instances,the commercial optimization software CPLEX is used to solve the instances to verify the correctness of the model.(2)Because the linear relaxation of the integer programming model provides weaker lower bounds and symmetry defects existence in the model structure.the commercial optimization software CPLEX can only solve small-scale instances.To solve the actual scale problem,the original integer programming model is reformulated by introducing the grouping mode,and the column generation algorithm is applied to solve the linear relaxation of the reformulated model to obtain the tighter lower bound.The column generation algorithm is embedded as a bounding mechanism in the branch and bound framework.By exploiting sparsity fefature of order-ingot compatibility matrix and using the constraint propagation strategy,a multi-level branching scheme is proposed to perform branch search procedure.Numerical experiments are carried out with instances.The results show that the proposed algorithm can be solved efficiently.(3)Based on the characteristics of the problem structure,a new decomposition idea is proposed to decompose the original model into a set-partitioning master problem including ingot selection and order allocation decisions,a set of intermediate problems each deals with the patterns selection decision,and a set of subproblems each deals with the pattern generation decision.A nested column generation algorithm with two loops is proposed to solve the master problem,the intermediate problems and the subproblems iteratively to obtain a tighter lower bound.To overcome the computational complexity due to the nested structure,a rounding heuristic,based on column generation is proposed to accelerate the solution process for the intermediate problem.Numerical experiments show that the nested column generation algorithm can obtain a tighter lower bound.