Modeling And Optimization Of Aluminum Smelting Production Scheduling Problem

As the most abundant metal element on the earth,aluminum has a wide range of applications in many fields.The characteristics of multi-varieties and small-batch of customers' orders have increased the difficulty of aluminum companies' production organization.At the same time,there are more and more strict requirements for on-time delivery.The products must to be completed within a given time window,which further increases the difficulty for the production scheduling.The aluminum processing involves several production processes,and the smelting stage is an important one.How to allocate different orders to different smelting furnaces has an important impact on improving production efficiency and reducing energy consumption.This thesis takes the aluminum smelting production process as the background,and extracts a new type of parallel machine scheduling problem for modeling and optimization algorithm research.The main contents of this thesis are as follows:1)Taking the allocation of orders to melting furnaces,and the times of washing furnace as decision variables,considering the constraints such as order requirements,washing furnace operation,an integer programming model of the aluminum smelting production scheduling problem is developed to minimize the makespan.The lower bound of the model is obtained by theoretical derivation and the upper bound is obtained by the differential evolution.Numerical experiments show that the gap between the upper bound solved by the differential evolution and the lower bound obtained by theoretical derivation is tighter.2)Taking the calculated lower bound and upper bound as input,a binary search based solution framework is proposed to solve the problem to optimum.To identify the upper bound and lower bound in binary search,the scheduling feasibility problem under a given makespan is transformed into a bin packing problem with setup time(BPPST)from the perspective of duality.A branch and price algorithm based on column generation is proposed to solve the BPPST problem.Numerical experiments show that the binary search can obtain the optimal solution of medium-scale problems in a reasonable time,and the effectiveness of the algorithm is verified.3)A new modeling method for aluminum smelting production scheduling problem with time window constraints is proposed.In the production process,the customers' orders often have the delivery time requirement.Therefore,the time window constraint is added to the above problem to ensure that the order is produced within the delivery period required by the user,and each order is given a certain flexible time for scheduling.Through the above analysis,the model of aluminum smelting production scheduling problem with time window is established based on the time block.Finally,the commercial software CPLEX is used to solve the problem.The correctness of the model is verified by experimental data comparison.