Application Of Generalized Cluster Regression In Sales Forecasting

There are many mathematical models have been applied in the field of commodity sales forecasting.Clustering linear regression(CLR)algorithm aims to obtain the global optimal solution,and the clustering and regression are carried out simultaneously.The obtained results are highly explanatory and have guiding significance in business management.In the retail industry,we can cluster commodities to increase the applicability and accuracy of linear regression model.However,different SKUs are affected by different seasonal factors and these are reflected in the corresponding regression coefficients,thus increasing the difficulty of this problem.A better solution is to perform cluster regression simultaneously,that is,the CLR problem.In order to solve the generalized CLR problem.From the perspective of optimization,the generalized CLR problem can be modeled as a mixed integer quadratic programming problem.However,it is difficult to solve this problem directly because of variable size and symmetry.Column generation is an algorithmic framework for solving large-scale linear integer programming.Using this framework,the original problem can be transformed into a main problem and its sub-problems.When the column generation algorithm is applied,in order to solve larger-scale problems,a heuristic column generation algorithm is proposed.In addition,some other heuristic algorithms have been proposed,such as the K-Means algorithm based on genetic algorithm(using the K-Means algorithm to find the local op.timal solution and the genetic algorithm to jump out the local optimal solution),a two-step and the Spath algorithm.Finally,on the real commodity sales data,the above algorithms are programmed and compared in terms of accuracy,stability,solution efficiency,model interpretability,etc.