A study of marking utility models based on principal component analysis and integer programming

Abstract

The establishment and analysis of a marking utility model is of great importance in achieving paperless marking and improving the accuracy and efficiency of marking. Through the application of modern technology, students' examination results can be evaluated more objectively and provide an important basis for determining the final effect of talent training. This paper provides a systematic analysis and modelling of the marking process, and uses a variety of techniques and methods to address the issue of marking staff arrangements. Firstly, the impact of the proportion of markers per question, the proportion of the average mark for each question to the total mark for that question, the proportion of blank papers and the error rate on the speed of marking was explored by analysing marker-related indicator variables and the basic requirements for completing the marking process. Then, principal component analysis was used to reduce the dimensionality of the four factor variables affecting marking speed, and two principal components with strong correlation with marking speed were obtained to provide a more systematic and comprehensive analysis of the influence of marking speed. Finally, an integer programming model and simulated annealing algorithm were used to solve for the optimal arrangement of markers to ensure that the requirement of simultaneous completion of workload for each question was met. In this paper, the optimal allocation of markers is analysed and the time required for all markers to complete the marking process at the same point in time is calculated to be 3.3 days. Two optimal allocations of markers are proposed for each question type per day and for each question type per hour in a day.