A Mathematical Analysis on Optimal Assignment in Limited-Cycle Multiple Periods Considering Quality and Due Time ~the Case of Two Worker Levels~

In recent years, problems of quality fraud, such as falsification of inspection data and inspections by unqualified inspectors, have come to light, shaking the confidence of companies. This is true even for global leading manufacturing companies. In addition, the increase in the number of foreign workers and differences in length of service have resulted in differences in workers’ abilities in Japan. Therefore, the objective is to find optimal worker assignment rules that take into account quality and worker levels in order to achieve efficient production. To solve this problem, we developed a mathematical model that introduces quality cost into the concept of the multi-period constraint cycle model. Numerical experiments were also conducted by varying the parameters of worker level and number of processes using programming and assuming various process situations. In this paper, we propose a mathematical model for optimal assignment of production line considering due time and quality in the case of two worker levels. Also, we provide the proof to generalize the rules of one special worker and two special worker cases. And numerical experiments confirm that the rule is satisfied.