A learning model for the allocation of training hours in a multistage setting

In line with the continuous improvement theory, the learning phenomenon is often incorporated into models for predicting the evolution of the unitary quality costs. In this paper, the quality metric predicted is the rate of supplied non-conforming units through a learning process with autonomous and induced sources of experience. The former is simply learning by doing, i.e. supplying, whilst the latter is driven by the allocation of training hours to suppliers. A revised learning model with time-varying learning rates is proposed for embracing both these effects into a multistage assembly/production setting. A single-period prevention–appraisal–failure cost function is achieved, and the sample inspection rates adopted among suppliers are also considered in order to evaluate their effect. If these sample rates are given, the goal of allocating the training hours among suppliers is pursued by means of integer linear programming. Otherwise, a mixed-integer quadratic problem arises for the concurrent allocation of training hours and inspection sample rates among suppliers. A case study is finally carried out for demonstrating the applicability of the model, as well as for providing managerial insights.