Mathematical models for developing a flexible workforce

As manufacturers seek ways to stay competitive in world matters, many are discovering that the most important resource they have is their employees. Consequently, at least in the United States, a renewed emphasis is being placed on employee development. For production environments adopting newer forms of manufacturing organizations, this has often resulted in more training and/or cross-training for employees. Decisions of whom to train and how much training should be done are often made in a qualitative fashion by human resource or personnel managers. Quantitative approaches have also been used but primarily when the focus has been on long term strategic staffing levels, or on short term staffing and cross-training levels to optimize specific operational performance measures. The problem of planning for cross-training to meet the requirements of a medium range production horizon in a manufacturing environment has not been addressed with quantitative models. The objective of this research was to develop formal models and optimal solution approaches for various worker training scenarios. The models were intended to assist managers in deciding optimum tactical plans for training/retraining a workforce according to the skills required by a forecasted production schedule for a definite planning horizon in a manufacturing plant. Four models were developed with objectives of (1) minimizing the total cost of training, (2) maximizing the flexibility of the workforce, (3) minimizing the total time required for training, and (4) optimizing the trade-off between minimizing the total cost of training and maximizing the flexibility of the workforce. Constraints in each of the models were developed with respect to production hours available, production requirements (from the master schedule), and budget. The paper discusses the reasoning behind the attributes used in the models as well as the formulation themselves. Significant effort is spent on discussing the applicability of the models, with attention being focused on the relative advantages, disadvantages, data requirements, and suitability of each model. Computational considerations are also presented.