A non-zero integer non-linear programming model for maintenance workforce sizing

This paper formulates a non-linear integer programming model to solve a maintenance workforce sizing problem with a productivity improvement goal. This problem is modelled in a bi-objective framework that minimises the number of maintenance personnel while maximising their productivity levels. Inputs into the optimisation model include monthly and routine maintenance periods, volume of production, contingency maintenance time, use factor and priority factor among others. The model has been validated with real-life detergent factory data, demonstrating its potential usefulness. A principal novelty of the model is the inclusion of use factor, which captures how often maintenance technicians are busy on the job with respect to assigned tasks, including unanticipated high maintenance workload. The model has been solved using a branch and bound algorithm. The impact of workforce structure and workers’ salaries on model’s performance has been studied and sensitivity analysis carried out to investigate the changes to the optimal solution as a result of changes in the input data. The results show a reduction in the number of maintenance workforce personnel in comparing values with and without use factor in the model. The model’s ability to obtain global optimal result depends on the value of the minimum routine maintenance time within each maintenance section. Also, the model is shown to be sensitive to priority factor, which captures the appropriate ratio of full- and part-time workers under the same category. The model provides both an easy-to-use practical tool for maintenance managers and supervisors as well as a scientific tool for determining optimal maintenance workforce size for a manufacturing plant.