Extended decomposition for mixed integer programming to solve a workforce scheduling and routing problem

We propose an approach based on mixed integer programming (MIP) with decomposition to solve a workforce scheduling and routing problem, in which a set of workers should be assigned to tasks that are distributed across different geographical locations. We present a mixed integer programming model that incorporates important real-world features of the problem such as defined geographical regions and flexibility in the workers’ availability. We decompose the problem based on geographical areas. The quality of the overall solution is affected by the ordering in which the sub-problems are tackled. Hence, we investigate different ordering strategies to solve the sub-problems. We also use a procedure to have additional workforce from neighbouring regions and this helps to improve results in some instances. We also developed a genetic algorithm to compare the results produced by the decomposition methods. Our experimental results show that although the decomposition method does not always outperform the genetic algorithm, it finds high quality solutions in practical computational times using an exact optimization method.